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This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
solve problems that involve finding and comparing percentages
Number Framework Links
Use this activity to help students consolidate and apply their knowledge of fractions, decimals, and percentages (stages 7 and 8).
Question 1 is designed to make students read all the information and think about it before getting into the detail. They should be able to look at 1/4 and 20% and say that 1/4 off is better than 20% off, so Bookz 4 U is never going to have the best deal.
The easiest way to answer question 2 is to create a spreadsheet or draw up a table, using a column for each number of notebooks and a column for each of the shops except for Bookz 4 U, which has been eliminated. If the students create a computer spreadsheet, they can use formulae to speed up the calculations, but they will need to be careful to apply them correctly: it is very easy to make mistakes. The students can shade or highlight the cells on the spreadsheet that have the best price.
The finished and highlighted spreadsheet organises the information in a way that makes it easy to answer question 3.
Students may have difficulty interpreting the way the discounts are to be applied, and you may need to clarify these points by discussion:
• One notebook at Mags & More will cost $5, but thanks to their discount, 2 books will also cost $5. Three or 4 books will cost a total of $10. All further books will cost a further $5.
• The 1/4 off discount at Sam’s Stationery effectively means that the cost of each book is $3.75.
• The 40% discount at Bargain Books means that for all books after the first 2, the cost is $3. (40% of $5 is $2.)
The discount at Books & Stuff means a saving of $20 on every 10 books bought. $20 is the cost of 4 books at their regular price, so 10 end up costing the same as 6. Rather remarkably, it is cheaper to buy 10 books than it is to buy 7–9. When entering the information in a spreadsheet, the students should keep adding $5 for each book until they get to 10. At that point, they deduct $20 from the cost and then start adding $5 to this new total for every additional book. They deduct a further $20 when the number of books gets to 20 and 30.
As long as the students have constructed a spreadsheet or table, question 3 becomes a matter of looking at some well-organised information. After 10 books, a pattern emerges:
• For numbers that end in 0 or 1, Books & Stuff has the best price.
• For numbers that end in 2, Books & Stuff and Bargain Books are equally the best.
• For numbers that end in 3–9, Bargain Books has the best price.
Students could cut out and collect newspaper advertisements or flyers illustrating different types of discount or different discounts being offered on the same or a similar item. They could then compare them, making a display of their findings.
Answers to Activities
1. Bookz 4 U is never the best because its discount of 20% is always beaten by the 1/4 (25%) discount offered by Sam’s Stationery.
3. Answers will vary. You could make points similar to these:
• The way the discount at Mags & More works means that no further discount is available after 4 items have been purchased. But if these were expensive items, the discount would save you quite a bit.
• Sam’s Stationery offers an excellent discount on any number of items, but it can only beat the discount offered elsewhere for 1 item.
• Bargain Books offers the best price most of the time – but only if you are buying quite a few of the same item.
• Books & Stuff offers the best deal if the cost of your purchase is just a little over a multiple of $50.