This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
A PDF of the student activity is included.
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find percentages
FIO, Level 3-4, Number, Book 2, Bargain Busters, page 17
Students who attempt this activity should be advanced multiplicative or beyond. The activity involves finding percentages of money amounts, but estimation also plays a key part. There are several mental strategies that use the students’ knowledge of unit fractions, place value, compensation from tidy numbers, and equivalent fractions.
Some possible strategies for question 1 are given in the Answers.
Question 2a requires the students to add up the items in each group, estimate the discount for each group, and then calculate the total discount for all the food. The students need to remember that some items are listed together, for example, 3 bottles for $1.99 each, and this must be taken into account when they are adding up all the items.
In question 3, the students can again use a variety of strategies to estimate whether each advertisement is correct. For example, in question 3a, they could find a quarter of $12.50 (halve then halve again) or divide by 4 or find 10 percent, double it, then add half of 10 percent. In question 3b, they could find 10 percent and double it.
The students need to discuss what is reasonable in terms of rounding to decide whether the advertising in question 3b is correct or not. They will have a variety of answers that need to be justified mathematically.
Answers to Activity
1. a. 25% is 1/4, so he could round the prices and divide by 4, or he could estimate 10% of the cost, double it, and add half of 10% (10% + 10% + 5% = 25%).
b. 30% is nearly 1/3, so he could round the prices and divide by 3, or he could estimate 10% (using place value knowledge) and add 3 lots of 10%.
2. a. i. Estimates may vary, but they should be close to the following:
Drinks: $20.70. (The drinks add up to approximately $23.00. 10% of that is
$2.30, so the approximate cost is $20.70.)
Freezer: $13.60. (20% of $17 is $3.40, so the approximate cost is $13.60.)
Fruit and vegetables: $25.50. (25% of $34 is $8.50, so the approximate cost
is $25.50.)
Breakfast food: $15.40. (30% of $22 is $6.60, so the approximate cost is
$15.40.)
ii. Drinks: $21.07. (10% of $23.41 is $2.34.)
Freezer: $13.65. (20% of $17.06 is $3.41.)
Fruit and vegetables: $24.39. (25% of $32.52 is $8.13.)
Breakfast food: $14.98. (30% of $21.40 is $6.42.)
b. $20.30
3. a. No. The price should be $9.38 or the saving shown as 20%.
b. With rounding, it is correct. $12 is the discounted price after taking 20% off $15.00.