B2.3 Use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50%, and 100%, and explain the strategies used.
Activity 1: Explain Your Strategy (Increasing and Decreasing a Whole Number)
Prepare a series of problems that will allow the student to use strategies to increase and decrease a whole number.
Divide students into teams of 3.
Project a problem on the whiteboard at the front of the classroom.
Give students time to think. Without necessarily solving it, each student must explain the strategy they would use to solve it. The use of a calculator, paper and pencil is not allowed. Emphasize the strategy, not the calculations.
Once each student has presented their strategy to their team members, they use a strategy to solve the problem. Students compare their answers.
Present students with 3 or 4 problems. Choose numbers that allow the student to make connections with mental math strategies.
Examples of problems
Problem 1:
A pair of sneakers that costs $120 is discounted by 25%.
How much will the discounted sneakers cost before tax?
Explain your strategy before solving the problem.
Possible answer for student 1: 25% is equivalent to the fraction \(\frac{1}{4}\) so I divide $120 by 4 and then subtract that answer from the original price.
Possible answer for student 2: A 25% discount is equivalent to saying that the sneakers are sold at 75% of their original value. 75% is equivalent to \(\frac{3}{4}\) so I divide $120 by 4 and multiply that value by 3.
Possible answer from student 3: A 25% discount is equivalent to saying that the sneakers are sold at 75% of their original value. Therefore, I would calculate 75% of 100 and 75% (or \(\frac{3}{4}\)) of 20.
It is important for the student to recognize at the outset whether the amount is increasing or decreasing based on what is being requested.
Problem 2:
The Harmonized Sales Tax (HST) in Ontario is 13%. What will the HST be on a television set that sells for $499.99?
Explain your strategy before solving the problem.
Note: Encourage the student to decompose the % for example \(13\;\% \; = \;10\;\% \; + \;1\;\% \; + \;1\;\% \ ;+\;1\;\%\)
Problem 3:
The volume of water that freezes increases by 8%. If there is 200 L of liquid water at the beginning, what will be the volume of the frozen water?
Explain your strategy before solving the problem.
Review with the class by questioning the students.
Examples of questions to focus on among team members and with the class:
- Is it an effective strategy? Why is it effective?
- How would you explain in your own words the strategy that was just presented?
- Which other teams have you seen who used this or a similar strategy?
- How does this strategy differ from that one?
- How else could this problem have been solved?
Source: Questions inspired by Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, p. 174.
Activity 2: What is the Tax? (Using Mental Math Strategies on Numbers and Percents to Estimate the Value of a Good or Service)
Materials
- flyers from many stores (see online)
- hotel/travel websites
The student is not allowed to use a calculator for this activity.
Initially, have a discussion with students about the HST by identifying the goods and services that are affected by this tax.
Then, form teams of 2 people. Each team must identify 5 goods and services that are affected by the HST.
Using the mental math strategies they've learned about numbers and %, they estimate the tax and total cost of the goods and services they've found.
Review with the class (see questions above if necessary).
After the initial activity: Students can check how close their estimate is to the true value using the calculator.