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 three.
Write a problem on the board or whiteboard at the front of the classroom.
Without necessarily solving it, each student must think about and be prepared to explain the strategy they would use to solve it. The use of a calculator or paper and pencil is not allowed. Emphasize the strategy, not the calculations. Give students individual think time, and then ask them to discuss their strategies with the other students on their team.
Once each student has presented their strategy to their team members, they are to use their own strategy to solve the problem. Students should then compare their answers.
Repeat the process with other 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 for 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 increases by 8% when it freezes. What will be the volume of 200 L of water when it is frozen?
Explain your strategy before solving the problem.
Once the students have had an opportunity to work on all of the problems, have a class discussion about the various strategies used for each.
Examples of questions include:
- In what ways is this an effective strategy?
- How would you explain this strategy in your own words?
- Which other teams used this or a similar strategy?
- How does this strategy differ from that one?
- How else could this problem have been solved?
Source: Questions translated and inspired by Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 3, Nombres décimaux et pourcentages, 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
To promote the use of mental math strategies, the students should not 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 two people. Each team must find five goods and services that are affected by the HST.
Then, using the mental math strategies they've learned about numbers and percents, students are to estimate the tax and total cost of the goods and services they've found.
Once students have had sufficient time to complete the task, have a class discussion about some of the strategies they used to calculate the HST (see questions from Activity 1).
After the initial activity: Students can check how close their estimate is to the actual value using the calculator.