B2.6 Represent and solve problems involving the division of two- or three-digit whole numbers by one-digit whole numbers, expressing the remainder as a fraction when appropriate, using appropriate tools, including arrays.
Activity 1: Types of Division
Present these two problems to students. Ask them to write a mathematical statement for each and to illustrate them.
- Danielle has invited some friends to her party. She wants to share 25 cookies equally among 6 friends. How will she do it?
- Joelle wants to give 6 marbles to each player. She has 25 marbles. How many players can participate in the game?
During a math exchange, have them compare the two problems and point out similarities and differences.
Point out that the two statements are written the same, but represent different types/contexts, either looking for the number of groups or the number of items in each group.
Activity 2: What Remains?
Material
Appendix 4.3 (What Remains?)
Distribute a copy of Appendix 4.3 to each team and ask them to solve the problems, taking into account the remainder appropriate to the context.
Once the problems have been solved, lead a math 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.
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 two of the teams and 7 students in the other two.)
Problem 2: The remainder increases the quotient by 1. (It will take 7 drivers to transport the students.)
Problem 3: The rest is ignored. (Each student must pick 6 potatoes.)
Problem 4: The remainder is expressed as a fraction. (Each team will receive either \(6\frac{2}{4}\) licorice or \(6\frac{1}{2}\) licorice.)
Problem 5: The rest is the answer. (Two jars will not be on the table.)
Problem 6: The remainder is expressed in decimal form. (There are 6.5 m between each cone.)
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.
Activity 3: What About the Remainder?
At a party, 324 chocolate chip cookies are divided equally among 9 tables. There are 8 people seated at each table.
How many cookies will each person have?
Source: translated from Les mathématiques... un peu, beaucoup, à la folie, Guide pédagogique, Numération et sens du nombre/Mesure, 4e, Module 2, Série 2, Introduction, p. 229.