B2.7 Represent and solve problems involving the division of three-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods, while expressing any remainder appropriately.
Activity 1: Order time!
Ask students to prepare an order for school supplies for future Grade 5 students. To do this, they should determine the number of pencils, erasers and rulers to order, knowing that there are 8 pencils per package, 15 erasers per package and 9 rulers per package.
To complete this task, students should estimate how many students there will be next year in Grade 5 and how many pencils, erasers, and rulers each should receive.
Note: In this activity, students should take the remainder into account. It is important that the teacher not specify the number of future Grade 5 students or the number of items each should receive. Estimating each of these quantities is part of the problem-solving process. Obviously, the answers will vary depending on the estimations used.
Source: Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, p. 209.
Activity 2: What is Unknown?
Distribute a copy of Appendix 4.2 (What is Unknown?) to each team.
Ask them to read the problems and, without solving them, to indicate for each one whether it is the size of the groups or the number of groups that is unknown.
Ask them to justify their answer and to write a new problem for each of the two types of situations.
Note: The purpose of this activity is not to solve problems, but rather to recognize the 2 meanings of division:
- The division in which the number of groups is unknown, namely the equal-grouping (or quotative) type;
- The division in which the size of the groups is unknown, namely the equal-sharing (or partitive) type.
Source: Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, p. 176-177.
Activity 3: What's Left?
Distribute a copy of Appendix 4.3 (What's Left?) to each team and ask them to solve the problems with the remainder in mind according to the context.
Note: The problems can be modified with larger numbers (divisions of three-digit numbers by two-digit numbers).
Once the problems have been solved, lead a mathematical exchange in which students can justify their answers. This discussion should highlight different ways of taking the remainder into account in an equal-sharing situation.
Note: In each problem, we are talking about dividing 26 into 4 groups, which results in a remainder of 2. Given the context of the problem, here is how to account for the remainder in each case.
Problem 1: The remainder is divided among the teams. (There will be 6 students in 2 of the teams and 7 students in the other 2)
Problem 2: The remainder increases the quotient by 1. (It will take 7 drivers to transport the students)
Problem 3: The remainder is ignored. (Each student must collect 6 potatoes)
Problem 4: The remainder is expressed as a fraction. (Each team will receive \(6 \frac{2}{4}\) licorice chews or \(6 \frac{1}{2}\) licorice chews.)
Problem 5 : The remainder is the answer. (2 jars will not be on the table.)
Problem 6 : The remainder is expressed as a decimal number. (There are 6.5 m between each terminal.)
Source: Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, p. 177.