1. VES Mathematics PLC Session 1 9/18/12

2. Video

3. What are the implications?

4. Student Behaviors The Problem The Problem Teacher Behaviors Problem Solving

5. Student Behaviors The Problem The Problem Teacher Behaviors Problem Solving What makes a good problem?

6. A “Fermi Question” is a question in physics or mathematics which seeks a fast rough estimate of quantity, which is either difficult or impossible to measure directly.

7. Student Behaviors The Problem The Problem Teacher Behaviors Problem Solving How did the problem encourage or elicit these behaviors? What behaviors did you exhibit that helped to support problem solving?

8. Let’s take a closer look at the problems we pose to our students in the mathematics classroom

9. Robert has two coins in his pocket that equal 35¢. What are the coins?

10. Robert has two coins. Neither coin is a silver dollar. How much money might Robert have in his pocket?

11. If you spend $1.85 and pay with a $10.00 bill, you get $8.15 in change. Notice that the digits in the change are the same as the digits in what you spent. There are four other amounts you could spend so that the change has the same digits. Find them.

13. Which is worth more... 1. A million nickels OR 2. A mile high stack of nickels?

14. Money, Money, Show Me the Money Andy has a stack of pennies that is 1-inch tall. Alisha has a row of pennies that is 1-foot long. Who has more pennies-Andy or Alisha? Predict who you think has more money. How can you represent your solution? Explain your reasoning. What about nickels? Dimes? Quarters?

15. Coins Stack 1-inch tall Row 1-foot long Pennies17¢16¢ Nickels65¢70¢ Dimes$2.00$1.70