Chapter 22 Writing your own conjectures task

Exercise 22.1 For this exercise, I want you to look back over all the previous conjectures we’ve proved and disproved and use your findings to write some new conjectures.

Here are the rules:

Each student should write at least two conjectures.

• The conjectures should be true.

• The conjectures should be provable using work which you and your classmates have previously done, and using the methods we’ve already met: direct proof and exhaustion.

• DON’T rush - take your time to write these conjectures.

• Post your conjectures onto the padlet.
  Note: Post each conjecture whenever it’s ready to go!

• If you still have time remaining in class OR as homework, try to solve some of your classmates’ conjectures. Post your proof underneath their post.
  Note: DON’T solve too many conjectures - leave some for other people to solve!!

• If there are no unsolved conjectures left on the padlet, try solving one of the conjectures already solved. Maybe you can solve it in a different way??

• If you think your classmate has written a conjecture which is actually false, tell them by posting a disproof (or counterexample) under their post.

• If your conjecture is disproved by a classmate, can you modify it to make it true?

Good luck!