2. Start with a 8.5” by 11” sheet of paper. Fold one corner of the paper so that the top of the paper lines up along one side. TOP (Repeat this procedure for 7 more sheets of paper.)

3. Cut off the rectangle along the bottom of the page.

4. Fold the square in half vertically and horizontally. Cut on the horizontal and vertical folds. Fold and cut each small square on the diagonal.

5. Each sheet will make 8 congruent triangles. You should have 64 triangles in 2 colors.

6. For this introductory challenge, you will use 2 triangles, one of each color. Just put the others aside…

7. Rules: Sides must be the same size. Sides must match exactly. Glue your shapes to a paper. Your task: Create unique shapes using 2 triangles.

8. Shape check: How can you check to see if a shape is a new, unique shape? Name each shape.

10. Same rules: Sides must be the same size. Sides must match exactly. Your task: Create unique shapes using 4 triangles. Glue your shapes to a paper.

17. Each partner selects a different shape made of 4 triangles. Make two columns: “Same” and “Different.”

19. You will need 4 triangles (2 of each color). You will also need the TRIANGLE you made using 4 triangles.

20. How many different color patterns did our class create? Are there any color patterns that we missed? How do we know when we have found all the color patterns?

23. Without looking at your triangle shapes, which of these do you think will have the greatest perimeter? The triangle One of the quadrilaterals One of the pentagons One of the hexagons

24. If the longest side of each triangle measures 6 units and the shorter sides measure 4 units, determine the perimeter of each shape.

25. Which shapes have the smallest perimeters?

26. Which shapes have the greatest perimeters? 32

27. 28 What is the perimeter of these shapes?

28. How can shapes with congruent areas have non-congruent perimeters? 32

29. If the area of this shape is 1 sq. unit, what is the area of one triangle?

30. 32 If the area of each triangle is 8 sq. units, what is the area of this shape?

31. If the area of this shape is 12 sq. units, what is the area shaded white?

32. 32 If the combined area of the two pink triangles is 13 sq. units, what is the area of this shape?