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GeoGebraGeoGebra Classroom

Whole Shapes

:: Making a WHOLE SHAPE with shape pieces.

We are going to make whole shapes from shape pieces. Click on a shape that you want to work with. Click in the space below. Click other places to create more of this shape. To move the shapes, click on the arrow on the top left, then click on the shape. You can click and drag. Or you can click on the small circle that appears and drag to rotate. Now create your own WHOLE SHAPE from ONE kind of shape pieces. • The shape for your whole shape must all be touching. • You much use MORE than TWO shape pieces to make your whole shape. Use the pen to write HOW MANY shape pieces you needed to create your whole shape.
If you want to, you can come up with a name for your whole shape.

:: Make two of your whole shapes

Now make TWO of your WHOLE SHAPES. When you are done, use the pen to write how many shape pieces you needed to create two of your whole shapes.
Without making them, can you figure out how many shape pieces would be in a THREE whole shapes? How would you do this? What if you wanted the number of shape pieces in FOUR whole shapes? How would you do this? Whacky: What if you wanted the number of shape pieces in a thousand of your whole shapes? Any guesses what that might be?

:: How many of your whole shapes can you create with SEVEN shape pieces?

If you have SEVEN shape pieces, show how many of your whole shapes can you create? Are there any left over? Write how many whole shapes. Then write the letter R and the number left over (if there are none left over, write R next to a 0).
If each of you whole shapes had more shape pieces, how would this change the number of whole shapes you could create with seven pieces? What might happen to the number of pieces left over? If each of you whole shapes had fewer shape pieces, how would this change the number of whole shapes you could create with seven pieces? What might happen to the number of pieces left over?

:: How many whole shapes using NINE pieces

If you have NINE shape pieces, show how many of your whole shapes can you create? Are there any left over? Write how many whole shapes. Then write the letter R and the number left over (if there are none left over, write R next to a 0).

Where to go from here...

How many shape pieces could you have so that there would be only ONE shape piece left over? How many shape pieces could you have so that there would be TWO shape piece left over?
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