https://wiki.geogebra.org/s/en/api.php?action=feedcontributions&user=Corinna&feedformat=atomGeoGebra Manual - User contributions [en]2024-03-29T02:33:08ZUser contributionsMediaWiki 1.35.1https://wiki.geogebra.org/s/en/index.php?title=File:Edge_surface.PNG&diff=26914File:Edge surface.PNG2012-07-09T09:31:51Z<p>Corinna: Corinna uploaded a new version of &quot;File:Edge surface.PNG&quot;</p>
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<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Edge_surface.PNG&diff=26911File:Edge surface.PNG2012-07-09T09:20:59Z<p>Corinna: </p>
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<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Spreadsheet1.PNG&diff=26907File:Spreadsheet1.PNG2012-07-09T09:08:00Z<p>Corinna: </p>
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<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26906Tutorial:Conditional Visibility & Sequences2012-07-09T09:04:04Z<p>Corinna: /* Construction Steps */</p>
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<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
[[Image:Sierpinski1.PNG|center]]<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
<br />
===Conditional Visibility===<br />
Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.<br />
<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Show_Hide_Object.gif]]||Hide all points except from A, B and C.<br />
|-<br />
|2||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the first stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 1<br />
<br />
Selected objects: Only the large white triangle and its sides.<br />
|-<br />
|3||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the<br />
white triangle and its sides can be hidden / shown.<br />
|-<br />
|4||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the second stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 2<br />
<br />
Selected objects: Three medium sized white triangles and their sides.<br />
|-<br />
|5||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the second stage of the Sierpinski triangle can be hidden / shown.<br />
|-<br />
|6||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the third stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 3<br />
<br />
Selected objects: Nine small white triangles and their sides.<br />
|-<br />
|7||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the third stage of the Sierpinski triangle can be hidden / shown.<br />
|}<br />
<br />
[[Image:Sierpinski2.PNG|center]]<br />
<br />
==Introducing Sequences==<br />
GeoGebra offers the command Sequence which produces a list of objects. Thereby, the type of object, the length of the sequence (that’s the number of objects created) and the step width (e.g. distance between the objects) can be set using the following command syntax:<br />
''Sequence[<expression>, <variable>, <from>, <to>, <step>]''<br />
<br />
Explanations:<br />
* <expression>: Determines the type of objects created. The expression needs to contain a variable (e.g. (i, 0) with variable i).<br />
* <variable>: Tells GeoGebra the name of the variable used.<br />
* <from>, <to>: Determine the interval for the variable used (e.g. from 1 to 10).<br />
* <step>: Is optional and determines the step width for the variable used (e.g. 0.5).<br />
<br />
===Examples for sequences===<br />
* Sequence[(n, 0), n, 0, 10]<br />
** Creates a list of 11 points along the x-axis.<br />
** Points have coordinates (0, 0), (1, 0), (2, 0), …, (10, 0).<br />
<br />
[[Image:sequence.PNG|center]]<br />
<br />
* Sequence[Segment[(a, 0), (0, a)], a, 1, 10, 0.5]<br />
** Creates a list of segments with distance 0.5.<br />
** Each segment connects a point on the x-axis with a point on the yaxis (e.g. points (1, 0) and (0, 1); points (2, 0) and (0, 2).<br />
<br />
* If s is a slider with interval from 1 to 10 and increment 1, then command Sequence[(i, i), i, 0, s]<br />
** creates a list of s + 1 points whose length can be changed dynamically by dragging slider s.<br />
** Points have coordinates (0, 0), (1, 1), …, (10, 10)<br />
<br />
[[Image:sequence2.PNG|center]]<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* Show the [[Input Bar]] ([[View Menu]]).<br />
* In the Options menu set the Labeling to ''All New Objects''.<br />
<br />
[[Image:multiplication.PNG|center]]<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Slider.gif]]||Crate a horizontal slider ''Columns'' for number with ''Interval'' from 1 to 10, Increment 1 and Width 300.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create a new point A.<br />
|-<br />
|3||[[Image:Tool_Segment_with_Given_Length_from_Point.gif]]||Construct segment a with given length ''Columns'' from point A.<br />
|-<br />
|4||[[Image:Tool_Move.gif]]||Move slider ''Columns'' to check the segment with given length.<br />
|-<br />
|5||[[Image:Tool_Perpendicular_Line.gif]]||Construct a perpendicular line b to segment a through point A.<br />
|-<br />
|6||[[Image:Tool_Perpendicular_Line.gif]]||Construct a perpendicular line c to segment a through point B.<br />
|-<br />
|7||[[Image:Tool_Slider.gif]]||Create a vertical slider ''Rows'' for number with ''Interval'' from 1 to 10, Increment 1 and Width 300.<br />
|-<br />
|8||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle d with center A and given radius ''Rows''.<br />
|-<br />
|9||[[Image:Tool_Move.gif]]||Move slider ''Rows'' to check the circle with given radius.<br />
|-<br />
|10||[[Image:Tool_Intersect_Two_Objects.gif]]||Intersect circle d with line c to get intersection point C.<br />
|-<br />
|11||[[Image:Tool_Parallel_Line.gif]]||Create a parallel line e to segment a through intersection point C.<br />
|-<br />
|12||[[Image:Tool_Intersect_Two_Objects.gif]]||Intersect lines c and e to get intersection point D.<br />
|-<br />
|13||[[Image:Tool_Polygon.gif]]||Construct a polygon ABDC.<br />
|-<br />
|14||[[Image:Tool_Show_Hide_Object.gif]]||Hide all lines, circle d and segment a.<br />
|-<br />
|15||||Hide labels of segments.<br />
|-<br />
|16||[[Image:Tool_Move.gif]]||Set both sliders ''Columns'' and ''Rows'' to value 10.<br />
|-<br />
|17|| ||Create a list of vertical segments.<br />
<br />
Sequence[Segment[A+i(1, 0), C+i(1, 0)], i, 1, Columns]<br />
{{note|A + i(1, 0) specifies a series of points starting at point A with distance 1 from each other. C + i(1, 0) specifies a series of points starting at point C with distance 1 from each other. Segment[A + i(1, 0), C + i(1, 0)] creates a list of segments between pairs of these points. Note, that the endpoints of the segments are not shown in the Graphics view. Slider ''Column'' determines the number of segments created.}}<br />
|-<br />
|18|| ||Create a list of horizontal segments.<br />
Sequence[Segment[A+i(0, 1), B+i(0, 1)], i, 1, Rows]<br />
|-<br />
|19||[[Image:Tool_Move.gif]]||Move sliders ''Columns'' and ''Rows'' to check the construction.<br />
|-<br />
|20||[[Image:Tool_Insert_Text.gif]]||Insert static and dynamic text that state the multiplication problem using the values of sliders ''Columns'' and ''Rows'' as the factors:<br />
<br />
text1: Columns<br />
<br />
text2: *<br />
<br />
text3: Rows<br />
<br />
text4: =<br />
|-<br />
|21|| ||Calculate the result of the multiplication: result = Columns * Rows<br />
|-<br />
|22||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text5: ''result''<br />
|-<br />
|23||[[Image:Tool_Show_Hide_Object.gif]]||Hide points A, B, C and D.<br />
|-<br />
|24||||Enhance your construction using the ''Properties dialog''.<br />
|}<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==<br />
Bézier curves are parametric curves used in computer graphics. For example, they are used in order to create smooth lines of vector fonts.<br />
Let’s create some ‘string art’ based on Bézier curves.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* Show the [[Input Bar]] ([[View Menu]]).<br />
* In the ''Options menu'' set the Labeling to ''All New Objects''.<br />
<br />
[[Image:bezier.PNG|center]]<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment a with endpoints A and B.<br />
|-<br />
|2||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment b with endpoints A and C.<br />
|-<br />
|3||[[Image:Tool_Slider.gif]][[Image:Tool_Move.gif]]||Create a slider for number n with Interval 0 to 50, Increment 1 and Width 200.<br />
|-<br />
|4||||Create Sequence[A + i/n (B - A), i, 1, n]. {{hint|This sequence creates a list of n points along segment AB with a distance of one nth of the length of segment a.}}<br />
|-<br />
|5||||Create Sequence[A + i/n (C - A), i, 1, n]. {{hint|This sequence creates a list of n points along segment AC with a distance of one nth of the length of segment b.}}<br />
|-<br />
|6||[[Image:Tool_Show_Hide_Object.gif]]||Hide both lists of points.<br />
|-<br />
|7||||Create a list of segments. Sequence[Segment[Element[list1,i],Element[list2,n-i]],i,1,n] {{hint|These segments connect the first and last, second and last but one,…, last and first point of list1 and list2.}}<br />
|-<br />
|8||||Enhance your construction using the Properties dialog.<br />
|-<br />
|9||[[Image:Tool_Move.gif]]||Move points A, B and C to change the shape of your Bézier curve.<br />
|-<br />
|10||[[Image:Tool_Move.gif]]||Drag slider n to change the number of segments that create the Bézier curve.<br />
|}<br />
<br />
<br />
{{note|The segments you just created are tangents to a quadratic Bézier curve.}}<br />
<br />
===Task===<br />
Create more ''string art'' with GeoGebra using sequences of points and segments.<br />
<br />
[[Image:bezier2.PNG|center]]</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26905Tutorial:Conditional Visibility & Sequences2012-07-09T09:03:33Z<p>Corinna: /* Challenge of the Day: String Art Based on Bézier Curves */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
[[Image:Sierpinski1.PNG|center]]<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
<br />
===Conditional Visibility===<br />
Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.<br />
<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Show_Hide_Object.gif]]||Hide all points except from A, B and C.<br />
|-<br />
|2||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the first stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 1<br />
<br />
Selected objects: Only the large white triangle and its sides.<br />
|-<br />
|3||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the<br />
white triangle and its sides can be hidden / shown.<br />
|-<br />
|4||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the second stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 2<br />
<br />
Selected objects: Three medium sized white triangles and their sides.<br />
|-<br />
|5||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the second stage of the Sierpinski triangle can be hidden / shown.<br />
|-<br />
|6||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the third stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 3<br />
<br />
Selected objects: Nine small white triangles and their sides.<br />
|-<br />
|7||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the third stage of the Sierpinski triangle can be hidden / shown.<br />
|}<br />
<br />
[[Image:Sierpinski2.PNG|center]]<br />
<br />
==Introducing Sequences==<br />
GeoGebra offers the command Sequence which produces a list of objects. Thereby, the type of object, the length of the sequence (that’s the number of objects created) and the step width (e.g. distance between the objects) can be set using the following command syntax:<br />
''Sequence[<expression>, <variable>, <from>, <to>, <step>]''<br />
<br />
Explanations:<br />
* <expression>: Determines the type of objects created. The expression needs to contain a variable (e.g. (i, 0) with variable i).<br />
* <variable>: Tells GeoGebra the name of the variable used.<br />
* <from>, <to>: Determine the interval for the variable used (e.g. from 1 to 10).<br />
* <step>: Is optional and determines the step width for the variable used (e.g. 0.5).<br />
<br />
===Examples for sequences===<br />
* Sequence[(n, 0), n, 0, 10]<br />
** Creates a list of 11 points along the x-axis.<br />
** Points have coordinates (0, 0), (1, 0), (2, 0), …, (10, 0).<br />
<br />
[[Image:sequence.PNG|center]]<br />
<br />
* Sequence[Segment[(a, 0), (0, a)], a, 1, 10, 0.5]<br />
** Creates a list of segments with distance 0.5.<br />
** Each segment connects a point on the x-axis with a point on the yaxis (e.g. points (1, 0) and (0, 1); points (2, 0) and (0, 2).<br />
<br />
* If s is a slider with interval from 1 to 10 and increment 1, then command Sequence[(i, i), i, 0, s]<br />
** creates a list of s + 1 points whose length can be changed dynamically by dragging slider s.<br />
** Points have coordinates (0, 0), (1, 1), …, (10, 10)<br />
<br />
[[Image:sequence2.PNG|center]]<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* Show the [[Input Bar]] ([[View Menu]]).<br />
* In the Options menu set the Labeling to ''All New Objects''.<br />
<br />
[[Image:multiplication.PNG|center]]<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Slider.gif]]||Crate a horizontal slider ''Columns'' for number with ''Interval'' from 1 to 10, Increment 1 and Width 300.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create a new point A.<br />
|-<br />
|3||[[Image:Tool_Segment_with_Given_Length_from_Point.gif]]||Construct segment a with given length ''Columns'' from point A.<br />
|-<br />
|4||[[Image:Tool_Move.gif]]||Move slider ''Columns'' to check the segment with given length.<br />
|-<br />
|5||[[Image:Tool_Perpendicular_Line.gif]]||Construct a perpendicular line b to segment a through point A.<br />
|-<br />
|6||[[Image:Tool_Perpendicular_Line.gif]]||Construct a perpendicular line c to segment a through point B.<br />
|-<br />
