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Direct Proportion: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Direct Proportion is a free printable maths worksheet for Year 7 (ages 11 to 12) in Key Stage 3. Children use the unitary method: find the amount for one, then scale up to answer each problem. The contexts are everyday, such as notebooks, apples, books, a tap and a machine. It takes about 20 minutes, needs only paper and a pencil, and page 2 gives the grown up notes, help, a stretch idea and answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to your child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children work through numbered questions, each with space to write an answer. Every question gives a real life amount, such as notebooks, apples, books, pencils, a tap or a machine, and asks for a different amount. Children find the value of one unit first, then multiply or divide to reach the answer. Some questions ask for a total and some ask for a time. The task is always the same: spot the link between the two amounts and keep it fixed.
- 3 notebooks weigh 450 g. How much do 7 notebooks weigh?
- 4 bags hold 24 apples in total. How many apples are in 9 bags?
- 8 identical books are 24 cm thick when stacked. How thick are 5 books?
- A tap fills 15 litres in 5 minutes. How long to fill 36 litres?
- 7 identical pencils weigh 63 g. How much do 12 pencils weigh?
- A machine makes 240 items in 8 minutes. How many in 15 minutes?
A worked example
10 identical plant pots cost £60. How much do 13 pots cost?
This is a different question from the ones on the sheet. It shows two ways to use the same idea.
Method 1: the unitary method- Find the cost of one pot. £60 ÷ 10 = £6.
- Multiply by the number of pots wanted. 13 × £6 = £78.
- Check that the answer makes sense. 13 pots is more than 10 pots, so the cost should be more than £60.
- 10 pots cost £60.
- Find the cost of the extra 3 pots. 3 × £6 = £18.
- Add the two parts. £60 + £18 = £78.
Ways to build the idea
Start with one
Ask what one item weighs, costs or holds before anything else. The amount for one is the key that unlocks every other amount in the problem.
Keep a two row table
Write the first amounts in the top row and the second amounts in the bottom row. Fill in the column for one first, then the column you need.
Say the rule aloud
Ask children to say it in words, for example, every notebook weighs the same, so more notebooks means more weight. Saying the rule makes it easier to trust.
Estimate, then check
Before calculating, decide whether the answer should be bigger or smaller than the starting amount. This catches slips quickly.
Why the unitary method works
Direct proportion describes two amounts that grow or shrink together at a steady rate. If one amount doubles, the other doubles too. If one is halved, so is the other. Finding the amount for one unit gives you that steady rate. Once you have it, any other amount is simply the rate multiplied by how many units you need.
In Key Stage 3 maths, ratio, proportion and rates of change is a key strand of the National Curriculum for England. The unitary method is a reliable first approach because each step is easy to explain. Later, children meet scale factors, graphs and formulas that describe the same idea in other ways.
Skills and curriculum link
- Unitary method
- Direct proportion
- Ratio
- Multiplying and dividing
- Problem solving
- Checking answers
Ideas to help you support your child
- What direct proportion meansTwo amounts are in direct proportion when one is always the same multiple of the other. Double one and the other doubles. Children often find it helps to say this in their own words.
- Why one is usefulThe amount for one unit is a rate. Rates such as cost per item or grams per pencil work for any number of items, so they make later steps simple.
- Multiply or divideTo find a total from a number of units, multiply by the rate. To find how many units are needed for a given total, divide by the rate. Ask which one the question wants.
- Units matterEach answer needs its unit, such as grams, centimetres or minutes. Writing the unit beside each number helps children see what they have found.
Key words
- Direct proportionTwo amounts that go up and down together at the same rate.
- Unitary methodFind the value of one unit first, then use it to find the value you need.
- Unit rateThe amount for exactly one of something, such as the weight of one pencil.
- Scale upMake an amount bigger by multiplying it.
- RatioA way to compare two amounts. It shows how much of one there is for each amount of the other.
- IdenticalExactly the same. Identical items all weigh or cost the same.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
- Read the first question together. Ask your child which two amounts are linked and what the question wants to find.
