Musical Chairs! Change your table groups. One person may remain at each table. Everyone else move to another table— each going to a different new table. All tables should have groups that have no more than one person from a previous group. Introduce yourselves to your new group members.

Children’s Thinking Videos In general, watch the videos, and try to notice: a) what is the child doing? b) mathematically, what is going on? c) mathematically, why is it correct or incorrect.

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.

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.

Models for Division Carlos has 24 apples. If each pie needs 4 apples, how many pies can he make? This is repeated subtraction. We start with the total number of items and take some fixed number of items away repeatedly until we can’t do it anymore. The answer is the total number of groups of items Carlos has 24 apples. If he wants to make 4 pies, how many apples will be in each pie? This is partitioning. We start with the number of groups and distribute the items equally in the groups until we can’t do it anymore. The answer is the number of items in each group.

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

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.

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

The number line! We use the number line with multiplication when we think about continuous models, or multiplication as repeated addition. What model of subtraction can be represented on by a number line?

No calculators! Do the following division problem 159 ÷ 13

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

Strategies for division Amelinda

Strategies for division Alosha

Strategies for division Elaine

Strategies for division Thomas

Strategies for division 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.

What Properties Hold for Division?

Dividing by Zero