|7||[[Image:Tool_Slider.gif]]||Create a vertical slider ''Rows'' for number with ''Interval'' from 1 to 10, Increment 1 and Width 300.<br />
|-<br />
|8||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle d with center A and given radius ''Rows''.<br />
|-<br />
|9||[[Image:Tool_Move.gif]]||Move slider ''Rows'' to check the circle with given radius.<br />
|-<br />
|10||[[Image:Tool_Intersect_Two_Objects.gif]]||Intersect circle d with line c to get intersection point C.<br />
|-<br />
|11||[[Image:Tool_Parallel_Line.gif]]||Create a parallel line e to segment a through intersection point C.<br />
|-<br />
|12||[[Image:Tool_Intersect_Two_Objects.gif]]||Intersect lines c and e to get intersection point D.<br />
|-<br />
|13||[[Image:Tool_Polygon.gif]]||Construct a polygon ABDC.<br />
|-<br />
|14||[[Image:Tool_Show_Hide_Object.gif]]||Hide all lines, circle d and segment a.<br />
|-<br />
|15||||Hide labels of segments.<br />
|-<br />
|16||[[Image:Tool_Move.gif]]||Set both sliders ''Columns'' and ''Rows'' to value 10.<br />
|-<br />
|17|| ||Create a list of vertical segments.<br />
<br />
Sequence[Segment[A+i(1, 0), C+i(1, 0)], i, 1, Columns]<br />
{{note|A + i(1, 0) specifies a series of points starting at point A with distance 1 from each other. C + i(1, 0) specifies a series of points starting at point C with distance 1 from each other. Segment[A + i(1, 0), C + i(1, 0)] creates a list of segments between pairs of these points. Note, that the endpoints of the segments are not shown in the Graphics view. Slider ''Column'' determines the number of segments created.}}<br />
|-<br />
|18|| ||Create a list of horizontal segments.<br />
Sequence[Segment[A+i(0, 1), B+i(0, 1)], i, 1, Rows]<br />
|-<br />
|19||[[Image:Tool_Move.gif]]||Move sliders ''Columns'' and ''Rows'' to check the construction.<br />
|-<br />
|20||[[Image:Tool_Insert_Text.gif]]||Insert static and dynamic text that state the multiplication problem using the values of sliders ''Columns'' and ''Rows'' as the factors:<br />
<br />
text1: Columns<br />
<br />
text2: *<br />
<br />
text3: Rows<br />
<br />
text4: =<br />
|-<br />
|21|| ||Calculate the result of the multiplication: result = Columns * Rows<br />
|-<br />
|22||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text5: ''result''<br />
|-<br />
|23||[[Image:Tool_Show_Hide_Object.gif]]||Hide points A, B, C and D.<br />
|-<br />
|24||||Enhance your construction using the ''Properties dialog''.<br />
|}<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==<br />
Bézier curves are parametric curves used in computer graphics. For example, they are used in order to create smooth lines of vector fonts.<br />
Let’s create some ‘string art’ based on Bézier curves.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* Show the [[Input Bar]] ([[View Menu]]).<br />
* In the ''Options menu'' set the Labeling to ''All New Objects''.<br />
<br />
[[Image:bezier.PNG|center]]<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment a with endpoints A and B.<br />
|-<br />
|2||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment b with endpoints A and C.<br />
|-<br />
|3||[[Image:Tool_Slider.gif]][[Image:Tool_Move.gif]]||Create a slider for number n with Interval 0 to 50, Increment 1 and Width 200.<br />
|-<br />
|4||||Create Sequence[A + i/n (B - A), i, 1, n]. {{hint|This sequence creates a list of n points along segment AB with a distance of one nth of the length of segment a.}}<br />
|-<br />
|5||||Create Sequence[A + i/n (C - A), i, 1, n]. {{hint|This sequence creates a list of n points along segment AC with a distance of one nth of the length of segment b.}}<br />
|-<br />
|6||[[Image:Tool_Show_Hide_Object.gif]]||Hide both lists of points.<br />
|-<br />
|7||||Create a list of segments. Sequence[Segment[Element[list1,i],Element[list2,n-i]],i,1,n] {{hnt|These segments connect the first and last, second and last but one,…, last and first point of list1 and list2.}}<br />
|-<br />
|8||||Enhance your construction using the Properties dialog.<br />
|-<br />
|9||[[Image:Tool_Move.gif]]||Move points A, B and C to change the shape of your Bézier curve.<br />
|-<br />
|10||[[Image:Tool_Move.gif]]||Drag slider n to change the number of segments that create the Bézier curve.<br />
|}<br />
<br />
{{note|The segments you just created are tangents to a quadratic Bézier curve.}}<br />
<br />
===Task===<br />
Create more ''string art'' with GeoGebra using sequences of points and segments.<br />
<br />
[[Image:bezier2.PNG|center]]</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Bezier2.PNG&diff=26904File:Bezier2.PNG2012-07-09T09:03:11Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Bezier.PNG&diff=26903File:Bezier.PNG2012-07-09T08:55:39Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26901Tutorial:Conditional Visibility & Sequences2012-07-09T08:54:09Z<p>Corinna: /* Visualizing Multiplication of Natural Numbers */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
[[Image:Sierpinski1.PNG|center]]<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
<br />
===Conditional Visibility===<br />
Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.<br />
<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Show_Hide_Object.gif]]||Hide all points except from A, B and C.<br />
|-<br />
|2||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the first stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 1<br />
<br />
Selected objects: Only the large white triangle and its sides.<br />
|-<br />
|3||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the<br />
white triangle and its sides can be hidden / shown.<br />
|-<br />
|4||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the second stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 2<br />
<br />
Selected objects: Three medium sized white triangles and their sides.<br />
|-<br />
|5||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the second stage of the Sierpinski triangle can be hidden / shown.<br />
|-<br />
|6||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the third stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 3<br />
<br />
Selected objects: Nine small white triangles and their sides.<br />
|-<br />
|7||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the third stage of the Sierpinski triangle can be hidden / shown.<br />
|}<br />
<br />
[[Image:Sierpinski2.PNG|center]]<br />
<br />
==Introducing Sequences==<br />
GeoGebra offers the command Sequence which produces a list of objects. Thereby, the type of object, the length of the sequence (that’s the number of objects created) and the step width (e.g. distance between the objects) can be set using the following command syntax:<br />
''Sequence[<expression>, <variable>, <from>, <to>, <step>]''<br />
<br />
Explanations:<br />
* <expression>: Determines the type of objects created. The expression needs to contain a variable (e.g. (i, 0) with variable i).<br />
* <variable>: Tells GeoGebra the name of the variable used.<br />
* <from>, <to>: Determine the interval for the variable used (e.g. from 1 to 10).<br />
* <step>: Is optional and determines the step width for the variable used (e.g. 0.5).<br />
<br />
===Examples for sequences===<br />
* Sequence[(n, 0), n, 0, 10]<br />
** Creates a list of 11 points along the x-axis.<br />
** Points have coordinates (0, 0), (1, 0), (2, 0), …, (10, 0).<br />
<br />
[[Image:sequence.PNG|center]]<br />
<br />
* Sequence[Segment[(a, 0), (0, a)], a, 1, 10, 0.5]<br />
** Creates a list of segments with distance 0.5.<br />
** Each segment connects a point on the x-axis with a point on the yaxis (e.g. points (1, 0) and (0, 1); points (2, 0) and (0, 2).<br />
<br />
* If s is a slider with interval from 1 to 10 and increment 1, then command Sequence[(i, i), i, 0, s]<br />
** creates a list of s + 1 points whose length can be changed dynamically by dragging slider s.<br />
** Points have coordinates (0, 0), (1, 1), …, (10, 10)<br />
<br />
[[Image:sequence2.PNG|center]]<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* Show the [[Input Bar]] ([[View Menu]]).<br />
* In the Options menu set the Labeling to ''All New Objects''.<br />
<br />
[[Image:multiplication.PNG|center]]<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Slider.gif]]||Crate a horizontal slider ''Columns'' for number with ''Interval'' from 1 to 10, Increment 1 and Width 300.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create a new point A.<br />
|-<br />
|3||[[Image:Tool_Segment_with_Given_Length_from_Point.gif]]||Construct segment a with given length ''Columns'' from point A.<br />
|-<br />
|4||[[Image:Tool_Move.gif]]||Move slider ''Columns'' to check the segment with given length.<br />
|-<br />
|5||[[Image:Tool_Perpendicular_Line.gif]]||Construct a perpendicular line b to segment a through point A.<br />
|-<br />
|6||[[Image:Tool_Perpendicular_Line.gif]]||Construct a perpendicular line c to segment a through point B.<br />
|-<br />
|7||[[Image:Tool_Slider.gif]]||Create a vertical slider ''Rows'' for number with ''Interval'' from 1 to 10, Increment 1 and Width 300.<br />
|-<br />
|8||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle d with center A and given radius ''Rows''.<br />
|-<br />
|9||[[Image:Tool_Move.gif]]||Move slider ''Rows'' to check the circle with given radius.<br />
|-<br />
|10||[[Image:Tool_Intersect_Two_Objects.gif]]||Intersect circle d with line c to get intersection point C.<br />
|-<br />
|11||[[Image:Tool_Parallel_Line.gif]]||Create a parallel line e to segment a through intersection point C.<br />
|-<br />
|12||[[Image:Tool_Intersect_Two_Objects.gif]]||Intersect lines c and e to get intersection point D.<br />
|-<br />
|13||[[Image:Tool_Polygon.gif]]||Construct a polygon ABDC.<br />
|-<br />
|14||[[Image:Tool_Show_Hide_Object.gif]]||Hide all lines, circle d and segment a.<br />
|-<br />
|15||||Hide labels of segments.<br />
|-<br />
|16||[[Image:Tool_Move.gif]]||Set both sliders ''Columns'' and ''Rows'' to value 10.<br />
|-<br />
|17|| ||Create a list of vertical segments.<br />
<br />
Sequence[Segment[A+i(1, 0), C+i(1, 0)], i, 1, Columns]<br />
{{note|A + i(1, 0) specifies a series of points starting at point A with distance 1 from each other. C + i(1, 0) specifies a series of points starting at point C with distance 1 from each other. Segment[A + i(1, 0), C + i(1, 0)] creates a list of segments between pairs of these points. Note, that the endpoints of the segments are not shown in the Graphics view. Slider ''Column'' determines the number of segments created.}}<br />
|-<br />
|18|| ||Create a list of horizontal segments.<br />
Sequence[Segment[A+i(0, 1), B+i(0, 1)], i, 1, Rows]<br />
|-<br />
|19||[[Image:Tool_Move.gif]]||Move sliders ''Columns'' and ''Rows'' to check the construction.<br />
|-<br />
|20||[[Image:Tool_Insert_Text.gif]]||Insert static and dynamic text that state the multiplication problem using the values of sliders ''Columns'' and ''Rows'' as the factors:<br />
<br />
text1: Columns<br />
<br />
text2: *<br />
<br />
text3: Rows<br />
<br />
text4: =<br />
|-<br />
|21|| ||Calculate the result of the multiplication: result = Columns * Rows<br />
|-<br />
|22||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text5: ''result''<br />
|-<br />
|23||[[Image:Tool_Show_Hide_Object.gif]]||Hide points A, B, C and D.<br />
|-<br />
|24||||Enhance your construction using the ''Properties dialog''.<br />
|}<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Multiplication.PNG&diff=26898File:Multiplication.PNG2012-07-09T08:43:36Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26897Tutorial:Conditional Visibility & Sequences2012-07-09T08:42:09Z<p>Corinna: /* Introducing Sequences */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
[[Image:Sierpinski1.PNG|center]]<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
<br />
===Conditional Visibility===<br />
Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.<br />
<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Show_Hide_Object.gif]]||Hide all points except from A, B and C.<br />
|-<br />
|2||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the first stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 1<br />
<br />
Selected objects: Only the large white triangle and its sides.<br />
|-<br />
|3||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the<br />
white triangle and its sides can be hidden / shown.<br />
|-<br />
|4||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the second stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 2<br />
<br />
Selected objects: Three medium sized white triangles and their sides.<br />
|-<br />
|5||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the second stage of the Sierpinski triangle can be hidden / shown.<br />
|-<br />
|6||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the third stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 3<br />
<br />
Selected objects: Nine small white triangles and their sides.<br />
|-<br />
|7||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the third stage of the Sierpinski triangle can be hidden / shown.<br />
|}<br />
<br />
[[Image:Sierpinski2.PNG|center]]<br />
<br />
==Introducing Sequences==<br />
GeoGebra offers the command Sequence which produces a list of objects. Thereby, the type of object, the length of the sequence (that’s the number of objects created) and the step width (e.g. distance between the objects) can be set using the following command syntax:<br />
''Sequence[<expression>, <variable>, <from>, <to>, <step>]''<br />
<br />
Explanations:<br />
* <expression>: Determines the type of objects created. The expression needs to contain a variable (e.g. (i, 0) with variable i).<br />
* <variable>: Tells GeoGebra the name of the variable used.<br />
* <from>, <to>: Determine the interval for the variable used (e.g. from 1 to 10).<br />
* <step>: Is optional and determines the step width for the variable used (e.g. 0.5).<br />
