Spending on Sport

For students who do not have a % button on their calculator or do not know how to use it, the key to solving question 1 on their calculator is being able to convert percentages and fractions to decimals. For example, with the archery set advertised as having 40% off, the students need to know that 40% is the same as 0.4. Similarly, with the stopwatch advertised as having one-quarter off, they need to know that 1/4 is the same as 0.25. (Some students may prefer to key in percentages such as 40% as x 40 ÷ 100 , even though it is not as efficient as converting to decimals.)
Another strategy for doing the calculations readily on their calculators is to use the complementary percentage or decimal. For example, with the archery set mentioned above, it is much easier to think of the sale price as being 60% or 0.6 of the original price. This means that all the students need to do is key in 0.6 x 139.95 and they immediately get the sale price, namely $83.97, in a single step.
The trickiest one is the skateboard, which has 1/3 off the advertised price. Using the thinking suggested, the students will see that the sale price is 2/3 of the original price, but to get an accurate sale price, they will need to key into their calculators 2 ÷ 3 x 119.50 = , which will give them 79.666658 or $79.67 (rounded to two decimal places). If they key in just 0.67 for the 2/3 , then they will get a sale price of $80.07, which is close but not accurate.
In question 2, the students’ solutions will vary. This will demonstrate for them yet again that in realistic problems, there is seldom one right answer. As with some previous problems, you can encourage your students to share their results for this activity with the class and to justify to others that their solutions are valid.
Question 3 challenges the students to use their calculators efficiently. The methods discussed above are all examples of efficient calculator use. Encourage the students to use these methods rather than the less efficient two-step methods such as finding the discounted price of the skateboard by dividing 119.50 by 3, recording the answer (on paper or in the calculator memory), clearing the calculator window, and keying in 119.50 – 39.83.
The students could set out their working as a table:

Answers to Activity

1. a. $103.96
b. $79.88
c. $125.04
d. $48.38
e. $58.27
f. $83.20
g. $53.96
h. $62.98
i. $83.97
j. $8.96
k. $42.46
l. $79.67
2 . a. Solutions will vary. One possibility is:
flippers $58.27
basketball $48.38
soccer ball $42.46
racquet $103.96
baseball and mitt $62.98
Total $316.05
b. Solutions will vary. For the example given above, the savings would be:
flippers $47.68
basketball $16.12
soccer ball $7.49
racquet $25.99
baseball and mitt $62.97
Total discount $160.25
c. Percentages will vary. For the example given above, the percentage can be worked out by: 162.25 ÷ (316.05 + 160.25) x 100 = 33.64%, which rounds to 33.6%.
3. Explanations will vary. For example, to find 40% of $139.95: The discount is 40%, so Philip would pay 60% of the full price. You can use your calculator
to work out 60% of $139.95 like this if you have a % button on your calculator: 139.95 x 60%. If you do not have a % button, you can go 60 ÷ 100 x 139.95 or 0.6 x 139.95. The same principle applies when you are finding discounted prices involving fractions.