The power of equivalence
Developed in partnership with Education Services Australia
The Australian Curriculum sets the goal for what all students should learn as they progress through their school life. Skills in the Year 5-6 curriculum include:
- solving problems using equivalent fractions, decimals and simple percentages through addition and subtraction
- visualising, describing and ordering equivalent fractions, decimals and simple percentages
(for example, 25% = 25 out of 100 = ¼ = 0.25)
- comparing, ordering and representing decimals up to thousandths and beyond
- finding a simple fraction or percentage of a quantity where the result is a whole number.
It’s easy to help your child practise these skills as part of everyday life – just use these simple ideas.
Equivalence sounds technical, but we use it every day to simply calculations – eg turning 33% x $300 into $300 divided by three. These ideas will help your child become familiar with these shortcuts, and master how to use them:
- when you're out shopping, talk aloud as you convert between percentages, decimals and fractions to make calculations easier
This $40 shirt is 50% off. That means it’s half price, so we can just divide the price by two. $40 divided by two is $20 – what a bargain!
- ask your child to ‘remind’ you of conversion shortcuts when calculating a saving
This wheelbarrow is 33% off. It sounds like a good deal, but I can’t remember the easy way to work out the saving. Can you remind me? (Answer: 33% is the same as one third, so divide the original price by 3)
- ask your child to work out discounts, and encourage them to use conversion shortcuts
Your favourite ice cream is 25% off this week. The usual price is $8, so how much will we save? (Shortcut: 25% is the same as one quarter, so divide $8 by 4)
- with more difficult calculations, talk through problems to show how you estimate the answer (and check it with a calculator if needed)
These $12 DVDs are marked down by 35%. That's just over 33%, which is one third, so the discount will be $12 divided by three = $4, plus a bit. Do you think that's a good deal?
For online reinforcement, Fraction fiddle: hit the apple will give your child practice at:
- making fractions that add up to one whole.
Playground percentages will give your child practice at:
- visualising equivalent fractions and percentages on a grid of 100 squares.