1. Exploration 3.15 Make up a story problem for 15 ÷ 3. Share them with your group. Compare the problems and discuss whether they are similar or if there are different types. Choose two of the problems. Then pair up and write each of the two problems on a white board.

2. What’s wrong? 49 12 49 + 1 is 50, so do 50 12, which is 600, and then subtract 1, and get 599.

3. Find the following products in Base 8: 25 8 57 8 ×13 8 ×64 8

4. Multiplication and Division In mathematics, we say that addition and subtraction are inverse operations. This is why there are related facts: 3 + 4 = 7 7 - 4 = 3 7 - 3 = 4 In this same way, multiplication and division are inverse operations: 3 4 = 12 12 ÷ 4 = 3 12 ÷ 3 = 4

5. Different Word Problems In any division problem: Dividend ÷ Divisor = Quotient. In word problems, we usually have a rate as part of the problem (apples per person). Where the rate appears determines the type of word problem.

6. Models for Division Carlos has 24 apples. If it takes 4 apples per pie, how many pies can he make? This is repeated subtraction. Carlos has 24 apples. If he wants to make 4 pies, how many apples will be in each pie? This is partitioning.

7. Missing Factor Model of Division 28 ÷ 4 = Can be thought of as 4 X ? = 28

8. Terminology b ÷ n = a iff a∙n = b b is the dividend n is the divisor a is the quotient a and n are the factors of b and b is a multiple of a and n.

9. The number line! We use the number line with multiplication when we think about continuous models, or multiplication as repeated addition. We can use the number line here to show division as repeated subtraction.

10. No calculators! Do the following division problem 159 ÷ 13

11. Division Can you divide without using the Long Division Algorithm? Hint: the answer is YES! Let’s see what students do.

12. Strategies Amelinda used repeated subtraction. Alosha added up, which is a variation of repeated subtraction. Elaine also added up but she used a “landmark” number to help her find the answer faster. Thomas used partitioning. He also used a “landmark” or “friendly” number to help him to the quotient.

13. What Properties Hold for Division?

15. Dividing by Zero