<br />
===Examples for sequences===<br />
* Sequence[(n, 0), n, 0, 10]<br />
** Creates a list of 11 points along the x-axis.<br />
** Points have coordinates (0, 0), (1, 0), (2, 0), …, (10, 0).<br />
<br />
[[Image:sequence.PNG|center]]<br />
<br />
* Sequence[Segment[(a, 0), (0, a)], a, 1, 10, 0.5]<br />
** Creates a list of segments with distance 0.5.<br />
** Each segment connects a point on the x-axis with a point on the yaxis (e.g. points (1, 0) and (0, 1); points (2, 0) and (0, 2).<br />
<br />
* If s is a slider with interval from 1 to 10 and increment 1, then command Sequence[(i, i), i, 0, s]<br />
** creates a list of s + 1 points whose length can be changed dynamically by dragging slider s.<br />
** Points have coordinates (0, 0), (1, 1), …, (10, 10)<br />
<br />
[[Image:sequence2.PNG|center]]<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Sequence2.PNG&diff=26896File:Sequence2.PNG2012-07-09T08:41:57Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Sequence.PNG&diff=26895File:Sequence.PNG2012-07-09T08:40:33Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26894Tutorial:Conditional Visibility & Sequences2012-07-09T08:38:45Z<p>Corinna: /* The Sierpinski Triangle */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
[[Image:Sierpinski1.PNG|center]]<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
<br />
===Conditional Visibility===<br />
Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.<br />
<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Show_Hide_Object.gif]]||Hide all points except from A, B and C.<br />
|-<br />
|2||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the first stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 1<br />
<br />
Selected objects: Only the large white triangle and its sides.<br />
|-<br />
|3||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the<br />
white triangle and its sides can be hidden / shown.<br />
|-<br />
|4||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the second stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 2<br />
<br />
Selected objects: Three medium sized white triangles and their sides.<br />
|-<br />
|5||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the second stage of the Sierpinski triangle can be hidden / shown.<br />
|-<br />
|6||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the third stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 3<br />
<br />
Selected objects: Nine small white triangles and their sides.<br />
|-<br />
|7||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the third stage of the Sierpinski triangle can be hidden / shown.<br />
|}<br />
<br />
[[Image:Sierpinski2.PNG|center]]<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26893Tutorial:Conditional Visibility & Sequences2012-07-09T08:37:41Z<p>Corinna: /* The Sierpinski Triangle */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
[[Image:Sierpinski1.PNG]]<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
<br />
===Conditional Visibility===<br />
Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.<br />
<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Show_Hide_Object.gif]]||Hide all points except from A, B and C.<br />
|-<br />
|2||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the first stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 1<br />
<br />
Selected objects: Only the large white triangle and its sides.<br />
|-<br />
|3||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the<br />
white triangle and its sides can be hidden / shown.<br />
|-<br />
|4||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the second stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 2<br />
<br />
Selected objects: Three medium sized white triangles and their sides.<br />
|-<br />
|5||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the second stage of the Sierpinski triangle can be hidden / shown.<br />
|-<br />
|6||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the third stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 3<br />
<br />
Selected objects: Nine small white triangles and their sides.<br />
|-<br />
|7||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the third stage of the Sierpinski triangle can be hidden / shown.<br />
|}<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Sierpinski2.PNG&diff=26892File:Sierpinski2.PNG2012-07-09T08:37:04Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:Sierpinski1.PNG&diff=26891File:Sierpinski1.PNG2012-07-09T08:36:46Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26890Tutorial:Conditional Visibility & Sequences2012-07-09T08:35:02Z<p>Corinna: /* Conditional Visibility */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
<br />
===Conditional Visibility===<br />
Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.<br />
<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Show_Hide_Object.gif]]||Hide all points except from A, B and C.<br />
|-<br />
|2||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the first stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 1<br />
<br />
Selected objects: Only the large white triangle and its sides.<br />
|-<br />
|3||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the<br />
white triangle and its sides can be hidden / shown.<br />
|-<br />
|4||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the second stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 2<br />
<br />
Selected objects: Three medium sized white triangles and their sides.<br />
|-<br />
|5||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the second stage of the Sierpinski triangle can be hidden / shown.<br />
|-<br />
|6||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the third stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 3<br />
<br />
Selected objects: Nine small white triangles and their sides.<br />
|-<br />
|7||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the third stage of the Sierpinski triangle can be hidden / shown.<br />
|}<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26889Tutorial:Conditional Visibility & Sequences2012-07-09T08:34:42Z<p>Corinna: /* The Sierpinski Triangle */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
===Conditional Visibility===<br />
Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.<br />
<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Show_Hide_Object.gif]]||Hide all points except from A, B and C.<br />
|-<br />
|2||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the first stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 1<br />
<br />
Selected objects: Only the large white triangle and its sides.<br />
|-<br />
|3||[[Image:Tool_Move.gif]]]||In Move mode check and uncheck the checkbox to try out if the<br />
white triangle and its sides can be hidden / shown.<br />
|-<br />
|4||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the second stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 2<br />
<br />
Selected objects: Three medium sized white triangles and their sides.<br />
|-<br />
|5||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the second stage of the Sierpinski triangle can be hidden / shown.<br />
|-<br />
|6||[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||Create a Check Box to Show / Hide Objects that shows / hides the third stage of the Sierpinski triangle.<br />
<br />
Caption: Stage 3<br />
<br />
Selected objects: Nine small white triangles and their sides.<br />
|-<br />
|7||[[Image:Tool_Move.gif]]||In Move mode check and uncheck the checkbox to try out if the third stage of the Sierpinski triangle can be hidden / shown.<br />
|}<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26888Tutorial:Conditional Visibility & Sequences2012-07-09T08:30:22Z<p>Corinna: /* The Sierpinski Triangle */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to Perspectives – Geometry.<br />
* In the ''Options menu'' set the Labeling to ''New Points Only''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Polygon.gif]]||Create an arbitrary triangle ABC.<br />
|-<br />
|2||||Change the color of the triangle to black (Properties dialog).<br />
|-<br />
|3||[[Image:Tool_Midpoint_or_Center.gif]][[Image:Tool_Move.gif]]||Create midpoint D of triangle side AB.<br />
|-<br />
|4||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint E of triangle side BC.<br />
|-<br />
|5||[[Image:Tool_Midpoint_or_Center.gif]]||Create midpoint F of triangle side AC.<br />
|-<br />
|6||[[Image:Tool_Move.gif]]||Construct a triangle DEF.<br />
|-<br />
|7||||Change the color of triangle DEF to white and increase the filling to 100% (Properties dialog).<br />
|-<br />
|8||||Change the color of the sides of triangle DEF to black (Properties dialog).<br />
|-<br />
|9||||Create a new tool called Sierpinski.<br />
<br />
Output objects: points D, E and F, triangle DEF, sides of triangle DEF<br />
<br />
Input objects: points A, B and C<br />
<br />
Name: Sierpinski<br />
<br />
Toolbar help: Click on three points<br />
|- <br />
|10||||Apply your custom tool to the three black triangles ADF, DBE and FEC to create the second stage of the Sierpinski triangle.<br />
|-<br />
|11||||Apply your custom tool to the nine black triangles to create the third stage of the Sierpinski triangle.<br />
|}<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26887Tutorial:Conditional Visibility & Sequences2012-07-09T08:18:23Z<p>Corinna: /* Boolean variables */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the ''Properties'' dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select ''text5'' from the list of objects in the ''Properties'' dialog.<br />
<br />
3. Click on tab ''Advanced'' and look at the text field called ''Condition to Show Object''. It shows the name of your checkbox j. {{hint|This means that the visibility of ''text5'' depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field ''Condition to Show Object''. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: ''text5'' (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26886Tutorial:Conditional Visibility & Sequences2012-07-09T08:17:10Z<p>Corinna: /* Boolean variables */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the Properties dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select text5 from the list of objects in the Properties dialog.<br />
<br />
3. Click on tab Advanced and look at the text field called Condition to Show Object. It shows the name of your checkbox j. {{hint|This means that the visibility of text5 depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field Condition to Show Object. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: text5 (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26885Tutorial:Conditional Visibility & Sequences2012-07-09T08:16:59Z<p>Corinna: /* Boolean variables */</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
<br />
1. Open the Properties dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
<br />
2. Select text5 from the list of objects in the Properties dialog.<br />
<br />
3. Click on tab Advanced and look at the text field called Condition to Show Object. It shows the name of your checkbox j. {{hint|This means that the visibility of text5 depends on the status of the checkbox.}}<br />
<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
<br />
5. Enter j into the text field Condition to Show Object. The visibility of point R is now connected to the checkbox as well.<br />
<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: text5 (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Conditional_Visibility_%26_Sequences&diff=26884Tutorial:Conditional Visibility & Sequences2012-07-09T08:16:34Z<p>Corinna: Created page with "==Visualizing Integer Addition on the Number Line== In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them befor..."</p>
<hr />
<div>==Visualizing Integer Addition on the Number Line==<br />
In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.<br />
<br />
{|border="1" cellpadding="10"<br />
|[[Image:Tool_Slider.gif]]||[[Slider Tool|Slider]]<br />
|-<br />
|[[Image:Tool_New_Point.gif]]||[[New Point Tool|New Point]]<br />
|-<br />
|[[Image:Tool_Vector_between_Two_Points.gif]]||[[Vector between Two Points Tool|Vector]]<br />
|-<br />
|[[Image:Tool_Move.gif]]||[[Move Tool|Move]]<br />
|-<br />
|[[Image:Tool_Segment_between_Two_Points.gif]]||[[Segment between Two Points Tool|Segment Between Two Points]]<br />
|-<br />
|[[Image:Tool_Insert_Text.gif]]||[[Insert Text Tool|Insert Text]]<br />
|-<br />
|[[Image:Tool_Check_Box_to_Show_Hide_Objects.gif]]||[[Check Box to Show / Hide Objects Tool|Checkbox to Show/Hide Objects]]<br />
|}<br />
<br />
===Construction Steps===<br />
1. Open a new GeoGebra window and hide the [[Algebra View]]. Set the labeling option to ''All new objects'' ([[Options Menu]]).<br />
<br />
2. Open the Properties dialog for the Graphics View. On tab ''yAxis'', uncheck ''Show yAxis''. On tab ''xAxis'', set the distance of tick marks to ''1'' by checking the box ''Distance'' and entering ''1'' into the text field. On tab ''Basic'' set the ''minimum'' of the x-Axis to ''-21'' and the ''maximum'' to ''21''.<br />
<br />
3. Create [[Slider Tool|sliders]] a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).<br />
<br />
4. Create points ''A = (0 , 1)'' and ''B = A + (a , 0)''.<br />
<br />
5. Create vector ''u = Vector[A, B]'' which has the length a.<br />
<br />
6. Create points ''C = B + (0 , 1)'' and ''D = C + (b , 0)'' as well as vector ''v = Vector[C , D]'' which has the length b.<br />
7. Create point ''R = (x(D) , 0)''. {{hint|x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.}}<br />
8. Create point ''Z = (0, 0)'' as well as the following segments: ''g = Segment[Z, A]'', ''h = Segment[B, C]'', ''i = Segment[D, R]''.<br />
<br />
9. Use the [[Properties Dialog]] to enhance your construction (e.g. change color, line style, fix sliders, hide labels).<br />
