# Tutorial:Practice Block II

## Contents

## Parameters of a Linear Equation

In this activity you are going to use the following tools, algebraic input, and commands. Make sure you know how to use them before you begin with the actual construction.

Slider | |

line: y = m x + b | |

Segment | |

Intersect[line, yAxis] | |

Intersect | |

Slope | |

Show / Hide Object | |

Move |

### Construction Steps

1. Enter: line: y = 0.8 x + 3.2

__Task 1: __Move the line in the algebra
view using the arrow keys. Which parameter are you able to change in this way?

__Task 2:__ Move line in the Graphics View with the mouse. Which transformation can you apply to the line in this way?

2. Delete the line. Create sliders m and b using the default settings of sliders.

3. Enter line: y = m x + b.**Hint:**Don’t forget to use an asterisk or space to indicate multiplication!

4. __Task 3:__ Write down directions for your students that guide them through examining the influence of the equation’s parameters on the line by using the sliders. These directions could be provided on paper along with the GeoGebra file.

**Hint:**Use tool Intersect or command

*Intersect[line, yAxis]*.

6. Create a point at the origin and draw a segment between these two points.

7. Use tool Slope and create the slope (triangle) of the line.

8. Hide unnecessary objects and modify the appearance of the other ones.

## Introducing Derivatives – The Slope Function

In this activity you are going to use the following tools, algebraic input, and commands. Make sure you know how to use them before you begin with the actual construction.

f(x) = x^2/2 + 1 | |

Point | |

Tangent | |

slope = Slope[t] | |

S = (x(A), slope) | |

Segment | |

Move |

### Construction Steps

1. Enter the polynomial: f(x) = x^2/2 + 1

2. Create new point A on function f.**Hint:**Move point A to check if it is really restricted to the function graph.

3. Create tangent t to function f through point A.

4. Create the slope of tangent t using: *slope = Slope[t]*

*S = (x(A), slope)*

**Hint:**x(A) gives you the x-coordinate of point A.

6. Connect points A and S using a segment.

7. __Task:__ Move point A along the function graph and make a conjecture about the shape of its path, which corresponds to the slope function.

**Hint:**Right click point S (MacOS: Ctrl + click) and select

*Trace on*.

9. Find the equation of the resulting slope function. Enter the function and move point A. If it is correct the trace of point S will match the graph.

10. Change the equation of the initial polynomial f to produce a new problem.

## Creating a "Function Domino" Game

In this activity you are going to practice exporting function graphs to the clipboard and inserting them into a word processing document in order to create cards for a "Function Domino" game. Make sure you know how to enter different types of functions before you begin with this activity.

### Construction Steps

1. Enter an arbitrary function.**Example:**e(x) = exp(x)

2. Move the function graph into the upper left corner of the Graphics View and adjust the size of the GeoGebra window.

3. Export the Graphics View to the clipboard (menu *File – Export – Graphics View to Clipboard*).

4. Open a new word processing document.

5. Create a table (menu *Insert – Table*…) with two columns and several rows.

6. Place the cursor in one of the table cells. Insert the function graph from the clipboard (menu *Home – Paste* or key combination Ctrl + V).

7. Adjust the size of the picture if necessary (double click the picture to open the *Format* tab and click on *Size*).

**Hint:**You might want to use an equation editor.

**Hint:**Make sure to put the equation and graph of each function on different domino cards.

## Creating a "Geometric Figures Memory" Game

In this activity you are going to practice exporting function graphs to the clipboard and inserting them into a word processing document in order to create cards for a memory game with geometric figures. Make sure you know how to construct different geometric figures (e.g. quadrilaterals, triangles) before you begin with this activity.

### Construction Steps

1. Create a geometric figure in GeoGebra (e.g. isosceles triangle).

2. Use the Properties Dialog to enhance your construction.

3. Move the figure into the upper left corner of the Graphics View and adjust the size of the GeoGebra window.

4. Export the Graphics View to the clipboard (menu *File – Export – Graphics View to Clipboard*).

5. Open a new word processing document.

6. Create a table (*Insert – Table*…) with three columns and several rows.

**Hint:**Place the cursor in the table and open the

*Table Properties*dialog with a right click. On tab

*Row*specify the row height. On tab

*Column*enter the preferred width. On tab

*Cell*set the vertical alignment to

*Center*. Click

*OK*when you are done.

8. Place the cursor in one of the table cells. Insert the picture from the clipboard (menu *File – Paste* or key combination Ctrl + V).

9. Adjust the size of the picture if necessary (double click the picture to open the *Format Picture* tab, click on *Size* and specify the size).

10. Enter the name of the geometric shape into another cell of the table.

11. Repeat steps 1 through 10 with different geometric figures (e.g. circle, quadrilaterals, triangles).