- Find the amount for one unit first, then multiply or divide to get the answer. Write the unit with every answer.
- Check against page 2. Ask, "How did you work that out?" The method matters as much as the answer.
- Come back another day to any questions that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Make a two row table with the first amount in the top row and the second in the bottom. Fill in the column for one first, then the column you need. Do the questions one at a time and take a break between them if needed.
To stretch confident children
Write a direct proportion question about a journey and another about a recipe. Swap with a partner and solve each other's. Then check the answers by working out the unit rate a different way.
Make it a game
Race a partner. Each person writes a direct proportion question for the other, then both solve the questions at the same time. Check each answer using the unit rate. One point for a correct answer and one for a clear method.
Mistakes to watch for
Watch forA child adds the same difference to both amounts. For example, 2 cakes cost £10, so a child says 9 cakes cost £17.
Try thisAsk what one cake costs. Explain that proportion is about multiplying, not adding. Then 9 cakes cost 9 times the price of one.
Watch forA child finds the amount for one, then stops and gives that as the answer.
Try thisUnderline what the question asks for. Write it at the end of the working, for example, cost of 9 cakes, so the last step is not missed.
Watch forA child multiplies when they should divide, such as when finding a time from a total amount.
Try thisAsk whether the answer should be bigger or smaller. Then ask how many of the rate fit into the total, which points to division.
Talk about it
- How can you tell that two amounts are in direct proportion?
- Why is it useful to find the amount for one first?
- Is there another way to reach the answer without finding one?
- Should your answer be bigger or smaller than the amount you started with? How do you know?
- What would go wrong if the items were not identical?
- Where have you seen something like this in real life, such as shopping or cooking?
Take it off the page
Recipe scaling
Choose a simple recipe and work out the amounts needed for a different number of people. Adults do any cooking, while children do the maths and write the new list.
Shop price hunt
Look at a shop receipt or catalogue. Find the price for several of the same item and work out the price of one. Predict the price for a different number.
Walking pace
Time how long it takes to walk a set distance at an even pace. Use that to estimate how long a longer walk would take and talk about why it might not be exact.
Who it is for
Parents
Sit with your child for the first question, then let them lead. About 20 minutes is plenty, and a break is fine. If they get stuck, ask them to find the amount for one. Praise clear thinking, not only correct answers.
Teachers
Use it as a starter, a plenary, an early finisher task, homework or a table activity. It needs no preparation beyond printing. Page 2 has support and stretch ideas for mixed ability groups, and the answers make marking quick.
Home educators
Print it as part of a wider maths plan. It pairs well with cooking, shopping and everyday talk about rates and prices. You can use it again for revision a few weeks later or for brothers and sisters.
Where this fits in maths
Before this, children need secure multiplication and division facts, confidence with fractions and an early sense of equivalent ratios. Earlier work on scaling recipes and sharing in a given ratio gives a good base for finding the amount for one.
After this, children move on to scale factors, ratio and proportion in more complex problems, percentages and graphs of proportional relationships. The unitary method stays useful, as a check and as a way into harder problems.
Questions parents and teachers ask
- What age is Direct Proportion for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. It also works as revision for older children who want to practise the unitary method, or as a stretch task for confident younger learners.
- What will children practise?
They practise the unitary method for direct proportion problems. They find the amount for one unit, then multiply or divide to get the amount asked for. They also practise setting out working clearly and checking answers.
- How long does it take?
It takes about 20 minutes for one student. Some children will be quicker and some will want a break. You can stop part way and return to the remaining questions another day.
- What if my child finds it hard?
Try a two row table with the first amounts in the top row and the second in the bottom. Fill in the column for one first. Work through one question together, then let them try the next on their own.
- Do I need to print in colour?
No. It prints well in black and white on plain A4 paper. Print both pages, give page 1 to the child and keep page 2 for the grown up.
- Can teachers use it in class?
Yes. It works as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 includes the answers and ideas for support and stretch.
- Is it free and screen free?
Yes to both. It is free to print for home and classroom use, and it needs only paper and a pencil. It works well for quiet time, rainy days and school holidays.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.