<br />
[[Image:13_integer.PNG|center]]<br />
<br />
===Insert dynamic text===<br />
Enhance your interactive figure by inserting [[Insert Text Tool|dynamic text]] that displays the corresponding addition problem.<br />
<br />
10. Calculate the result of the addition problem: ''r = a + b''<br />
<br />
11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step.<br />
a. Insert text1: Select a from Objects<br />
b. Insert text2: +<br />
c. Insert text3: Select b from Objects<br />
d. Insert text4: =<br />
e. Insert text5: Select r from Objects<br />
<br />
12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text ([[Properties Dialog]]).<br />
<br />
13. Export the interactive figure as a dynamic worksheet.<br />
<br />
[[Image:13_integer2.PNG|center]]<br />
<br />
==Conditional Formatting – Inserting Checkboxes==<br />
===Construction Steps===<br />
Insert a [[Check Box to Show / Hide Objects Tool|checkbox]] into the [[Graphics View]] that allows you to show or hide the result of the addition problem (text5, point R, and segment i).<br />
<br />
1. Activate tool [[Check Box to Show / Hide Objects Tool|Checkbox]] to show and hide objects.<br />
<br />
2. Click on the graphics view next to the result of the addition problem.<br />
<br />
3. Enter ''Show result'' into the ''Caption'' text field.<br />
<br />
4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).<br />
<br />
5. Click ''Apply'' to create the checkbox.<br />
<br />
6. In ''Move'' mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.<br />
<br />
7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).<br />
<br />
8. Export this new interactive figure as a dynamic worksheet. {{hint|You might want to use a different name for this worksheet.}}<br />
<br />
[[Image:13_integer3.PNG|center]]<br />
<br />
===Boolean variables===<br />
A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.<br />
1. Open the Properties dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.<br />
2. Select text5 from the list of objects in the Properties dialog.<br />
3. Click on tab Advanced and look at the text field called Condition to Show Object. It shows the name of your checkbox j. {{hint|This means that the visibility of text5 depends on the status of the checkbox.}}<br />
4. Select point R from the list of objects in the Properties dialog. Click on tab ''Advanced''. The text field Condition to Show Object is empty.<br />
5. Enter j into the text field Condition to Show Object. The visibility of point R is now connected to the checkbox as well.<br />
6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.<br />
<br />
{{hint|Now the checkbox controls three objects of your dynamic figure: text5 (which shows the result of the addition), point R and segment i (which show the result on the number line).}}<br />
<br />
==The Sierpinski Triangle==<br />
<br />
==Introducing Sequences==<br />
<br />
==Visualizing Multiplication of Natural Numbers==<br />
<br />
==Challenge of the Day: String Art Based on Bézier Curves==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_and_Enhancing_Dynamic_Worksheets_with_GeoGebra&diff=26784Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra2012-07-04T11:42:21Z<p>Corinna: </p>
<hr />
<div>==Lower and Upper Sum==<br />
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between<br />
a function and the x-axis, which can be used to introduce the concept of integral to students.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Algebra & Graphics''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial ''f(x) = -0.5x3 + 2x2 – x + 1''.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis. {{hint|These points will determine the interval which restricts the area between the function and the x-axis.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create slider for the number n with Interval 1 to 50 and Increment 1.<br />
|-<br />
|4||||Enter ''uppersum = UpperSum[f, x(A), x(B), n]''. {{hint|x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.}}<br />
|-<br />
|5||||Enter ''lowersum = LowerSum[f, x(A), x(B), n]''.<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum = '' and select uppersum from Objects.<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum = '' and select lowersum from Objects.<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''.<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Difference = '' and select diff from Objects.<br />
|-<br />
|10||||Enter ''integral = Integral[f, x(A), x(B)]''.<br />
|-<br />
|11||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Integral = '' and select integral from Objects.<br />
|-<br />
|12|| ||Fix slider and text using the [[Properties Dialog]].<br />
|}<br />
<br />
===Task===<br />
Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum.<br />
1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice?<br />
2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
==Reducing the Size of the GeoGebra Window==<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
==Upload to GeoGebra==<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
==Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)==<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.<br />
<br />
===Enhancing Dynamic Worksheets===<br />
The export dialog window for Export as Webpage consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.<br />
<br />
==Visualizing Triangle Inequalities==<br />
You will now create a dynamic worksheet that illustrates the construction steps for a triangle whose three side lengths a, b and c are given. Additionally, this worksheet will allow your students to discover triangle inequalities.<br />
{{note|The triangle inequalities a+b>c, b+c>a, and a+c>b state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.}}<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Geometry''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Slider.gif]]||Create sliders a, b and c for the side lengths of the triangle with an Interval from 0 to 10 and Increment 0.5.<br />
|-<br />
|2||[[Image:Tool_Move.gif]]||Set the sliders to a = 8, b = 6.5 and c = 10.<br />
|-<br />
|3||[[Image:Tool_Segment_with_Given_Length_from_Point.gif]]||Create segment d with given length c. {{hint|Points A and B are the endpoints of the segment.}}<br />
|-<br />
|4||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle e with center A and radius b.<br />
|-<br />
|5||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle f with center B and radius a.<br />
|-<br />
|6||[[Image:Tool_Intersect_Two_Objects.gif]]||Construct the intersection point C of the two circles e and f.<br />
|-<br />
|7||[[Image:Tool_Polygon.gif]]||Create the triangle ABC.<br />
|-<br />
|8||[[Image:Tool_Angle.gif]]||Create interior angles α, β and γ of triangle ABC.<br />
|}<br />
<br />
===Enhancements===<br />
{|border="1" cellpadding="15" <br />
|9||[[Image:Tool_New_Point.gif]]||Create a point D on circle e.<br />
|-<br />
|10||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment g between the points A and D.<br />
|-<br />
|11||[[Image:Tool_Midpoint_or_Center.gif]]||Construct the midpoint E of segment g.<br />
|-<br />
|12||[[Image:Tool_Insert_Text.gif]]||Enter text1: ''b'' and attach it to point E.<br />
|-<br />
|13||[[Image:Tool_New_Point.gif]]||Create a point F on circle f.<br />
|-<br />
|14||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment h between points B and F.<br />
|-<br />
|15||[[Image:Tool_Midpoint_or_Center.gif]]||Construct the midpoint G of segment h.<br />
|-<br />
|16||[[Image:Tool_Insert_Text.gif]]||Enter text2: ''a'' and attach it to point G.<br />
|-<br />
|17|| ||Match colors of corresponding objects.<br />
|-<br />
|18|| ||Show the Navigation bar for Construction Steps ([[View Menu]]).<br />
|-<br />
|19|| ||Show the Button to open construction protocol (menu ''View – Navigation bar for Construction Steps'').<br />
|-<br />
|20|| ||Open the [[Construction Protocol]].<br />
|-<br />
|21|| ||Show the column ''Breakpoint''.<br />
|-<br />
|22|| ||Change the order of construction steps so that the radius of the circles and the attached text show up at the same time. {{hint|You might also set some other breakpoints (e.g. show all sliders at the same time).}}<br />
|-<br />
|23|| ||Now check ''Show Only Breakpoints''.<br />
|}<br />
<br />
===Tasks===<br />
(a) Export your triangle construction as a dynamic worksheet.<br />
<br />
(b) Come up with explanations and tasks for your students that guide them through the construction process of the triangle and help them explore the triangle inequalities by modifying the given side lengths using the sliders.<br />
<br />
==Design Guidelines for Dynamic Worksheets==<br />
The following design guidelines for dynamic worksheets are the result of a formative evaluation of dynamic worksheets created by teachers in our NSF MSP classes during fall 2006 and spring 2007. The guidelines are based on design principles for multimedia learning stated by Clark and Mayer.<br />
These guidelines were summarized to address and avoid common mistakes during the creation process of dynamic worksheets as well as to increase their quality with the hope that they will foster more effective learning. Although some of these guidelines may seem obvious, we have found it very important in our work with teachers to discuss and explain them in detail. The following figure shows an entire dynamic worksheet created with GeoGebra that allows students to explore properties of the orthocenter of a triangle. By modifying the dynamic construction students can examine the orthocenter of a great variety of triangles instead of just one special case. Several key words within the explanation and tasks match the color of the corresponding objects in order to facilitate finding them within the construction. Furthermore, the tasks are placed next to the dynamic construction in order to fit all information on one screen and avoid additional cognitive load through scrolling.<br />
<br />
===Design Guidelines 1: Layout of Dynamic Worksheets===<br />
====Avoid scrolling====<br />
Your entire worksheet should fit on one screen. Students should not have to scroll between the tasks and the interactive figure. We consider 1024x768 or 1280x1024 pixels as today's usual screen size which constrains the size of the dynamic worksheet. Using an HTML editor like NVU you can use tables to arrange text, images and interactive figures so they fit on one screen. If this is not possible, consider breaking the dynamic worksheet into several pages. <br />
<br />
====Short explanation ====<br />
At the beginning of a dynamic worksheet, you should give an explanation of its content. Keep the text short (no more than one or two sentences) and write it in a personal style.<br />
<br />
====Few tasks====<br />
You will usually add questions or tasks to make sure that your students use the worksheet actively. Place these tasks close to the interactive applet (e.g. directly below it). Don't use more than three or four questions / tasks to avoid scrolling. If you have more tasks, consider breaking your worksheet into several pages.<br />
<br />
====Avoid distractions====<br />
Make sure that your dynamic worksheet just contains objects that are relevant for the objectives. Neither use unnecessary background or purely decorative images, nor background music on the web page in order not to distract your students from reaching the objectives.<br />
<br />
===Design Guidelines 2: Dynamic Figures===<br />
====Interactivity====<br />
Allow as much interactivity as possible in your dynamic figure. As a rule of thumb, all visible objects should be movable or changeable in some way. Your dynamic figure should provide plenty of freedom to explore the relations of its mathematical objects and discover mathematical concepts.<br />
<br />
====Easy-to-use====<br />
Try to make your dynamic figure as easy to use as possible. If an object can be moved or changed, try to make this obvious, e.g. all movable points could be red or larger in size. If you don't want objects to be changed, fix them (e.g. text, functions or slider positions) so they cannot be moved accidentally.<br />
<br />
====Size matters====<br />
Your dynamic figure should be large enough to allow all intended manipulations, but small enough to fit on one screen and still leave sufficient space for explanations and questions on the surrounding web page.<br />
<br />
====Use dynamic text====<br />
Dynamic text, like the length of a changeable segment, should be placed close to the corresponding object in your applet.<br />
<br />
====Avoid static text====<br />
Too much text can easily clutter your interactive applet. Instead, place static text like explanations or questions on the web page that includes your dynamic figure.<br />
<br />
====First appearance====<br />
When a dynamic worksheet is opened you should be able to read all labels and important information. For example, a point label should not be crossed by a line.<br />
<br />
===Design Guidelines 3: Explanations and Tasks===<br />
====Short, clear and personal style====<br />
Try to write your explanations and questions in a short, clear and conversational style. Use the term ‘you' within the text and try to address the students directly.<br />
<br />
====Small number of questions====<br />
Limit your number of questions or tasks per worksheet to three or four to avoid scrolling. If you want to ask more questions, create a new worksheet.<br />
<br />
====Use specific questions====<br />
Avoid general questions like ‘What is always true about X?' and make clear what the students should do, e.g. `What happens to X when you move Y?'. We recommend that your students should take notes while they work with a dynamic worksheet. If you want them to write down their answers on paper, say so on the worksheet.<br />
<br />
