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Level Five > Number and Algebra

Percentages Problems in Two Steps

Achievement Objectives:

Achievement Objective: NA5-3: Understand operations on fractions, decimals, percentages, and integers.
AO elaboration and other teaching resources

Specific Learning Outcomes: 

Estimate and find percentages of whole number and decimal amounts.

Description of mathematics: 

Number Framework Stage 8

Required Resource Materials: 
Percetnage in Two Steps (Material Master 8-20).

Students find mark-up problems easier to do by calculating the amount of mark-up as  the first step, then adding this to the original as the second step. This delays the problem of percentages over 100%.


Using Number Properties


Problem: “Matt buys shirts to sell in his clothing store. He pays $24.85 for each shirt. What does he charge his customers?”

Discuss why the mark-up is 0.79 x 24.85 and write this on the board. (Answer: 79% of 24.85 = 0.79 x 24.85.)

Why should this answer not be rounded yet? (Answer: As a general rule, calculations should be rounded after the last calculation  to avoid errors.)

Discuss why the price to the customer is 19.6315 + 24.85 and write it on the board. Discuss how to enter this on a calculator. (Answer: 19.6315 is already showing on the calculator so adding 24.85 does not  require re-entering 19.6315.)

Discuss rounding the answer sensibly. (Answer: 44.4815 = 44.48 to the nearest cent – fractions of a cent are not allowed.)

Problem: “At the vegetable shop, the owner Mrs Brown buys 450 tomatoes for resale. Before they can be sold, 14% of the tomatoes spoil. How many tomatoes does Mrs Brown sell?”

Discuss why 0.14 x 450 is the number of spoiled tomatoes and why Mrs Brown sells 387 tomatoes. (Answer: 0.14 x 450 = 63, 450 – 63 = 387.)


Examples : Worksheet (Material Master 8–20).

Understanding Number Properties:

Make up a mark-up or a discount problem and solve it. Explain the steps you took.