1. *Don’t forget to sign in!* Take a story problem (not your own) and on a piece of paper (to turn in) do the following: 1.Identify the division model 2.Identify the rate (units!) 3.Rewrite the problem so that it illustrates the other model (note this can be done two ways: you can illustrate the same division problem or, if it makes more sense, illustrate a related division problem)

2. Agenda Zero: The dangerous idea returns Estimation and division (see Estimating Quotients on page 2 of your Division Worksheet) Children’s Thinking Activity 3

3. To consider: If I have 30 party favors to put into 6 bags, how many party favors should I put in each bag? If I have 0 party favors to put into 6 bags, how many party favors should I put in each bag? If I have 30 party favors to put into 0 bags, how many party favors should I put in each bag?

4. Zero is special Let’s look at related word problems. If I have 30 party favors to put into 6 bags, how many party favors should I put in each bag? If I have 0 party favors to put into 6 bags, how many party favors should I put in each bag?

5. Zero is special Let’s look at related word problems. If I have 30 party favors to put into 6 bags, how many party favors should I put in each bag? If I have 30 party favors to put into 0 bags, how many party favors should I put in each bag?

6. Zero is Special Because the first related problem is silly, but still makes sense, we can think about a solution: 0 party favors per bag. However, the second related problem is silly and makes no sense--if I have no bags, the rate favors per bag is meaningless. For this reason, we say that division by 0 is undefined.

7. 1 and 0 are special We know that the product of any number and 1 yields the original number. This is known as the multiplicative identity. It is the only number for which this is true! We know that the sum of any number and 0 yields the original number. This is known as the additive identity. It is the only number for which this is true!

8. Additionally… The product of 0 and any number is always 0. This is always true, and it is only true for 0. We call this the multiplication property of zero. Since multiplication and division are inverses, however, this property of 0 creates some difficulties.

9. Zero is special Another way to think about it: If 30 ÷ 6 = 5, then 30 ÷ 5 = 6; 5 6 = 30; 6 5 = 30. If 30 ÷ 0 = some value, call it V, then 30 ÷ V = 0; V 0 = 30; 0 V = 30. But related facts are supposed to show that multiplication and division are inverses.

10. Estimating Quotients

11. Children’s Thinking Activity 3

12. Homework Children’s thinking Activity Finish estimation section of Division Worksheet