====Refer to your applet====<br />
Your text should support the use of your interactive applet. For example, try to explain a new term by referring to your applet instead of using an isolated textual definition. Additionally, you can color certain keywords to match the formatting style of the object they refer to. This makes the text easier to read and helps your students to find corresponding representations of the same object.<br />
<br />
====Your audience are learners====<br />
If you want to provide information for other educators (e.g. lesson plan, solutions) do so in a separate document (e.g. web page, pdf-document). Your students should not be distracted or confused by such information. <br />
<br />
====Demonstration figure====<br />
If your interactive figure is meant for presentation only it might be better to have no tasks or questions on the web page. If you include text, it should be understandable for students as well.<br />
<br />
==Creating a Tangram Puzzle==<br />
In this activity you will create the "Tangram" puzzle. It consists of 7 geometric shapes which can all be constructed using the side length a (see [http://www.geogebra.org/book/intro-en/topics/files/12_Practice_Block_IV/A_4d_tangram_puzzle.html Tangram_puzzle.html]).<br />
<br />
[[Image:13_tangram.PNG|center]]<br />
<br />
===Task 1: Figure out the side lengths of each part===<br />
In order to construct the parts of the ''Tangram'' puzzle you need to figure out the individual side lengths of the seven geometric figures first. They all depend on the side length a of the main square. {{hint|In some cases you might want to look at the diagonals or height. Their<br />
lengths can be expressed more easily using the variable a than the lengths of the corresponding sides.}}<br />
<br />
===Task 2: Construct the individual parts of the Tangram===<br />
1. Enter the number a = 6. It will provide a basis for the construction of all triangles and quadrilaterals necessary for a "Tangram" puzzle.<br />
2. Try to figure out the side lengths of the geometric shapes. {{hint|In some cases you might want to look at the diagonals or height. Their lengths can be expressed more easily using the variable a than the lengths of the corresponding sides.}}<br />
3. Begin each of the geometric figures using a [[Segment with Given Length from Point Tool|segment with given length]]. This will allow you to drag and rotate the figure later on.<br />
<br />
4. Construction hints:<br />
<br />
a. If the height of a right triangle is half the length of the hypotenuse you might want to use the theorem of Thales for the construction (see [[Tutorial:Practice Block I|practice block 1]]).<br />
<br />
b. If you know the legs of a right triangle you might want to construct it similar to a square construction.<br />
<br />
c. For constructing a square using its diagonals, it is helpful to know that they are perpendicular and bisect each other.<br />
<br />
d. For constructing the parallelogram it is helpful to know the size of the acute angle.<br />
<br />
5. Check your construction by trying out if you can manage to create a square with side length a using all figures.<br />
<br />
<br />
==Challenge of the Day: Enhance Your Tangram Puzzle==<br />
With these geometric shapes other figures than a square can be created as well. Search the Internet for a "Tangram" figure other than a square and import this figure into the [[Graphics View]]. Export the GeoGebra construction again using a different name and different instructions.<br />
<br />
[[Image:13_cat.PNG|center]]</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_and_Enhancing_Dynamic_Worksheets_with_GeoGebra&diff=26783Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra2012-07-04T11:38:25Z<p>Corinna: /* Design Guidelines for Dynamic Worksheets */</p>
<hr />
<div>==Lower and Upper Sum==<br />
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between<br />
a function and the x-axis, which can be used to introduce the concept of integral to students.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Algebra & Graphics''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial ''f(x) = -0.5x3 + 2x2 – x + 1''.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis. {{hint|These points will determine the interval which restricts the area between the function and the x-axis.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create slider for the number n with Interval 1 to 50 and Increment 1.<br />
|-<br />
|4||||Enter ''uppersum = UpperSum[f, x(A), x(B), n]''. {{hint|x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.}}<br />
|-<br />
|5||||Enter ''lowersum = LowerSum[f, x(A), x(B), n]''.<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum = '' and select uppersum from Objects.<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum = '' and select lowersum from Objects.<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''.<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Difference = '' and select diff from Objects.<br />
|-<br />
|10||||Enter ''integral = Integral[f, x(A), x(B)]''.<br />
|-<br />
|11||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Integral = '' and select integral from Objects.<br />
|-<br />
|12|| ||Fix slider and text using the [[Properties Dialog]].<br />
|}<br />
<br />
===Task===<br />
Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum.<br />
1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice?<br />
2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
==Reducing the Size of the GeoGebra Window==<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
==Upload to GeoGebra==<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
==Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)==<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.<br />
<br />
===Enhancing Dynamic Worksheets===<br />
The export dialog window for Export as Webpage consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.<br />
<br />
==Visualizing Triangle Inequalities==<br />
You will now create a dynamic worksheet that illustrates the construction steps for a triangle whose three side lengths a, b and c are given. Additionally, this worksheet will allow your students to discover triangle inequalities.<br />
{{note|The triangle inequalities a+b>c, b+c>a, and a+c>b state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.}}<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Geometry''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Slider.gif]]||Create sliders a, b and c for the side lengths of the triangle with an Interval from 0 to 10 and Increment 0.5.<br />
|-<br />
|2||[[Image:Tool_Move.gif]]||Set the sliders to a = 8, b = 6.5 and c = 10.<br />
|-<br />
|3||[[Image:Tool_Segment_with_Given_Length_from_Point.gif]]||Create segment d with given length c. {{hint|Points A and B are the endpoints of the segment.}}<br />
|-<br />
|4||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle e with center A and radius b.<br />
|-<br />
|5||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle f with center B and radius a.<br />
|-<br />
|6||[[Image:Tool_Intersect_Two_Objects.gif]]||Construct the intersection point C of the two circles e and f.<br />
|-<br />
|7||[[Image:Tool_Polygon.gif]]||Create the triangle ABC.<br />
|-<br />
|8||[[Image:Tool_Angle.gif]]||Create interior angles α, β and γ of triangle ABC.<br />
|}<br />
<br />
===Enhancements===<br />
{|border="1" cellpadding="15" <br />
|9||[[Image:Tool_New_Point.gif]]||Create a point D on circle e.<br />
|-<br />
|10||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment g between the points A and D.<br />
|-<br />
|11||[[Image:Tool_Midpoint_or_Center.gif]]||Construct the midpoint E of segment g.<br />
|-<br />
|12||[[Image:Tool_Insert_Text.gif]]||Enter text1: ''b'' and attach it to point E.<br />
|-<br />
|13||[[Image:Tool_New_Point.gif]]||Create a point F on circle f.<br />
|-<br />
|14||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment h between points B and F.<br />
|-<br />
|15||[[Image:Tool_Midpoint_or_Center.gif]]||Construct the midpoint G of segment h.<br />
|-<br />
|16||[[Image:Tool_Insert_Text.gif]]||Enter text2: ''a'' and attach it to point G.<br />
|-<br />
|17|| ||Match colors of corresponding objects.<br />
|-<br />
|18|| ||Show the Navigation bar for Construction Steps ([[View Menu]]).<br />
|-<br />
|19|| ||Show the Button to open construction protocol (menu ''View – Navigation bar for Construction Steps'').<br />
|-<br />
|20|| ||Open the [[Construction Protocol]].<br />
|-<br />
|21|| ||Show the column ''Breakpoint''.<br />
|-<br />
|22|| ||Change the order of construction steps so that the radius of the circles and the attached text show up at the same time. {{hint|You might also set some other breakpoints (e.g. show all sliders at the same time).}}<br />
|-<br />
|23|| ||Now check ''Show Only Breakpoints''.<br />
|}<br />
<br />
===Tasks===<br />
(a) Export your triangle construction as a dynamic worksheet.<br />
<br />
(b) Come up with explanations and tasks for your students that guide them through the construction process of the triangle and help them explore the triangle inequalities by modifying the given side lengths using the sliders.<br />
<br />
==Design Guidelines for Dynamic Worksheets==<br />
The following design guidelines for dynamic worksheets are the result of a formative evaluation of dynamic worksheets created by teachers in our NSF MSP classes during fall 2006 and spring 2007. The guidelines are based on design principles for multimedia learning stated by Clark and Mayer.<br />
These guidelines were summarized to address and avoid common mistakes during the creation process of dynamic worksheets as well as to increase their quality with the hope that they will foster more effective learning. Although some of these guidelines may seem obvious, we have found it very important in our work with teachers to discuss and explain them in detail. The following figure shows an entire dynamic worksheet created with GeoGebra that allows students to explore properties of the orthocenter of a triangle. By modifying the dynamic construction students can examine the orthocenter of a great variety of triangles instead of just one special case. Several key words within the explanation and tasks match the color of the corresponding objects in order to facilitate finding them within the construction. Furthermore, the tasks are placed next to the dynamic construction in order to fit all information on one screen and avoid additional cognitive load through scrolling.<br />
<br />
===Design Guidelines 1: Layout of Dynamic Worksheets===<br />
====Avoid scrolling====<br />
Your entire worksheet should fit on one screen. Students should not have to scroll between the tasks and the interactive figure. We consider 1024x768 or 1280x1024 pixels as today's usual screen size which constrains the size of the dynamic worksheet. Using an HTML editor like NVU you can use tables to arrange text, images and interactive figures so they fit on one screen. If this is not possible, consider breaking the dynamic worksheet into several pages. <br />
<br />
====Short explanation ====<br />
At the beginning of a dynamic worksheet, you should give an explanation of its content. Keep the text short (no more than one or two sentences) and write it in a personal style.<br />
<br />
====Few tasks====<br />
You will usually add questions or tasks to make sure that your students use the worksheet actively. Place these tasks close to the interactive applet (e.g. directly below it). Don't use more than three or four questions / tasks to avoid scrolling. If you have more tasks, consider breaking your worksheet into several pages.<br />
<br />
====Avoid distractions====<br />
Make sure that your dynamic worksheet just contains objects that are relevant for the objectives. Neither use unnecessary background or purely decorative images, nor background music on the web page in order not to distract your students from reaching the objectives.<br />
<br />
===Design Guidelines 2: Dynamic Figures===<br />
====Interactivity====<br />
Allow as much interactivity as possible in your dynamic figure. As a rule of thumb, all visible objects should be movable or changeable in some way. Your dynamic figure should provide plenty of freedom to explore the relations of its mathematical objects and discover mathematical concepts.<br />
<br />
====Easy-to-use====<br />
Try to make your dynamic figure as easy to use as possible. If an object can be moved or changed, try to make this obvious, e.g. all movable points could be red or larger in size. If you don't want objects to be changed, fix them (e.g. text, functions or slider positions) so they cannot be moved accidentally.<br />
<br />
====Size matters====<br />
Your dynamic figure should be large enough to allow all intended manipulations, but small enough to fit on one screen and still leave sufficient space for explanations and questions on the surrounding web page.<br />
<br />
====Use dynamic text====<br />
Dynamic text, like the length of a changeable segment, should be placed close to the corresponding object in your applet.<br />
<br />
====Avoid static text====<br />
Too much text can easily clutter your interactive applet. Instead, place static text like explanations or questions on the web page that includes your dynamic figure.<br />
<br />
====First appearance====<br />
When a dynamic worksheet is opened you should be able to read all labels and important information. For example, a point label should not be crossed by a line.<br />
<br />
===Design Guidelines 3: Explanations and Tasks===<br />
====Short, clear and personal style====<br />
Try to write your explanations and questions in a short, clear and conversational style. Use the term ‘you' within the text and try to address the students directly.<br />
<br />
====Small number of questions====<br />
