Course Guide - USAID Teacher Education Project

12 ÷ 3 = 4we also can create fact families for integers:(-3) x 4 = - 12(-3) x (-4) = 12-12 ÷ (-3) = 412 ÷ (-3) = - 424. How children think about these concepts• All the concerns noted in this week’s Session 1 still apply to the multiplication anddivision of integers.• Youngsters become confused by the apparent contradiction that when you add twonegative numbers the result is negative. But when you multiply two negativenumbers the result is positive.• Even if youngsters can apply the rules for operations with signed numbers, it is noguarantee they understand what those rules mean.25. What is essential to know or do (in class)• Introduce models for multiplication of integers, beginning with visuals such as thenumber line and 2-colour counters, then moving to patterns• Introduce models for division of integers, continuing the emphasis on patterns and theconsistency of our number system.a. Relate each of the above to children’s thinking.b. Have students reflect in writing and then in a whole class discussion on their learningduring Unit 1.26. Class Activitiesa. Begin by asking what students recall about multiplication and division of integers andby what methods they learned them.b. Introduce integer multiplication by reminding students how they could modelnegative numbers with 2-colour counters. Ask them how they might multiply 4 x (-3)by using the 2-colour counters. How might they model the same 4 x (-3) by using anumber line?c. Remind students that although multiplication is more than repeated addition, repeatedaddition can help them understand integer multiplication. Ask them how they wouldmultiply 4 x (-3) by using the repeated addition method. Then ask how we couldmultiply (-3) by 4, noting the commutative property of multiplication if no onesuggests it.d. As you begin to introduce the multiplication of two negative numbers, ask studentshow they might model this. Note where there may be misconceptions. Also noteanyone who suggests using patterns and ask for elaboration. If necessary, recreate thepattern list above on the board and ask what is happening to the products. Emphasizethat our number system is consistent and that because of opposites, the product of (-3) x (-1) cannot be equal to the product of (-3) x (+ 1).e. Ask if anyone can share a real life example of multiplication of two negative integers.If not, offer the idea of past time (if modelled on a time line); past time can be