1. Ready for a fold?

2. Carefully observe the folded sheet. How many folds do you see?

3. How could you describe the differences between the two different folds?

4. This fold runs vertically, (up and down).
This is a “mountain” fold.
It looks like you fold to the back
Fold 1.

5. This fold runs diagonally from top left to bottom right.
This is a “valley” fold. (It looks like you fold forward)
Fold 2.

6. Diagonal actually is used to describe a line segment that connects interior angles of a polygon. In this case the “diagonal” fold line does follow the diagonal of the square.

7. We like to name a line that sits on a slant as diagonal
but it might be more mathematically correct to call it
an oblique line....
Something to think about and maybe investigate?

8. Now imagine folding the paper along the fold lines.
If you did, what shape would the paper turn into.
Draw the shape it will turn into.

9. Getting started can be tough.
Try gesturing in the air to pretend you are folding, or start by drawing the paper with its fold lines....

10. Explain and compare with a partner......
Make changes if you think you need to

11. These are some examples students have drawn
These are some examples students have drawn. Can you explain what each person is “thinking”.

12. Go ahead and fold to see if your visualization was accurate.....

13. When I look at the picture, I suspect that folding the top right vertex down to meet the bottom left vertex is the way to start.....
Do you see why?

14. If you fold the triangle first, you can easily see where the vertical fold will be. If you fold the vertical fold first, and estimate poorly, the triangles do not match up.

15. Ready for a fold?

16. Carefully observe the folded sheet. How many folds do you see?

17. How could you describe the differences between the two different folds?

18. They are both mountain folds. One is longer than the other
They are both mountain folds. One is longer than the other. They both are on a “slant”. Neither one is a diagonal (do not go corner to corner). One starts at the bottom left vertex. The two folds meet at the top but not the middle of the top of the page.

19. This is a mountain fold.
It starts at the bottom left vertex and runs up to the top right edge but not the right corner (vertex) It stops about three quarters of the way to the right.
Fold 1.

20. This is also a mountain fold
This is also a mountain fold. It slants away from the first fold but starts at the top of the page where the first fold ends.
It starts at the top right where the first fold ended and slants obliquely or diagonally down to the right. It stop about one quarter of the way down the side or edge.
Fold 2.

21. Now imagine folding the paper along the fold lines.
If you did, what shape would the paper turn into.
Draw the shape it will turn into.

22. Getting started can be tough.
Try gesturing in the air to pretend you are folding, or start by drawing the paper with its fold lines....

23. Explain and compare with a partner......
Make changes if you think you need to

24. Go ahead and fold to see if your visualization was accurate.....

25. Explain the sequence of folds. Where did you start. Then what
Explain the sequence of folds. Where did you start? Then what.... Be specific...

26. Ready for a fold?

27. Carefully observe the folded sheet. How many folds do you see?

28. How could you describe the differences between the two different folds?

29. They are both mountain folds. One is longer than the other
They are both mountain folds. One is longer than the other. They both are on a “slant”. Neither one is a diagonal (do not go corner to corner).

30. One starts at the bottom left vertex
One starts at the bottom left vertex. The other starts at the bottom right vertex. The two folds meet at the top but not the middle of the top of the page.

31. Now imagine folding the paper along the fold lines.
If you did, what shape would the paper turn into.
Draw the shape it will turn into.

32. Getting started can be tough.
Try gesturing in the air to pretend you are folding, or start by drawing the paper with its fold lines....

33. Explain and compare with a partner......
Make changes if you think you need to

34. Go ahead and fold to see if your visualization was accurate.....

35. Explain the sequence of folds. Where did you start. Then what
Explain the sequence of folds. Where did you start? Then what.... Be specific...

36. Ready for a fold?

37. Carefully observe the folded sheet. How many folds do you see?

38. How could you describe the differences between the different folds?

39. None of the folds crosses a diagonal.
There seems to be 3 mountain folds and one valley.
The folds are different lengths.
One starts at the bottom left vertex and one at the bottom right vertex.

40. Are there just 2 folds? Three different folds?
Or four different folds?

41. Try using your hands to act out how you would fold it
Try using your hands to act out how you would fold it.... Work with a partner

42. If you are completely stuck, try drawing the sheet below
If you are completely stuck, try drawing the sheet below. Be careful to put the folds in the right places.

43. Show someone your drawing and see if they agree that it is the same as mine. Then try folding the paper the same way.

44. Look carefully. We found a way to do it with 2 folds but we had to “play” and think a lot.
(Half an hour of folding with 20 of us)

45. You have completed 4 Green Paper folds.
Time to make your own.
Take a picture and build a set of questions.

46. Mix and Cheng, 2012, gave students tasks that practiced spatial reasoning skills.
The tasks had nothing to do with numbers.
Paper folding is one such task.

47. After several weeks, they checked the students’ arithmetic skills and found there was a very clear improvement.
especially on missing number questions like ? = 8

48. Paper folding improves your ability to reason and think
Paper folding improves your ability to reason and think. It increases achievement in both mathematics and science.
It makes you smarter.

49. Paper-folding activities in mathematics address some of the goals for teaching and learning mathematics in the 21st century as identified by English (2002):
mathematical modeling
visualizing
algebraic/relational thinking
problem-solving

50. https://diypuzzles. wordpress