Stage 4 fractions and decimals
Strategies
Students can:
- simplify a fraction
- convert a percentage to a fraction or decimal
- find the percentage of a given amount
- increase or decrease an amount by a given percentage
Activities to support the strategies
Activity 1 - fractions and decimals
1. The teacher models these processes for calculating with fractions and decimals.
- finding equivalent fractions
- simplifying fractions
- adding and subtracting fractions by finding a common denominator
- multiplying fractions by multiplying the numerators and denominators
- dividing fractions by changing the division sign to a multiplication sign and inverting the second fraction
- ordering fractions with different denominators by finding a common denominator
- converting fractions to decimals
- students complete examples of simplifying fractions and finding equivalent fractions.
2. Students use interactive games and activities to explore fractions and decimals.
Activity 2 – percentages
When calculating with percentages, it is important that students can represent percentages as simple fractions. Explicit teaching strategies should include exploring relationships using simple percentages and using simple percentage calculations to answer harder questions. Students should also develop mental strategies, recognise equivalences and explain their answers.
1. The teacher models the steps to change:
- a percentage to a fraction
- a fraction to a percentage
- a percentage to a decimal
- a decimal to a percentage
Work through examples of each, demonstrating how to simplify fractions where necessary, by dividing the numerator and denominator by the same number, e.g.
2. Students work in pairs and write percentages for their partner to convert into fractions and decimals.
Print a table for each student with some of the important and common conversions for students to learn.
3. The teacher models how to find a percentage of an amount, for example
Students complete a worksheet to calculate percentages, e.g.
a) find 25% of 164
b) find 80% of $1250
c) find 12½% of 600 ml
d) find 62½% of 500 kg
View and print- Fractions, decimals and percentages (PDF 40.46KB)
4. The following card matching activity will assist students to develop their computation skills when calculating and working with percentages.
Look at the information in the table.
| Example | Example | Example |
|---|---|---|
| 10% of 50 = 5 | 15% of 40 = 6 | 20% of 10 = 2 |
| 25% of 80 = 20 | 50% of 30 = 15 | 75% of 40 = 30 |
View and print – Some calculations with percentages (PDF 40.44KB) and give each student a copy.
| Find | Solution | Find | Solution |
|---|---|---|---|
| 10% of 100 | 10 | 25% of 40 | 10 |
| 10% 300 | 30 | 25% of 160 | 40 |
| 10% of 150 | 15 | 25% of 20 | 5 |
| 50% of 60 | 30 | 75% of 120 | 90 |
| 50% of 90 | 45 | 75% of 20 | 15 |
| 50% of 270 | 135 | 75% of 180 | 135 |
| 20% of 20 | 14 | 15% of 80 | 12 |
| 20% of 70 | 14 | 15% of 120 | 18 |
| 20% of 90 | 18 | 15% of 20 | 3 |
View and print – Card matching activity (PDF 40.26KB)
Rewrite the Find and Solution information from the Card Matching Activity table onto individual cards.
In small groups students match the cards using the information in the table Some calculations with percentages (PDF 40.44KB).
Note : Your observations of the strategies used by groups of students will be considered during the following discussion.
As a whole class activity:
- have a representative from each group explain the strategies they used to complete the activity
- ask other groups of students to comment on and evaluate the effectiveness of strategies used by each group.
Use probing and prompting questions to elicit responses that will emphasise the relationships between the calculations, e.g.
- What if I wanted to find 25% of 400?
- What strategies could I use?
5. The teacher models how to increase and decrease an amount by a given percentage
To increase a quantity by a given percentage means that an amount is being made larger by adding the percentage to it. To Increase an amount by a percentage:
- find the percentage of the amount, then
- add this amount to the original amount.
To decrease a quantity by a given percentage means that an amount is being made smaller by subtracting the percentage from it. To decrease an amount by a percentage:
- find the percentage of the amount, then
- subtract this amount from the original amount
References
Australian curriculum
ACMNA154: Multiply and divide fractions and decimals using efficient written strategies and digital technologies, ACMNA157: Connect fractions, decimals and percentages and carry out simple conversions.
NSW syllabus
MA4-5NA: Operates with fractions, decimals and percentages.