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*Don’t forget to sign in!*

*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: Identify the division model Identify the rate (units!)

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*Don’t forget to sign in!*

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  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: • Identify the division model • Identify the rate (units!) • 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, then30 ÷ 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

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