Course Guide - USAID Teacher Education Project

Unit 1 Number and OperationsWeek 5, Session 3: Multiplication and Division of Integers, Reflection on PracticeThis last session of this Number and Operations unit will be a time for students to considerthe mathematical processes that were used during the unit:• Modelling and multiple representations• Mathematical communication• Problem solving• Connections both to real life situations and to other areas of mathematics (algebra,geometry, and Information handling)Please allow time after the mathematics content of this session so that students can completethe reflection pages and have a whole group discussion about their thoughts.23. Maths Concepts to be studied• While physical and visual models were helpful when learning about the addition andsubtraction of integers, they are less helpful when dealing with integer multiplicationand division. To introduce integer multiplication and division, have students build onwhat they already have learned about addition and subtraction of integers,multiplication and division of whole numbers, pattern continuation, and the overallconsistency of our number system. Thus, this session will be somewhat more abstractthan the prior session.• Models for multiplication of integers:Although we discussed earlier that multiplication was more than repeated addition,the repeated addition model is helpful in understanding integer multiplication. Thismay be shown by:a) Repeated leaps of the same size on a number lineb) Laying out 3 rows of -4 (red) chips:c) Repeated addition equations such as:3 x (-4) = (-4) + (-4) + (-4) = -12Notice that the sign of the product is negative, as it would be if we started at 0 andtook 3 leaps of (-4) in the negative direction.Since multiplication is commutative, the expression (-3) x 4 can be rewritten as 4 x (-3), and then solved in the same manner as above. Again, the sign of the product isnegative.After doing several of these it should be obvious one can simply multiply the twonumbers and if one is positive and the other negative, the sign of the product isnegative.