Limit your number of questions or tasks per worksheet to three or four to avoid scrolling. If you want to ask more questions, create a new worksheet.<br />
<br />
====Use specific questions====<br />
Avoid general questions like ‘What is always true about X?' and make clear what the students should do, e.g. `What happens to X when you move Y?'. We recommend that your students should take notes while they work with a dynamic worksheet. If you want them to write down their answers on paper, say so on the worksheet.<br />
<br />
====Refer to your applet====<br />
Your text should support the use of your interactive applet. For example, try to explain a new term by referring to your applet instead of using an isolated textual definition. Additionally, you can color certain keywords to match the formatting style of the object they refer to. This makes the text easier to read and helps your students to find corresponding representations of the same object.<br />
<br />
====Your audience are learners====<br />
If you want to provide information for other educators (e.g. lesson plan, solutions) do so in a separate document (e.g. web page, pdf-document). Your students should not be distracted or confused by such information. <br />
<br />
====Demonstration figure====<br />
If your interactive figure is meant for presentation only it might be better to have no tasks or questions on the web page. If you include text, it should be understandable for students as well.<br />
<br />
==Creating a Tangram Puzzle==<br />
<br />
==Challenge of the Day: Enhance Your Tangram Puzzle==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_and_Enhancing_Dynamic_Worksheets_with_GeoGebra&diff=26782Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra2012-07-04T11:23:16Z<p>Corinna: /* Tasks */</p>
<hr />
<div>==Lower and Upper Sum==<br />
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between<br />
a function and the x-axis, which can be used to introduce the concept of integral to students.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Algebra & Graphics''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial ''f(x) = -0.5x3 + 2x2 – x + 1''.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis. {{hint|These points will determine the interval which restricts the area between the function and the x-axis.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create slider for the number n with Interval 1 to 50 and Increment 1.<br />
|-<br />
|4||||Enter ''uppersum = UpperSum[f, x(A), x(B), n]''. {{hint|x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.}}<br />
|-<br />
|5||||Enter ''lowersum = LowerSum[f, x(A), x(B), n]''.<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum = '' and select uppersum from Objects.<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum = '' and select lowersum from Objects.<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''.<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Difference = '' and select diff from Objects.<br />
|-<br />
|10||||Enter ''integral = Integral[f, x(A), x(B)]''.<br />
|-<br />
|11||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Integral = '' and select integral from Objects.<br />
|-<br />
|12|| ||Fix slider and text using the [[Properties Dialog]].<br />
|}<br />
<br />
===Task===<br />
Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum.<br />
1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice?<br />
2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
==Reducing the Size of the GeoGebra Window==<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
==Upload to GeoGebra==<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
==Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)==<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.<br />
<br />
===Enhancing Dynamic Worksheets===<br />
The export dialog window for Export as Webpage consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.<br />
<br />
==Visualizing Triangle Inequalities==<br />
You will now create a dynamic worksheet that illustrates the construction steps for a triangle whose three side lengths a, b and c are given. Additionally, this worksheet will allow your students to discover triangle inequalities.<br />
{{note|The triangle inequalities a+b>c, b+c>a, and a+c>b state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.}}<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Geometry''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Slider.gif]]||Create sliders a, b and c for the side lengths of the triangle with an Interval from 0 to 10 and Increment 0.5.<br />
|-<br />
|2||[[Image:Tool_Move.gif]]||Set the sliders to a = 8, b = 6.5 and c = 10.<br />
|-<br />
|3||[[Image:Tool_Segment_with_Given_Length_from_Point.gif]]||Create segment d with given length c. {{hint|Points A and B are the endpoints of the segment.}}<br />
|-<br />
|4||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle e with center A and radius b.<br />
|-<br />
|5||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle f with center B and radius a.<br />
|-<br />
|6||[[Image:Tool_Intersect_Two_Objects.gif]]||Construct the intersection point C of the two circles e and f.<br />
|-<br />
|7||[[Image:Tool_Polygon.gif]]||Create the triangle ABC.<br />
|-<br />
|8||[[Image:Tool_Angle.gif]]||Create interior angles α, β and γ of triangle ABC.<br />
|}<br />
<br />
===Enhancements===<br />
{|border="1" cellpadding="15" <br />
|9||[[Image:Tool_New_Point.gif]]||Create a point D on circle e.<br />
|-<br />
|10||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment g between the points A and D.<br />
|-<br />
|11||[[Image:Tool_Midpoint_or_Center.gif]]||Construct the midpoint E of segment g.<br />
|-<br />
|12||[[Image:Tool_Insert_Text.gif]]||Enter text1: ''b'' and attach it to point E.<br />
|-<br />
|13||[[Image:Tool_New_Point.gif]]||Create a point F on circle f.<br />
|-<br />
|14||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment h between points B and F.<br />
|-<br />
|15||[[Image:Tool_Midpoint_or_Center.gif]]||Construct the midpoint G of segment h.<br />
|-<br />
|16||[[Image:Tool_Insert_Text.gif]]||Enter text2: ''a'' and attach it to point G.<br />
|-<br />
|17|| ||Match colors of corresponding objects.<br />
|-<br />
|18|| ||Show the Navigation bar for Construction Steps ([[View Menu]]).<br />
|-<br />
|19|| ||Show the Button to open construction protocol (menu ''View – Navigation bar for Construction Steps'').<br />
|-<br />
|20|| ||Open the [[Construction Protocol]].<br />
|-<br />
|21|| ||Show the column ''Breakpoint''.<br />
|-<br />
|22|| ||Change the order of construction steps so that the radius of the circles and the attached text show up at the same time. {{hint|You might also set some other breakpoints (e.g. show all sliders at the same time).}}<br />
|-<br />
|23|| ||Now check ''Show Only Breakpoints''.<br />
|}<br />
<br />
===Tasks===<br />
(a) Export your triangle construction as a dynamic worksheet.<br />
<br />
(b) Come up with explanations and tasks for your students that guide them through the construction process of the triangle and help them explore the triangle inequalities by modifying the given side lengths using the sliders.<br />
<br />
==Design Guidelines for Dynamic Worksheets==<br />
<br />
==Creating a Tangram Puzzle==<br />
<br />
==Challenge of the Day: Enhance Your Tangram Puzzle==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_and_Enhancing_Dynamic_Worksheets_with_GeoGebra&diff=26781Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra2012-07-04T11:22:33Z<p>Corinna: /* Construction Steps */</p>
<hr />
<div>==Lower and Upper Sum==<br />
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between<br />
a function and the x-axis, which can be used to introduce the concept of integral to students.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Algebra & Graphics''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial ''f(x) = -0.5x3 + 2x2 – x + 1''.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis. {{hint|These points will determine the interval which restricts the area between the function and the x-axis.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create slider for the number n with Interval 1 to 50 and Increment 1.<br />
|-<br />
|4||||Enter ''uppersum = UpperSum[f, x(A), x(B), n]''. {{hint|x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.}}<br />
|-<br />
|5||||Enter ''lowersum = LowerSum[f, x(A), x(B), n]''.<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum = '' and select uppersum from Objects.<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum = '' and select lowersum from Objects.<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''.<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Difference = '' and select diff from Objects.<br />
|-<br />
|10||||Enter ''integral = Integral[f, x(A), x(B)]''.<br />
|-<br />
|11||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Integral = '' and select integral from Objects.<br />
|-<br />
|12|| ||Fix slider and text using the [[Properties Dialog]].<br />
|}<br />
<br />
===Task===<br />
Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum.<br />
1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice?<br />
2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
==Reducing the Size of the GeoGebra Window==<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
==Upload to GeoGebra==<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
==Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)==<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.<br />
<br />
===Enhancing Dynamic Worksheets===<br />
The export dialog window for Export as Webpage consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.<br />
<br />
==Visualizing Triangle Inequalities==<br />
You will now create a dynamic worksheet that illustrates the construction steps for a triangle whose three side lengths a, b and c are given. Additionally, this worksheet will allow your students to discover triangle inequalities.<br />
{{note|The triangle inequalities a+b>c, b+c>a, and a+c>b state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.}}<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Geometry''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Slider.gif]]||Create sliders a, b and c for the side lengths of the triangle with an Interval from 0 to 10 and Increment 0.5.<br />
|-<br />
|2||[[Image:Tool_Move.gif]]||Set the sliders to a = 8, b = 6.5 and c = 10.<br />
|-<br />
|3||[[Image:Tool_Segment_with_Given_Length_from_Point.gif]]||Create segment d with given length c. {{hint|Points A and B are the endpoints of the segment.}}<br />
|-<br />
|4||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle e with center A and radius b.<br />
|-<br />
|5||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle f with center B and radius a.<br />
|-<br />
|6||[[Image:Tool_Intersect_Two_Objects.gif]]||Construct the intersection point C of the two circles e and f.<br />
|-<br />
|7||[[Image:Tool_Polygon.gif]]||Create the triangle ABC.<br />
|-<br />
|8||[[Image:Tool_Angle.gif]]||Create interior angles α, β and γ of triangle ABC.<br />
|}<br />
<br />
===Enhancements===<br />
{|border="1" cellpadding="15" <br />
|9||[[Image:Tool_New_Point.gif]]||Create a point D on circle e.<br />
|-<br />
|10||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment g between the points A and D.<br />
|-<br />
|11||[[Image:Tool_Midpoint_or_Center.gif]]||Construct the midpoint E of segment g.<br />
|-<br />
|12||[[Image:Tool_Insert_Text.gif]]||Enter text1: ''b'' and attach it to point E.<br />
|-<br />
|13||[[Image:Tool_New_Point.gif]]||Create a point F on circle f.<br />
|-<br />
|14||[[Image:Tool_Segment_between_Two_Points.gif]]||Create segment h between points B and F.<br />
|-<br />
|15||[[Image:Tool_Midpoint_or_Center.gif]]||Construct the midpoint G of segment h.<br />
|-<br />
|16||[[Image:Tool_Insert_Text.gif]]||Enter text2: ''a'' and attach it to point G.<br />
|-<br />
|17|| ||Match colors of corresponding objects.<br />
|-<br />
|18|| ||Show the Navigation bar for Construction Steps ([[View Menu]]).<br />
|-<br />
|19|| ||Show the Button to open construction protocol (menu ''View – Navigation bar for Construction Steps'').<br />
|-<br />
|20|| ||Open the [[Construction Protocol]].<br />
|-<br />
|21|| ||Show the column ''Breakpoint''.<br />
|-<br />
|22|| ||Change the order of construction steps so that the radius of the circles and the attached text show up at the same time. {{hint|You might also set some other breakpoints (e.g. show all sliders at the same time).}}<br />
|-<br />
|23|| ||Now check ''Show Only Breakpoints''.<br />
|}<br />
<br />
===Tasks===<br />
(a) Export your triangle construction as a dynamic worksheet.<br />
(b) Come up with explanations and tasks for your students that guide them through the construction process of the triangle and help them explore the triangle inequalities by modifying the given side lengths using the sliders.<br />
<br />
==Design Guidelines for Dynamic Worksheets==<br />
<br />
==Creating a Tangram Puzzle==<br />
<br />
==Challenge of the Day: Enhance Your Tangram Puzzle==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_and_Enhancing_Dynamic_Worksheets_with_GeoGebra&diff=26780Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra2012-07-04T11:14:18Z<p>Corinna: </p>
<hr />
<div>==Lower and Upper Sum==<br />
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between<br />
a function and the x-axis, which can be used to introduce the concept of integral to students.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Algebra & Graphics''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial ''f(x) = -0.5x3 + 2x2 – x + 1''.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis. {{hint|These points will determine the interval which restricts the area between the function and the x-axis.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create slider for the number n with Interval 1 to 50 and Increment 1.<br />
