B2.9 multiply whole numbers by proper fractions, using appropriate tools and strategies
Activity 1: Multiply a Whole Number by a Proper Fraction
Present the following scenario to the students.
Marion is the student responsible for feeding Cleo, the class goldfish. Her teacher recommends that she feed Cleo one teaspoon of flakes per day. With 3 teaspoons of flakes left in the container, will Marion have enough to feed Cleo for a week?
Source: A Guide to Effective Instruction in Mathematics, Grades 4-6, p. 82.
Ask students to share with the class the strategies they used to multiply \(5\; \times \;\frac{1}{4}\) and compare them.
Activity 2: The Kitchen Staff
This activity allows students to realize that changing the yield of a recipe requires multiplying quantities that are sometimes expressed as fractions. Teachers first present the following situation to the class as follows:
In order to raise the necessary funds for their end-of-year outing, the Grade 6 students at À tire-d'aile school decided to sell pastries. Florence and her friends chose to make healthy carrot, apple and raisin muffins. As they read the recipe, they realize that one recipe only makes eight muffins. However, they want to prepare two dozen.
Teachers provide students with a copy of the recipe and take the opportunity to draw their attention to the fact that quantities are expressed using imperial measurements.
Healthy Carrot, Apple and Raisin Muffins
Yield : 8 muffins
Ingredients
\(2\frac{2}{3}\) cups of flour
2 cups of sugar
\(\frac{1}{2}\) cup golden raisins
\(1\frac{1}{4}\) cup apples, diced
\(1\frac{3}{4}\) cup grated carrots
\(\frac{1}{2}\) tsp. baking powder
\(2\frac{1}{2}\) tsp. baking soda
3 eggs
\(\frac{3}{4}\) cup vegetable oil
1 tsp. vanilla extract
\(\frac{3}{4}\) tsp. cinnamon
\(\frac{1}{2}\) cup of milk
Steps
- Preheat oven to 375ºF.
- In a bowl, combine liquid ingredients: eggs, vegetable oil, vanilla and milk. Set aside.
- In another bowl, mix all dry ingredients: flour, sugar, baking powder, baking soda, cinnamon.
- Add grapes, apples and carrots to dry ingredients. Stir.
- Gradually add liquid ingredients to dry ingredients while stirring.
- Pour the mixture into a greased 8-muffin pan.
- Cook for 10 to 15 minutes.
Group the students in pairs and ask them to adjust the quantities so that Florence's team can make two dozen muffins. Then facilitate a discussion to highlight the challenges, strategies, differences and similarities. It is important to point out that the temperature and baking time should never be changed in baking since the size of the muffins has not been changed.
Since this is a real recipe, students can be encouraged to make these healthy muffins in class or at home, modifying the amount of ingredients to meet a specific need.
Source: Adapted from A Guide to Effective Instruction in Mathematics, Grades 4-6, p 103-104.