Activity 2: Draw Stick Figures

In this activity, your group will create a drawing like the one below by creating points, lines, segments and circles. You will drag these figures to see how they are connected. This will prepare you for the geometric constructions in the rest of the activities.

Preparations

Open the GeoGebra tab and identify the parts listed in this figure. You will be using this GeoGebra tab in the rest of the activities.

The GeoGebra tab for this activity should have a special tool bar like this:

If the GeoGebra tab does not have this tool bar, then load the Perspective stick_figure from the “Perspectives” menu in the GeoGebra menu bar.

In the View menu of the menu bar, select “Labels” and check the option “No labels”. Otherwise your picture will have lots of letters labeling all the points.

Take turns

This is a multi-user version of GeoGebra. What you see in the GeoGebra tab is the same as what everyone in the VMT chat room with you also sees in their GeoGebra tab (except that they may have their view options set differently, like having the tab opened wider or smaller than you do).

Two people cannot be creating and manipulating objects at the same time in GeoGebra, so you have to take turns. While someone else is constructing or dragging, you can be watching and chatting. Use the chat to let people know when you want to “take control” of the GeoGebra construction. Use the chat to tell people what you notice and what you are wondering about the construction.

Decide in the chat who will go first. That person should press the “Take Control” button and draw a figure. Then release control and let the others draw their figures.

Before you start to draw your figure, say in the chat what you plan to do. After you release control, say in the chat what you discovered if anything surprised you. You can also ask other people in your group questions about what they drew and how they did it.

Drawing tools in GeoGebra

Here is how to use the tool buttons – in the order they appear in the tool bar:

Use the move tool to select a point or segment or circle and drag it to a new position. Everyone will see an object being dragged.

Use the point tool to create some points. Each place you click with the point tool will leave a point. These points will appear in the GeoGebra tab of everyone in your chat room.

Use the line tool to create lines with no endpoints. The line has to go through two points. You can either select two existing points or click with the line tool to create the points while you are constructing the line. Use the line tool to create ground or horizon for your picture.

Use the segment tool to connect two points with a line segment. You can also create points as you click for the ends of the segment. Use the segment tool to create stick figures. See what happens when two segments use the same point for one of their endpoints.

Use the circle tool to draw a circle. You must click to place a point at the center and then click again for a point on the perimeter of the circle. Use the circle tool to create a sun, flowers or a stick-person’s head.

Use the move graphic tool to rearrange your view of the construction area.

To delete a point, either use the delete tool or select the object and press the delete button on your keyboard. You can also use the undo button at the far right of the tool bar to remove the last item. Before you delete something that someone else created, be sure to ask in the chat if everyone agrees that it should be deleted.

You can use the zoom in and zoom out tools to change the scale of your view of the construction area. You can also use two-finger gestures for zooming. Changing your view will not affect what others see in their views.

Use the un-do tool to return to the state before the last construction action. Use the re-do tool to restore an action that was un-done. Remember, do not un-do someone else’s action without their agreement in the chat.

Drew picture

Now draw a picture in the GeoGebra tab using these tools. Take turns. Discuss what you are doing as a group. Include points, lines, segments and circles. Connect some of the segments with shared points to form stick figures.

The “drag test”

Select a part of a stick figure with the move tool . Drag the object by holding down the move tool on the object and moving it. Observe how other parts move with the selected object. That is because the other parts are “dependent” on the part you are dragging. For instance, a segment depends on its end-points; when the points move, the segment must also move. If two segments both depend on the same point, then they will always move together; if you drag one of the two segments, it will drag the common end-point, which will drag the other segment. Dragging is an important way to check that parts have the correct connections or “dependencies” on other parts. GeoGebra lets you construct objects that have the dependencies that are important in geometry and in other branches of mathematics.

Explore!

Pose questions in chat about how the figures are connected. State what you think will happen if certain objects are dragged. Then ask to have control to try it out. Take control and drag part of a figure. Release control and chat about what happened. Can you make a stick-person dance?

Hint

If two elements share a point – for instance, if the segment for a stick-man’s body starts at a point on his head’s perimeter, then we say there is a dependency between the segment and the circle. That is, the position of the segment depends on the position of the circle, and when you move one, the other also moves. Geometry is all about such dependencies. A dynamic-math environment lets you see how the dependencies work and lets you explore them. Check out these videos of dependencies: http://www.youtube.com/watch?v=Oyj64QnZIe4&NR=1 and http://www.youtube.com/watch?v=-GgOn66knqA&NR=1.

Draw two triangles

One person should draw 3 points and then connect them with three segments to form an equilateral triangle. (You can use the move graphic tool to make room for the triangle.)

Another person should draw 3 points and then connect them with three segments to form a right triangle.

Other people in your group should move these triangles around.

What do you notice about them? If you change the lengths of the sides are the triangles still equilateral or right triangles?

Discussion

What is the difference between a drawing (like in Activity 1) and a construction (like a connected stick-man in this activity)?

What is the “drag test” and why is it important?

Why is it important to construct figures in interactive geometry software instead of just drawing them?

What do we have to know about a geometric figure before we are able to construct it using dynamic-mathematics software?