Course Guide - USAID Teacher Education Project

a) Begin by reminding students how last week they used an addition chart todecompose the number 12 into (5 + 7), (6 + 6), etc. and how they then used that samechart to show subtraction (12 - 5 = 7, 12 - 6 = 6, etc.). Remind students that just asthere is an inverse relationship between addition and subtraction, where one operation"undoes" the other, there is an inverse relationship for the operations of division andmultiplication: one operation "undoes" the other as in:3 x 6 = 186 x 3 = 1818 ÷ 3 = 618 ÷ 6 = 3b) Briefly review the array and area models for multiplication, noting how thesemodels could be used for division: beginning with the product, and then finding thefactors of that product.c) Have students consider how the number line model for multiplication may or maynot model division of whole numbers by using the equations 18 ÷3 and 19 ÷ 3.d) As the main class activity, introduce the model of sharing or distribution byhaving students, in groups of 3, use counters to solve the following equations bydistributing the counters to each other:18 ÷ 3 =17 ÷ 3 =19 ÷ 3 =In the class summary have students note that in the case of 18 when dividing by 3,the distribution created equal shares. For 17, the distribution could be termed either"2 more" or "1 less” of equal shares. 19 allows for “1 more” than equal shares. Havestudents describe what is happening with the remainder in each case.e) As students work with the sharing or distribution model, have them explain how itis different from products in the array and area models that were based on wholenumber factors.f) Introduce different ways of interpreting the remainder by using story problemssuch as:• Suppose our class had 26 students and one instructor. We want to visit aschool 20 km from here. Several of you have access to cars and offered todrive. Each car can hold 6 people. How many cars and drivers do we need?Students should note that although 27 ÷ 6 equals 4.5, it can also be thought ofas 4 with a remainder of 3. However, in practical terms, there cannot be half acar. Or 4 cars with 3 people remaining behind. In this context, the remainderneeds to increase by one more than the whole number quotient. Thus whilethe purely mathematical answer to the problem is 4.5, the realistic answer is:you need 5 cars.• Suppose I have 9 pencils to share amongst 5 students. How many pencils doeseach student get?