B2.7 represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms.
Activity 1: The Recipe
Share the following situation with students:
A community gathering is being held at the school in one month. There are 120 guests in the school gym. Each class has its responsibilities, and the students in our class are responsible for the food. Deli dishes will be served.
Provide a list of foods that contains its mass per serving. Explain to students that each person will eat approximately 3 servings of food. Invite students to choose the foods that will be eaten by the guests and use a strategy of their choice to calculate the total mass of each food.
Example
Brie: 30.2 g/slice
Camembert : 28,4 g/slice
Smoked turkey: 89.9 g/slice
White ham: 85.3 g/slice
Grapes: 180.3 g/serving
Crackers: 62.1/serving
Ask students questions such as:
- How much Brie should they order? Smoked turkey? White ham? Grapes? Crackers? How do you know?
- If only 110 guests show up for the event, how much of each food item will they need to prepare? Justify your answer.
- If the supplier unfortunately does not have smoked turkey in stock, what could students do to remedy the situation? How much of each food item will they need to order? Explain your choice.
- Which algorithm can be used to solve the problem? What is the reason for this?
- When comparing the different algorithms used, what do we notice?
- How can we ensure that our calculations are plausible? Justify your answer.
Activity 2: I Estimate the Result of Multiplication
Introduce students to related sets of operations.
Example
Continue this activity by creating other sets of related operations. By developing and using their number sense, students learn to determine the position of the decimal point in the product.
Source: A Guide to Effective Instruction in Mathematics, Grades 4-6, p. 83.
Activity 3: Walking for Terry Fox
Present the following problem to students:
For Terry Fox Day, all students in the school participate in a walk. If the 278 students in the elementary school walk a distance of 0.9 km each, how many kilometres in total will they have walked?
Allow students to choose a strategy to solve the problem.
Example
Multiplication performed with an array
I estimate that the students will have walked a little less than 278 km since \(278\; \times \;0.9\; \approx \;278\; \times \;1\). I perform the multiplication using the rectangular layout. I decompose 278 into \(200\; + \;70\; + \;8\) and multiply each term by 0.9. I then add the partial products to find the total.
Ask students questions such as:
- In this case, will the product be larger or smaller than the multiplicand? How do you know?
- Which algorithm can be used to solve the problem? What is the reason for this?
- When comparing the different algorithms used, what do we notice?
- How can we ensure that our calculation is plausible? Justify your answer.
The students walked a total of 250.2 km.