B. Number · Operations: Divisibility, Decimals, Fractions, Ratios and Percents

Mental Math with Percents

B2.3 A1About 40 minutes

Learning goals

I can find 50%, 25%, 10% and 1% of a whole number in my head.
I can use 10% to find 5% and 15%.
I can explain the strategy I used.

Words to know

percent (%)
A part out of 100. 25% means 25 out of 100.

benchmark percent
A friendly percent that is easy to work with, like 50%, 25%, 10% or 1%.

tip
Extra money some people give for service, for example at a restaurant. It is often found as a percent of the bill.

Remember from Grade 5

In Grade 5 you learned that percent means out of 100, and you matched fractions, decimals and percents, like 1/4 = 0.25 = 25%. Now you'll use those connections to find a percent of a number in your head.

Let's start with a sale

A hockey stick costs $80. The sign says 25% off. How much do you save?

25% is the same as 1/4. One quarter of $80 is $20. You save $20, so the stick costs $60.

You didn't need a calculator. Knowing a few benchmark percents makes this kind of math fast.

The benchmark strategies

50% is one half. Divide by 2.
25% is one quarter. Divide by 4, or take half of the half.
10% is one tenth. Divide by 10. (Each digit moves one place to the right.)
1% is one hundredth. Divide by 100. (Each digit moves two places to the right.)
5% is half of 10%.
15% is 10% + 5%.

You can build other percents too. 20% = 2 × 10%. 75% = 50% + 25%.

Bars drawn to scale. Each benchmark comes from another: halve 100% to get 50%, halve again for 25%, divide by 10 for 10%, and halve that for 5%.

Percent	Fraction	Strategy	Percent of 240
50%	1/2	Divide by 2	120
25%	1/4	Half of 50%	60
10%	1/10	Divide by 10	24
5%	1/20	Half of 10%	12
15%	3/20	10% + 5%	24 + 12 = 36
1%	1/100	Divide by 100	2.4

Benchmark percents of 240. Notice how each one comes from another.

Worked example

Example 1: Find 25% of 84

Find 25% of 84 in your head.

25% is one quarter. Take half, then half again.
Half of 84 is 42. Half of 42 is 21.

25% of 84 = 21

Worked example

Example 2: A 15% tip

Ana's family has a restaurant bill of $60. They want to leave a 15% tip. How much is the tip?

Find 10%: $60 ÷ 10 = $6.
Find 5%: half of $6 is $3.
Add: 15% = 10% + 5% = $6 + $3 = $9.

The tip is $9.

Cut $60 into 10 equal parts: each is 10% = $6. Half a part is 5% = $3. Together, 15% is $9.

Worked example

Example 3: Find 1% and 5%

Find 1% of 3 500 and 5% of 3 500.

1%: divide by 100. 3 500 ÷ 100 = 35.
5%: first find 10%: 3 500 ÷ 10 = 350. Then take half: 350 ÷ 2 = 175.
Check another way: 5% = 5 × 1% = 5 × 35 = 175. ✓

1% of 3 500 = 35 and 5% of 3 500 = 175

Explain your thinking

When you explain a strategy, say each step out loud: "First I found 10% by dividing by 10. Then I took half to get 5%. Then I added them." Explaining helps you catch mistakes and helps other people learn your strategy.

Just for fun

Coaches love to say "Give 110%!" In math, 110% of you would be all of you plus another tenth of you. That's a lot of you!

Hands-on activity

Flyer percent hunt

You need: a store flyer (paper or online), paper and a pencil.

Choose 5 items with whole-dollar prices (or round the price to the nearest dollar).
For each item, find 50%, 25%, 10%, 5% and 1% of the price in your head. Write them in a table.
Pretend each item is 15% off. How much would you save?
Explain one of your strategies to a grown-up.
Check one answer with a calculator: to find 15% of a number, multiply it by 0.15.

Math talk: "Which percent was easiest to find? Which percent helped you find another one?"

Your turn

50% of 86 = ?

10% of 340 = ?

25% of 120 = ?

1% of 800 = ?

5% of 60 = ?

15% of 80 = ?

1% of 450 = ?

More practice: warm-up

50% of 20 = ?

10% of 70 = ?

25% of 40 = ?

1% of 300 = ?

10% of 500 = ?

More practice: on your own

15% of 240 = ?

5% of 180 = ?

25% of 360 = ?

1% of 2 500 = ?

20% of 45 = ?

Challenge

A family's restaurant bill is $46. Find a 15% tip in your head.

A winter jacket costs $64. It is 25% off. What is the sale price?

Show two different ways to find 75% of 200.

Check your understanding

Quiz

What is 10% of 650?

What is a good strategy to find 5% of a number?

What is 25% of 48?

What is 15% of 60?

What is 1% of 700?

What is 50% of 3 500?

For parents and teachers

Big idea: B2.3 asks Grade 6 students to use mental math to calculate percents of whole numbers, including 1%, 5%, 10%, 15%, 25% and 50%, and to explain the strategies used. The key relationships: 50% = 1/2, 25% = 1/4, 10% = 1/10, 1% = 1/100, 5% = half of 10%, and 15% = 10% + 5%.

Common difficulties:

Dividing by 5 to find 5% (that gives 20%).
Moving digits the wrong way when dividing by 10 or 100.
Giving the discount instead of the sale price. Ask: "Is the question asking how much you save or how much you pay?"

How to help: At a restaurant or store, ask your child to work out a 15% tip or a 25% discount in their head, then explain their steps. Explaining is part of the expectation and builds the A1 skill of communicating mathematical thinking.