|-<br />
|4||||Enter ''uppersum = UpperSum[f, x(A), x(B), n]''. {{hint|x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.}}<br />
|-<br />
|5||||Enter ''lowersum = LowerSum[f, x(A), x(B), n]''.<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum = '' and select uppersum from Objects.<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum = '' and select lowersum from Objects.<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''.<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Difference = '' and select diff from Objects.<br />
|-<br />
|10||||Enter ''integral = Integral[f, x(A), x(B)]''.<br />
|-<br />
|11||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Integral = '' and select integral from Objects.<br />
|-<br />
|12|| ||Fix slider and text using the [[Properties Dialog]].<br />
|}<br />
<br />
===Task===<br />
Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum.<br />
1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice?<br />
2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
==Reducing the Size of the GeoGebra Window==<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
==Upload to GeoGebra==<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
==Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)==<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.<br />
<br />
===Enhancing Dynamic Worksheets===<br />
The export dialog window for Export as Webpage consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.<br />
<br />
==Visualizing Triangle Inequalities==<br />
You will now create a dynamic worksheet that illustrates the construction steps for a triangle whose three side lengths a, b and c are given. Additionally, this worksheet will allow your students to discover triangle inequalities.<br />
{{note|The triangle inequalities a+b>c, b+c>a, and a+c>b state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.}}<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Geometry''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||[[Image:Tool_Slider.gif]]||Create sliders a, b and c for the side lengths of the triangle with an Interval from 0 to 10 and Increment 0.5.<br />
|-<br />
|2||[[Image:Tool_Move.gif]]||Set the sliders to a = 8, b = 6.5 and c = 10.<br />
|-<br />
|3||[[Image:Tool_Segment_with_Given_Length_from_Point.gif]]||Create segment d with given length c. {{hint|Points A and B are the endpoints of the segment.}}<br />
|-<br />
|4||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle e with center A and radius b.<br />
|-<br />
|5||[[Image:Tool_Circle_Center_Radius.gif]]||Create a circle f with center B and radius a.<br />
|-<br />
|6||[[Image:Tool_Intersect.gif]]||Construct the intersection point C of the two circles e and f.<br />
|-<br />
|7||[[Image:Tool_Polygon.gif]]||Create the triangle ABC.<br />
|-<br />
|8||[[Image:Tool_Angle.gif]]||Create interior angles α, β and γ of triangle ABC.<br />
|}<br />
<br />
==Design Guidelines for Dynamic Worksheets==<br />
<br />
==Creating a Tangram Puzzle==<br />
<br />
==Challenge of the Day: Enhance Your Tangram Puzzle==</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_and_Enhancing_Dynamic_Worksheets_with_GeoGebra&diff=26777Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra2012-07-04T09:45:12Z<p>Corinna: </p>
<hr />
<div>==Lower and Upper Sum==<br />
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between<br />
a function and the x-axis, which can be used to introduce the concept of integral to students.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Algebra & Graphics''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial ''f(x) = -0.5x3 + 2x2 – x + 1''.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis. {{hint|These points will determine the interval which restricts the area between the function and the x-axis.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create slider for the number n with Interval 1 to 50 and Increment 1.<br />
|-<br />
|4||||Enter ''uppersum = UpperSum[f, x(A), x(B), n]''. {{hint|x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.}}<br />
|-<br />
|5||||Enter ''lowersum = LowerSum[f, x(A), x(B), n]''.<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum = '' and select uppersum from Objects.<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum = '' and select lowersum from Objects.<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''.<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Difference = '' and select diff from Objects.<br />
|-<br />
|10||||Enter ''integral = Integral[f, x(A), x(B)]''.<br />
|-<br />
|11||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Integral = '' and select integral from Objects.<br />
|-<br />
|12|| ||Fix slider and text using the [[Properties Dialog]].<br />
|}<br />
<br />
===Task===<br />
Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum.<br />
1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice?<br />
2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
==Reducing the Size of the GeoGebra Window==<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
==Upload to GeoGebra==<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
==Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)==<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.<br />
<br />
===Enhancing Dynamic Worksheets===<br />
The export dialog window for Export as Webpage consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.<br />
<br />
==Visualizing Triangle Inequalities==<br />
You will now create a dynamic worksheet that illustrates the construction steps for a triangle whose three side lengths a, b and c are given. Additionally, this worksheet will allow your students to discover triangle inequalities.<br />
{{note|The triangle inequalities a+b>c, b+c>a, and a+c>b state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.}}<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Geometry''.<br />
<br />
===Construction Steps===</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_and_Enhancing_Dynamic_Worksheets_with_GeoGebra&diff=26776Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra2012-07-04T09:09:19Z<p>Corinna: </p>
<hr />
<div>==Lower and Upper Sum==<br />
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between<br />
a function and the x-axis, which can be used to introduce the concept of integral to students.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Algebra & Graphics''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial ''f(x) = -0.5x3 + 2x2 – x + 1''.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis. {{hint|These points will determine the interval which restricts the area between the function and the x-axis.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create slider for the number n with Interval 1 to 50 and Increment 1.<br />
|-<br />
|4||||Enter ''uppersum = UpperSum[f, x(A), x(B), n]''. {{hint|x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.}}<br />
|-<br />
|5||||Enter ''lowersum = LowerSum[f, x(A), x(B), n]''.<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum = '' and select uppersum from Objects.<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum = '' and select lowersum from Objects.<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''.<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Difference = '' and select diff from Objects.<br />
|-<br />
|10||||Enter ''integral = Integral[f, x(A), x(B)]''.<br />
|-<br />
|11||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Integral = '' and select integral from Objects.<br />
|-<br />
|12|| ||Fix slider and text using the [[Properties Dialog]].<br />
|}<br />
<br />
===Task===<br />
Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum.<br />
1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice?<br />
2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
==Reducing the Size of the GeoGebra Window==<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
==Upload to GeoGebra==<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
==Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)==<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.<br />
<br />
===Enhancing Dynamic Worksheets===<br />
The export dialog window for Export as Webpage consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_and_Enhancing_Dynamic_Worksheets_with_GeoGebra&diff=26775Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra2012-07-04T09:05:16Z<p>Corinna: Created page with "==Lower and Upper Sum== You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between a function a..."</p>
<hr />
<div>==Lower and Upper Sum==<br />
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between<br />
a function and the x-axis, which can be used to introduce the concept of integral to students.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Switch to ''Perspectives – Algebra & Graphics''.<br />
<br />
===Construction Steps===<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial ''f(x) = -0.5x3 + 2x2 – x + 1''.<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis. {{hint|These points will determine the interval which restricts the area between the function and the x-axis.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create slider for the number n with Interval 1 to 50 and Increment 1.<br />
|-<br />
|4||||Enter ''uppersum = UpperSum[f, x(A), x(B), n]''. {{hint|x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.}}<br />
|-<br />
|5||||Enter ''lowersum = LowerSum[f, x(A), x(B), n]''.<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum = '' and select uppersum from Objects.<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum = '' and select lowersum from Objects.<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''.<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Difference = '' and select diff from Objects.<br />
|-<br />
|10||||Enter ''integral = Integral[f, x(A), x(B)]''.<br />
|-<br />
|11||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Integral = '' and select integral from Objects.<br />
|-<br />
|12|| ||Fix slider and text using the [[Properties Dialog]].<br />
|}</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Inserting_Text_into_the_Graphics_View&diff=26762Tutorial:Inserting Text into the Graphics View2012-07-04T07:52:08Z<p>Corinna: Corinna moved page Tutorial:Inserting Text into the Graphics View to Tutorial:Inserting Static and Dynamic Text into the GeoGebra’s Graphics View</p>
<hr />
<div>#REDIRECT [[Tutorial:Inserting Static and Dynamic Text into the GeoGebra’s Graphics View]]</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Installation_and_Introduction&diff=26477Tutorial:Installation and Introduction2012-06-13T08:44:25Z<p>Corinna: moved Tutorial:Installation and Introduction to Tutorial:Installation & Introduction, Drawing vs Geometric Construction</p>
<hr />
<div>#REDIRECT [[Tutorial:Installation & Introduction, Drawing vs Geometric Construction]]</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Translation:Introductory_Book&diff=25571Translation:Introductory Book2012-04-18T07:45:07Z<p>Corinna: </p>
<hr />
<div>Thank you for your interest in translating the GeoGebra Introductory Book to your language! Please note that the book chapters now contain the old workshop materials as well. <br />
<br />
The GeoGebra Introductory Book covers the basic introduction to the dynamic mathematics software GeoGebra. It can be used both for workshops and for self learning and includes some chapters with practice examples. The book is written in Open Office Writer / Microsoft Word format. Open Office can be downloaded for free from [http://www.openoffice.org www.openoffice.org]. This document describes how to translate the GeoGebra Introductory Book from scratch or how to update your previous translation to the latest version using Open Office Writer or Microsoft Word.<br />
<br />
==Download Files==<br />
Download the latest version of the English Introductory Book and the accompanying GeoGebra files from <br />
[http://www.geogebra.org/book/intro-en.zip http://www.geogebra.org/book/intro-en.zip]. The zip file contains the English version (.doc) as the basis for your GeoGebra constructions, dynamic worksheets, and picture files the Introductory Book is referring to.<br />
<br />
'''Updating translators''': Download the last version of the GeoGebra Introductory Book in your language. In order to update this existing version of your translated book, we provide a file that tells you about the changes to be made. For example, there is a text file in the zip file of the GeoGebra 4 introductory book telling you about changes compared to the previous 3.2 version of the book.<br />
<br />
==Translation==<br />
<br />
===Open the Files in MS Word / Open Office Writer===<br />
'''First time translators''': Open the English Introductory Book document and save it under a name that shows your language, e.g. ggb-intro-es40.doc (“es” for Spanish).<br />
<br />
'''Updating translators''': Open the latest help document (doc format) in your language.<br />
<br />
===Translate the Text===<br />
'''First time translators''': In order to translate the text, replace the English text by your translated text. Make sure to read the notes below carefully.<br />
<br />
'''Updating translators''': Use the changes txt file found in the zip file to update your translation.<br />
<br />
'''Important Notes for Everyone''': <br />
* DO NOT translate the table of contents at the beginning of the document! It will be generated automatically. <br />
* DO NOT delete any hyperlinks (see Translate Hyperlinks).<br />
* DO NOT delete any images (e.g. toolbar icons).<br />
* DO NOT change any formatting of the text (i.e. font size, bold, italics)<br />
<br />
===Translate the Hyperlinks===<br />
