brain drain! a math-y puzzle DRAFT DRAFT DRAFT brain drain! a math-y puzzle Institute for Advanced Study/Park City Math Institute Summer 2010 Secondary School Teachers Program/Lesson Study

1. If you have a rectangle on your paper… …then sketch a square around it.

2. If you have a triangle on your paper… …then sketch a congruent triangle approximately three inches to the right.

3. If you do not have a triangle on your paper… …then sketch an equilateral triangle above the largest quadrilateral.

4. If you have exactly two triangles on your paper… …then sketch a square using the top vertices of the two triangles as the base of the square.

5. If you have a square on your paper… …then sketch a circle in the upper right hand corner of your paper.

6. If you don't have two triangles on your paper and do not have a circle on your paper… …then sketch a flower in the lower right hand corner of your paper.

7. If you have only one triangle on your paper… …then sketch a thin rectangle sticking out of the left hand side of the triangle.

8. If you have a flower on your paper… …then sketch two more flowers next to it.

9. If you have two triangles and one square on your paper… …then sketch a smaller square on top of the square.

10. If you have a single circle and no flowers on your paper… …then sketch a smiley face in the circle.

11. If you do not have a flower and you have an even number of squares and triangles… …then sketch a sad face in the smaller square.

12. If you don't have any flowers on your paper… …then sketch five flowers on the right side of your paper, slightly above the line that was on your paper when you received it.

13. If you don't have a smiley face on your paper… …then don't sign your name on the bottom left corner of your paper.

14. If you have more than one flower on your paper… …then don't sketch three more flowers.

15. If you have a circle in a corner of your paper and an even number of squares and an even number of triangles… …then sketch two thin rectangles coming out of the left and right sides of the largest square.

16. If you don't have an even number of flowers… …then sketch two stick figures on the left side of your paper, slightly above the line that was on your paper when you received it.

17. If you don't have an odd number of flowers… …then sketch three stick figures on the left side of your paper.

18. If you have more than one stick figure… …then sign your name on the bottom right corner of your paper.

Table and Poster Paper -Work in pairs to complete the table Table and Poster Paper -Work in pairs to complete the table. - Make sure to have the statements written on the poster paper as well!

Example: Every person who has a driver’s license must be at least 16 years old.

at least 16 years old have a driver’s license

people people at least 16 years old Which is right? Why? have a driver’s license Which is right? Why? people have a driver’s license at least 16 years old

people at least 16 years old have a driver’s license

people Alex at least 16 years old have a driver’s license Jamie Maria

Which one of these goes inside the other, and why? hint: come up with examples of things in each circle… not at least 16 years old not having a driver’s license

people not having a driver’s license not at least 16 years old

people not having a driver’s license not at least 16 years old John Lucy Cheng

Use your diagram to decide the truth or falsity with your partner… Use your diagram to decide the truth or falsity of the inverse and contrapositive.

closed five-sided figures pentagons

closed five-sided figures shapes closed five-sided figures pentagons