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 3/8 of the way. In the afternoon, she travels 2/4 of the way. How much of the journey did she make during the day?
Source: En avant, les maths, ML, Nombres, 6e, p. 4.
Ask students questions such as:
- What operation do you need to perform to find out the total distance Zahra has traveled?
- What model, what strategies can you use to solve the problem?
- How would you determine how far you have 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 exchange to expose students to different ideas, models or tools used.
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 data of 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 fraction is the difference between the two?
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 harms the wires. How tall will the tree be when Jeremy cuts it down?
5. At the restaurant "À la bonne franquette", you need \(2\frac{3}{4}\) cases of eggs every morning for breakfast. Every morning, the wholesaler delivers \(5\frac{1}{2}\) cases. How many crates are left in the restaurant to prepare lunch and dinner?
Source : L’@telier - Ressources pédagogiques en ligne (atelier.on.ca).
After each problem solving, 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 data in the problem? Demonstrate it.
- Did you solve the problem with different or common denominators? Why or why not?
- What do you need to do to find common denominators? Explain your approach.
Activity 3: Add Fractions Without Common 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 length does he have left to install?
Here are the dimensions of his fence.
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 common 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 data in the problem? Demonstrate it.
- How big is the perimeter of Amanda's fence? How do you know?