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 in Grade 5 next year 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: translated from Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 1, Nombres naturels, p. 209.
Activity 2: What Remains?
Distribute a copy of Appendix 4.3 (What Remains?) to each team and ask them to solve the problems, keeping in mind the context as they decide how to deal with any remainders. In each problem, 26 is divided into 4 groups, which results in a remainder of 2. Given the context of the problem, the students must account for the remainder in each case. The problems can be modified with larger numbers (divisions of three-digit numbers by two-digit numbers), if appropriate.
Once the problems have been solved, lead a mathematical discussion in which students can justify their answers. This discussion should highlight different ways of taking the remainder into account in an equal-sharing situation.
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: translated from Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 1, Nombres naturels, p. 177.