6. Percentages

6.1 Introduction

Percentages are one of the most common means that people use to describe what’s happening in our world. In the media they are used to describe unemployment rates, a plethora of health and welfare statistics and the allocation of government resources, such as how much is spent on education or the military in comparison to other countries.

In more personal and immediate matters, percentages are used to inform us about interest rates on credit cards and loans, to explain salary deductions, to announce increases in pensions and allowances, and of course, to entice us to save (or spend) money with discount offers.

6.2 Matching Percentages 1

This activity can be used in a variety of ways:

• As a non threatening introduction to percentages

• As a link between commonly used fractions and equivalent percentages (e.g. ½ = 50%, ¼ = 25%)

• As a chance to observe students’ familiarity with simple percentage and fraction concepts

• As a foundation for shortcut percentage calculations

• To extend students’ understanding of the concept of percentage.

6.3 Matching Percentages 2

This activity can be used to make links between fractions and percentages commonly used in Australian society and to explore their relative sizes. It also provides an opportunity to reinforce both fraction and percentage concepts. It is a quick, non-threatening activity which encourages student discussion and cooperation in pairs or small groups, so provides a useful variation from individual calculation exercises. The matching activities should not be done one after the other.

6.4 Shortcut Percentages: 50% 25% 75%

This activity explores how knowing that 50% = ½ and 25% = ¼ gives us the power to do shortcut percentage calculations without formulas. This activity ideally follows the Matching Percentages activity.

6.5 Shortcut Percentages: 10%

This activity is designed to introduce students to the method of calculating 10% by finding a tenth (or dividing by 10). It also provides opportunity to revise the fundamental meaning of percentage and simple fraction concepts. Ideally this activity should be done after students have been introduced to shortcut methods for 50% and 25% by halving.

6.6 Shortcut Percentages: 20% 30% ... 5%

This activity extends the previous activity by exploring how the 10% shortcut can be used as a stepping stone for calculating percentages such as 20%, 30% ... as well as 5%, 15%.

6.7 Percentages In Circles

This activity is a way of bringing together the shortcut percentage methods based on division by 10 and halving. It can be used to:

• Revise the methods introduced in previous activities

• Graduate the level of difficulty of calculations for individual students

• Develop individualised homework and revision exercises

• Introduce and practise estimation of percentages

6.8 Shortcut Percentages: 1%

This activity is designed to introduce students to the very useful method of calculating 1% by finding one hundredth (or dividing by 100). 1% can be used to find 2%, 3% … and these in turn can be added to 10%, 20% … to calculate other percentages such as 23%, 34%, 12%.

The activity also provides opportunity to revise the fundamental meaning of percentage and simple fraction concepts.

6.9 Percentage Of Our Lives

This activity introduces a range of percentages related to adult life in Australia whist exploring

the meaning of ‘percent’ as well as common diagrams used to represent percentages. It is an

activity rich in opportunities for small group and whole class discussion: a worthwhile variation

from individual calculation exercises.

For higher level numeracy students or Australian workplace learners it can be an interesting,

adult appropriate introduction to percentages. It provides a chance to:

• Observe learners’ existing knowledge of percentage concepts

• Explore and clarify some percentages which affect students’ lives

• Build a strong foundation for ‘in the head’ percentage calculations.

For less experienced numeracy students the activity can be used during a series of

percentage activities. It provides a chance to:

• Revise and reinforce percentage concepts

• Explore percentages affecting students’ lives

• Introduce common diagrams used for representing percentages.

6.10 Shortcut Percentages: Per Hundred Method

This activity uses the concept of a percentage rise in wages or allowances to present a shortcut or ‘in the head’ method for calculating percentages. Two versions of the method are introduced to cater for different levels of student ability. Both are based on understanding percentage as ‘per hundred’ or ‘in every hundred’.

Ideally this activity follows Percentages of our lives which explores this meaning of percentage.

6.11 Shortcut Percentages: Cents In The Dollar

This activity introduces the cents in the dollar approach to calculating discounts. Ideally it follows on from the previous activity: Shortcut percentages: The ‘per 100’ method

6.12 Percentages On The Calculator

This activity introduces students to the % button on their calculators and how to use it. It is best done after students have gained confidence at some of the shortcut percentage calculation strategies.

6.13 Percentage Target Game

This activity is designed to encourage students to estimate percentages and to use the percentage function on their calculator to check these estimates. The aim of the game is to achieve the target on their calculator display in the minimum number of tries. As a game for two students in competition, it motivates students to focus on their estimates in order to win. As a game for one person this motivation comes from trying to improve on their previous score.