After translating all text of the GeoGebra Introductory Book, you should go through all hyperlinks to check if they are in your language:<br />
<br />
# In order to translate a hyperlink, click into the middle of the word of the hyperlink and start typing your translation. This keeps the hyperlink and lets you insert your translated hyperlink text. Then delete the English letters at the beginning and the end of your translated hyperlink text.<br />
# Repeat step 1 for every hyperlink that is not in your language yet.<br />
# Many of the hyperlinks in this document link to the corresponding GeoGebra files or to pictures. If you plan to translate their file names as well, please change the hyperlinks accordingly.<br />
<br />
===Translators===<br />
Please add a section "Translated by" with your names below the authors.<br />
<br />
==Submitting your Translation==<br />
After finishing your translation please save your file in .doc format and send it to [mailto:translation@geogebra.org translation@geogebra.org] via e-mail. If you have also translated the GeoGebra files, please pack everything into a zip file and send it too.<br />
<br />
----<br />
<br />
Thank you for your work and support of GeoGebra!<br />
The GeoGebra Team<br />
<br />
[[Category:Translation]]</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:13_cat.PNG&diff=25188File:13 cat.PNG2012-03-06T16:29:42Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:13_tangram.PNG&diff=25187File:13 tangram.PNG2012-03-06T16:28:34Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:13_integer3.PNG&diff=25181File:13 integer3.PNG2012-03-06T16:18:29Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:13_integer2.PNG&diff=25180File:13 integer2.PNG2012-03-06T16:16:00Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:13_integer.PNG&diff=25179File:13 integer.PNG2012-03-06T16:14:13Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:13_anglesum.PNG&diff=25178File:13 anglesum.PNG2012-03-06T16:05:42Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:13_squares.PNG&diff=25170File:13 squares.PNG2012-03-06T15:48:04Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_Dynamic_Worksheets&diff=25152Tutorial:Creating Dynamic Worksheets2012-03-05T18:39:26Z<p>Corinna: </p>
<hr />
<div>==Creating Dynamic Worksheets==<br />
In this activity you will learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between a function and the x-axis.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Show the [[Algebra View]], [[Input Bar]] and coordinate axes ([[View Menu]]).<br />
<br />
===Construction Steps===<br />
<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial f(x) = -0.5x³ + 2x³ – x + 1<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis {{hint|These points will determine the interval.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create a slider for the number n (interval 1 to 50; increment 1)<br />
|-<br />
|4||||Create ''uppersum = uppersum[f, x(A), x(B), n]'' {{hint|x(A) gives you the x-coordinate of point A.}}<br />
|-<br />
|5||||Create ''lowersum = lowersum[f, x(A), x(B), n]''<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum ='' and select ''uppersum'' from ''Objects''<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum ='' and select ''lowersum'' from ''Objects''<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif ]]||Insert dynamic text ''Difference ='' and select ''diff'' from ''Objects'' {{hint|Fix the slider and the text using the Properties dialog.}}<br />
|}<br />
<br />
<u>Task:</u> Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
===Reducing the Size of the GeoGebra Window===<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
===Upload to GeoGebra===<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
===Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)===<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.<br />
<br />
To enhance your dynamic worksheet by including different features using the tab ''Advanced'' read through [[Export as html Webpage]].<br />
<br />
==Providing Dynamic Worksheets to Students==<br />
You can provide your dynamic worksheets in several ways to your students. However, in all cases it is very important to keep all the files together which were created during the export process.<br />
{{note|The files created have different file name extensions (.ggb, .html, .jar). If one of these files is missing your dynamic worksheet won’t function any more.}}<br />
<br />
===Local Storage Device===<br />
Copy all files into the same folder before saving this folder on a local storage device (e.g. flash drive, CD). Have your students copy the whole folder on their computers. Your students will have to open the file with the name extension ''.html'' in their Internet browser.</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:12_advanced.PNG&diff=25151File:12 advanced.PNG2012-03-05T18:35:59Z<p>Corinna: </p>
<hr />
<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_Dynamic_Worksheets&diff=25150Tutorial:Creating Dynamic Worksheets2012-03-05T18:33:59Z<p>Corinna: </p>
<hr />
<div>==Creating Dynamic Worksheets==<br />
In this activity you will learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between a function and the x-axis.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Show the [[Algebra View]], [[Input Bar]] and coordinate axes ([[View Menu]]).<br />
<br />
===Construction Steps===<br />
<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial f(x) = -0.5x³ + 2x³ – x + 1<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis {{hint|These points will determine the interval.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create a slider for the number n (interval 1 to 50; increment 1)<br />
|-<br />
|4||||Create ''uppersum = uppersum[f, x(A), x(B), n]'' {{hint|x(A) gives you the x-coordinate of point A.}}<br />
|-<br />
|5||||Create ''lowersum = lowersum[f, x(A), x(B), n]''<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum ='' and select ''uppersum'' from ''Objects''<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum ='' and select ''lowersum'' from ''Objects''<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif ]]||Insert dynamic text ''Difference ='' and select ''diff'' from ''Objects'' {{hint|Fix the slider and the text using the Properties dialog.}}<br />
|}<br />
<br />
<u>Task:</u> Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
===Reducing the Size of the GeoGebra Window===<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
===Upload to GeoGebra===<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
===Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)===<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_Dynamic_Worksheets&diff=25149Tutorial:Creating Dynamic Worksheets2012-03-05T18:33:07Z<p>Corinna: </p>
<hr />
<div>==Creating Dynamic Worksheets==<br />
In this activity you will learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between a function and the x-axis.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Show the [[Algebra View]], [[Input Bar]] and coordinate axes ([[View Menu]]).<br />
<br />
===Construction Steps===<br />
<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial f(x) = -0.5x³ + 2x³ – x + 1<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis {{hint|These points will determine the interval.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create a slider for the number n (interval 1 to 50; increment 1)<br />
|-<br />
|4||||Create ''uppersum = uppersum[f, x(A), x(B), n]'' {{hint|x(A) gives you the x-coordinate of point A.}}<br />
|-<br />
|5||||Create ''lowersum = lowersum[f, x(A), x(B), n]''<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Upper Sum ='' and select ''uppersum'' from ''Objects''<br />
|-<br />
|7||[[Image:Tool_Insert_Text.gif]]||Insert dynamic text ''Lower Sum ='' and select ''lowersum'' from ''Objects''<br />
|-<br />
|8||||Calculate the difference ''diff = uppersum – lowersum''<br />
|-<br />
|9||[[Image:Tool_Insert_Text.gif ]]||Insert dynamic text ''Difference ='' and select ''diff'' from ''Objects'' {{hint|Fix the slider and the text using the Properties dialog.}}<br />
}<br />
<br />
<u>Task:</u> Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?<br />
<br />
===Reducing the Size of the GeoGebra Window===<br />
GeoGebra will export the algebra and graphics view into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export.<br />
* If you don’t want to include the [[Algebra View]] you need to hide it prior to the export.<br />
* Move your figure (or the relevant section) to the upper left corner of the [[Graphics View]] using the [[Move Graphics View Tool]]. {{hint|You might want to use tools [[Zoom In Tool|Zoom in]] and [[Zoom Out Tool|Zoom out]] in order to prepare your figure for the export process.}}<br />
* Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). {{hint|The pointer will change its shape when hovering above an edge or corner of the GeoGebra window.}}<br />
{{note|Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.}}<br />
<br />
===Upload to GeoGebra===<br />
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the [[File Menu]].<br />
* ''File – Share''…<br />
<br />
[[Image:12_share.PNG|center]]<br />
<br />
* The [http://www.geogebra.org/ GeoGebra website] opens automatically where you have to login (or register if you do not have an account yet) before you are able to continue your upload.<br />
<br />
[[Image:12_upload.PNG|center]]<br />
<br />
* Fill in the information for your students. If you want, you can also select to show the [[Toolbar]], the [[Input Bar]] or the [[Menubar]]. Click ''Continue''.<br />
* Type a short explanation for other teachers, so that they are able to use your materials, too. This information is not shown on the student worksheet. Choose a target group and select tags that describe your material to help others with searching.<br />
* Finish your Upload with the ''Save'' button.<br />
<br />
Your worksheet is now saved on GeoGebra where people are able to like/dislike the material or write comments.<br />
<br />
===Exporting a Dynamic Worksheet to a Webpage (for Advanced Users)===<br />
Instead of uploading to GeoGebra it is possible to export your dynamic worksheet to a webpage.<br />
* ''Export – Dynamic Worksheet as Webpage'' {{hint|You could also use the key combination {{KeyCode|Ctrl}} + {{KeyCode|Shift}} + {{KeyCode|W}}.}}<br />
<br />
[[Image:12_export.PNG|center]]<br />
<br />
* Fill in the text fields in the appearing window in the ''Export as Webpage Tab'' (title of the worksheet, name of the author, and date).<br />
* Type a short explanation of the dynamic figure into the text field ''Text above the construction''.<br />
* Enter tasks and directions for students into the text field ''Text below the construction''.<br />
* Click ''Export'' and save your dynamic worksheet. {{hint|GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creation of a new folder (e.g. Dynamic_Worksheets) within the ''GeoGebra_Introduction'' folder prior to saving your dynamic worksheet.}}<br />
<br />
===Tips and Tricks for Creating Dynamic Worksheets===<br />
* After saving the dynamic worksheet it will be automatically opened up in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. {{hint|You can change the text of the dynamic worksheet in the same way.}}<br />
* GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on.<br />
* Make sure your applet is not too big. Your students shouldn’t have to scroll between the tasks and the figure because this makes learning more difficult.<br />
* Your dynamic worksheet should fit on one screen. If you want to include more than 3 tasks you should consider creation of another worksheet that includes the same dynamic figure but different tasks.</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:12_export.PNG&diff=25148File:12 export.PNG2012-03-05T18:30:24Z<p>Corinna: </p>
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<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:12_upload.PNG&diff=25147File:12 upload.PNG2012-03-05T18:26:53Z<p>Corinna: </p>
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<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:12_share.PNG&diff=25146File:12 share.PNG2012-03-05T18:25:24Z<p>Corinna: </p>
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<div></div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=Tutorial:Creating_Dynamic_Worksheets&diff=25145Tutorial:Creating Dynamic Worksheets2012-03-05T18:19:25Z<p>Corinna: Created page with "==Creating Dynamic Worksheets== In this activity you will learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area be..."</p>
<hr />
<div>==Creating Dynamic Worksheets==<br />
In this activity you will learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between a function and the x-axis.<br />
<br />
===Preparations===<br />
* Open a new GeoGebra window.<br />
* Show the [[Algebra View]], [[Input Bar]] and coordinate axes ([[View Menu]]).<br />
<br />
===Construction Steps===<br />
<br />
{|border="1" cellpadding="15" <br />
|1||||Enter the cubic polynomial f(x) = -0.5x³ + 2x³ – x + 1<br />
|-<br />
|2||[[Image:Tool_New_Point.gif]]||Create two points A and B on the x-axis {{hint: These points will determine the interval.}}<br />
|-<br />
|3||[[Image:Tool_Slider.gif]]||Create a slider for the number n (interval 1 to 50; increment 1)<br />
|-<br />
|4||||Create ''uppersum = uppersum[f, x(A), x(B), n]'' {{hint|x(A) gives you the x-coordinate of point A.}}<br />
|-<br />
|5||||Create ''lowersum = lowersum[f, x(A), x(B), n]''<br />
|-<br />
|6||[[Image:Tool_Insert_Text.gif ]]||Insert dynamic text ''Upper Sum ='' and select ''uppersum'' from ''Objects''</div>Corinnahttps://wiki.geogebra.org/s/en/index.php?title=File:11_oowriter1.PNG&diff=25139File:11 oowriter1.PNG2012-03-05T18:10:44Z<p>Corinna: </p>
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<div></div>Corinna