Course Guide - USAID Teacher Education Project

Unit 1 Number and OperationsWeek 2, Session 3: Division of Whole Numbers1. What are the important concepts?a) Multiplication and Division are inverse operations. They “undo” the action ofeach other in the same way that addition “undoes” the action of subtraction (and viceversa).b) Because multiplication and division are inverse operations, there are “factfamilies” of numbers in relationship with each other (such as 3, 6, and 18) that giverise to the following four equations:3 x 6 = 186 x 3 = 1818 ÷ 3 = 618 ÷ 6 = 3This relationship between multiplication and division parallels the relationship foraddition and subtraction (as in "fact family" of 5, 7, and 12 discussed last week):5 + 7 = 127 + 5 = 1212 - 5 = 712 - 7 = 5c) Multiplication (like addition) is commutative (6 x 3 = 3 x 6). However division,like subtraction, is not commutative (18 ÷ 3 ≠ 3 ÷ 18).d) Models for Division:• The array and area models that were used to visualize multiplication also canbe used to visualize division. When using these two models for division,however, one needs to notice the whole (the product) first, and then notice thefactors (the labels for the rows and columns).• When multiplying, this array of 6 coins is product of factors: 3 (columns) x 2(rows). But this same array also can be interpreted as 6 coins (the totalnumber ofcoins) ÷ 3 (columns) = 2 (rows).