B2.5 Add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts.
Activity 1: Visit to the Family
Present the following situation to students:
Zahra has to travel a long distance to visit her brother. In the morning, she travels \(\frac{3}{8}\) of the way. In the afternoon, she travels \(\frac{2}{4}\) of the way. How much of the journey did she make during the day?
Source: translated from En avant, les maths, ML, Nombres, 6e, p. 4.
Ask students questions such as:
- What operation can you use to find out the total distance Zahra has traveled?
- What model or strategies can you use to solve the problem?
- How would you determine how much farther Zahra has to go?
Did Zahra travel more or less than half way?
Activity 2: Subtracting Fractions
The following is a list of contexts for exploring fraction subtraction with students. It is important to have a strategy gallery and a mathematical discussions to introduce students to different ideas, models or tools that can be used to solve the problems.
1. Luigi put \(10\frac{1}{2}\) litres of water in his aquarium to fill it. After 2 weeks, a quantity of water had evaporated and only \(8\frac{3}{4}\) litres of water remained. How many litres of water did Luigi have to add to refill his aquarium? Using manipulatives, represent the problem and find the solution.
2. Mariette has 12 cups of flour left in her container. To make a cake, she needs 3 cups of flour. To make pancakes she needs 2 cups of flour and to make cookies she needs 2 cups of flour. How much flour will she have left when she finishes the cake, pancake batter and cookies?
3. It takes Marianne an hour to get to her school by bus. It takes Margaret an hour to get to her school. Which girl spends more time on the bus? What is the difference in their travel times?
4. Jeremy has to cut down a tree that is affecting the electrical wires in front of his house. The tree is \(5\frac{1}{2}\) metres high. He must cut at least \(2\frac{3}{4}\) metres so that the tree no longer interferes with the wires. How tall will the tree be when Jeremy cuts it down?
5. The restaurant "Good Morning Eatery" needs \(2\frac{3}{4}\) cartons of eggs every morning for breakfast. Every morning, the wholesaler delivers \(5\frac{1}{2}\) cartons. How many cartons are left to prepare lunch and dinner?
Source: translated from L’@telier - Ressources pédagogiques en ligne (atelier.on.ca).
After each problem solving opportunity, ask students questions such as:
- What does the numerator represent? The denominator? How do you know?
- What manipulatives or strategy did you use to solve the problem? Explain your choice.
- How can you represent the problem?
- Did you solve the problem with like or unlike denominators? Explain your thinking.
- What do you need to do to find common denominators? Explain your approach.
Activity 3: Add Fractions With Unlike Denominators
Present the problem below to the students.
Amanda needs to calculate the length of the fence she and her father put up as she is about to paint it.
- How much fence has Amanda already put up?
- How much fence do they have left to install?
The dimensions of the fence are shown below:
Ask students questions such as:
- What does the denominator represent? The numerator?
- How can we solve the problem? Do you think we should find a like denominator or not? Why or why not?
- What manipulatives or strategy did you use to solve the problem? Explain your choice.
- How can you represent the problem?
- What is the perimeter of Amanda's fence? How do you know?