brain drain!a math-y puzzle

DRAFT DRAFT DRAFT

Institute for Advanced Study/Park City Math Institute Summer 2010Secondary 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.

- 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

peopleat least 16 years old

have a driver’s license

peoplehave a driver’s license

at least 16 years old

Which is right? Why?

people

at least 16 years old

have a driver’s license

people

at least 16 years old

have a driver’s license

Alex

Jamie Maria

not at least 16 years old

not having a driver’s license

Which one of these goes inside the other, and why?hint: come up with examples of things in each circle…

people

not having a driver’s license

not at least16 years old

people

not having a driver’s license

not at least16 years old

John

Cheng

Lucy

Use your diagram to decide the truth or falsity

of the inverse and contrapositive.

with your partner…

closed five-sided figures

pentagons

shapes

closed five-sided figures

pentagons