Click on the image to enlarge it. Click again to close. Download PDF (178 KB)
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
find percentages of a money amount
For this activity, the students need to be familiar with showing a fraction as a percentage, and they need to understand that a percentage is a part of a whole expressed in hundredths. The whole is 100/100 or 1, which is 100 percent (%). 20 is 20/100. The students need to be able to multiply and divide by hundreds and tens, especially in terms of money (for example, 10% of $1.20 is $0.12). The activity also involves adding and subtracting amounts of money.
Before they do this activity, the students need to have had experience with showing how fractions and percentages are related. They could use a hundreds board or grid for this, covering different amounts with pieces of paper and describing fractions that have 100 as a denominator. Encourage the students to describe these fractions as equivalent fractions, such as 1/2, 3/4, 9/10, and so on. (See the activity on the previous page.) For example, the paper covers the fraction 50/100, which
is also 5/10 or 1/2 (or 50%).
You could also show the students how fractions and percentages can be drawn on a double number line:
Revise multiplying by 10 and 100 and encourage the students to see that multiplying by 40 is the same as multiplying by 10 and then multiplying by 4 (or vice versa). These skills are necessary when finding 30% of something because a good strategy is to find 10% and then multiply it by 3.
Newspapers or advertising materials are useful sources for the students to explore how businesses advertise reductions of 10%, 25%, and so on.
The questions in this activity focus on a chart showing two different shops with various discounts. The students have to find the sale price of the items in order to complete the table. Encourage the students to notice that most of the percentages are easy to work with. For example, for 30%, they can find 10% and multiply by 3, and 25% is the same as 1/4. The only difficult percentage to be found is 45%. This could be found by first finding 10%, multiplying it by 4 to find 40%, finding 1/2 of 10% to get 5%, and adding this amount to the 40% amount. Make sure the students realise
that they have to subtract the percentage amount from the price each time to find the actual cost of those items.
To do question 2, the students need to be able to compare values and also subtract one from the other. If they have difficulty, get them to calculate the amounts using play money.
In question 3, where the students make up their own sale problems, encourage them to make up a chart similar to the one given on the page.
Further discussion and investigation
Collect advertising materials that show percentage reductions and have the students work out the sale prices. Have them find similar items sold by different companies and compare their prices.
Give the students a budget for an activity, such as buying sports equipment for the school or books and CDs for the library. Have them use the advertising material to make a list of realistic retail prices and sale prices. They can then work out the total they would save if they bought all the items at a sale.
Answers to Activity
1. i. a. The Surf Shop. ($42 vs $43.20)
ii. a. Surf the Waves Company. ($76.80 vs $84)
iii. a. The Surf Shop. ($33.60 vs $37.40)
iv. a. Surf the Waves Company. ($48 vs $60.20)
2. a. $200.40
3. Problems will vary.