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Proportion Word Problems: Free Printable Worksheet for Year 6
- ForYear 6
- StageKey Stage 2
- CostFree
- FormatPrintable PDF
Proportion Word Problems is a free printable maths worksheet for Year 6 (ages 10 to 11). Children read short everyday problems and scale an amount up or down, from a recipe to a car journey. It takes about 20 minutes, needs only a pencil, and page 2 gives the grown up notes, help ideas, a stretch task and the 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 read short word problems and decide how to scale an amount up or down. The settings are everyday ones, such as pencils, a recipe, paint, a car journey, balloons and stickers. Each problem gives an amount for a set number of items, and children find the amount for a different number. There is space to answer under each question, so children can show their working.
- 4 pencils weigh 20g. How much do 10 pencils weigh?
- A recipe uses 200g flour for 4 people. How much for 6 people?
- 3 pots of paint cover 12 sheets. How many sheets do 5 pots cover?
- A car goes 60 miles in 2 hours. How far in 5 hours at the same speed?
- 5 balloons need 10 breaths. How many breaths for 8 balloons?
- 2 packets hold 24 stickers. How many in 5 packets?
Worked example: tickets
9 tickets cost £27. How much do 15 tickets cost?
This is a different problem from the sheet, with different numbers. It shows two ways to scale an amount.
Method 1: find the cost of one- Divide the cost by the number of tickets: £27 ÷ 9 = £3 for one ticket.
- Multiply by the new number of tickets: £3 × 15.
- £3 × 15 = £45.
- Find a smaller group that fits both numbers. 9 tickets split into 3 equal groups, so 3 tickets cost £27 ÷ 3 = £9.
- 15 tickets is 5 groups of 3 tickets.
- Multiply the cost of one group by 5: £9 × 5 = £45.
Ways to think about proportion
Find one first
Work out the amount for one item or one person, then multiply to reach the amount you need. This method works for almost every problem.
Use a scale factor
If the new number is a whole number of times bigger or smaller, multiply or divide both amounts by that same number.
Build a table
Write the two amounts in two rows. Fill in the steps between, such as one, two and so on. A table keeps the working tidy.
Draw a bar
Draw one bar for one share and repeat it. Seeing equal shares makes it clear why the amounts grow together.
What proportion means
Two amounts are in proportion when they grow or shrink together in a steady way. If you double one amount, you double the other. If you halve one, you halve the other. This is why a recipe can feed more people when every ingredient is scaled by the same amount. The key idea is that the same rule is applied to both quantities.
Proportion only works when the rate stays steady. A car travelling at the same speed covers the same distance in each hour, so the distance grows in step with the time. Children need to ask, "What stays the same here?" Spotting that fixed rate is the first step in choosing whether to multiply, divide, or find the amount for one.
If you cook a scaled recipe, adults do all the oven, hob, knife and hot item work. Children can help read the recipe, check the numbers and measure cold ingredients.
Skills and curriculum link
- Proportion
- Scaling up and down
- Multiplying and dividing
- Reasoning
- Checking answers
This sheet supports the area below. It is matched to the published England framework. Please check it against your own school plan.
| Framework | Subject or area | Strand | Year |
|---|---|---|---|
| National Curriculum (England) | Maths | Ratio and proportion | Year 6 |
What children will be able to do
- I can scale an amount up using proportion.
- I can scale an amount down using proportion.
- I can explain how I know the amounts stay in proportion.
Ideas that help with proportion
- Same rule on both sidesWhatever you do to one amount, do to the other. If one is multiplied by a number, multiply the other by that number too.
- Find one firstFinding the amount for one item makes the next step simple. Then multiply to reach the number you need.
- Estimate before you startAsk whether the answer should be bigger or smaller than the amount you started with. This catches many slips.
- Keep units with the numbersWrite grams, miles, sheets or breaths beside each number. It shows what each amount is measuring.
Key words
- ProportionTwo amounts that change together in a steady way. When one doubles, so does the other.
- Scale upMake an amount bigger by multiplying everything by the same number.
- Scale downMake an amount smaller by dividing everything by the same number.
- Unit amountThe amount for just one item or one person.
- RateHow much of one thing goes with a set amount of another, such as miles in one hour.
- MultiplyFind the total of equal groups. 3 groups of 4 is 3 × 4.
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 problem aloud together. Ask, "What stays the same here?" before any sums.
- Let your child choose a method: find one first, use a table, or draw a bar. Allow about 20 minutes in total.
- Check against page 2. Ask, "How did you decide what to multiply or divide by?" A calculator can help check answers.
- Come back another day and redo any problems that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Draw a bar to show one share, such as the amount for one pencil or one person. Then draw the bar again for each share you need and count the total. Try the first few questions first, and say aloud what stays the same each time.
To stretch confident children
Write your own proportion problem using a recipe. Choose an amount for a small number of people, then ask for a much bigger group. Swap with someone, solve each other's, and check by working a second way.
Make it a game
Pick a simple family recipe and scale it up on paper for more people. If you cook it, an adult does all the oven, hob and knife work. Your child measures cold ingredients and checks each new amount against the working.
Mistakes to watch for
Watch forA child adds the same amount to both numbers. If 2 bags hold 14 sweets, they say 3 bags hold 15.
Try thisAsk what one bag holds. Each extra bag adds a whole bag of sweets, so multiply, do not add the difference.
Watch forA child multiplies when the problem needs them to scale down, or the other way round.
Try thisAsk whether the answer should be bigger or smaller. If fewer items are needed, the amount should get smaller, so divide.
Watch forA child finds the amount for one item but forgets the last step and stops there.
Try thisReread the question and ask, "How many do we actually need?" Then multiply the amount for one by that number.
Talk about it
- What stays the same in this problem, and what changes?
- Do you need to multiply or divide? How do you know?
- Should the answer be bigger or smaller than the amount you started with? Why?
- Can you find the amount for just one? Does that help?
- Can you check your answer a second way?
- Where might you scale an amount up or down at home?
Take it off the page
Kitchen scaling
Pick a recipe that serves a small group. Write a new list of ingredients for a bigger group. An adult does all the cooking, if you decide to make it.
Shop price table
Choose an item sold in packs. Make a table showing the cost for one pack, two packs and so on. Use it to find the cost of more packs.
Journey planner
Imagine a walk or cycle at a steady pace. Work out how far you would go in different amounts of time and draw it as a chart.
Who it is for
Parents
Sit beside your child for the first problem, then let them lead. Short sessions of about 20 minutes work well. If they get stuck, ask them to draw a bar for one share and repeat it.
Teachers
Use it as a starter, plenary, early finisher task or homework after teaching ratio and proportion. The problems share one idea, so you can see who chooses to find one first and who uses a scale factor.
Home educators
Pair it with real scaling, such as halving or doubling a recipe, with an adult doing the cooking. Print it again for revision a few weeks later, or for brothers and sisters.
Where this fits
Before this, children need secure times tables, division facts and confidence finding fractions of amounts. Those skills help them scale quantities up and down. Earlier years also build the idea of equal groups, which sits underneath proportion.
After this, children can meet ratio notation, scale factors in similar shapes, unequal sharing and percentages. In secondary maths, proportion grows into rates, graphs of steady change and algebra.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- How did you decide what to multiply or divide by?
- How could you check your answer?
- Can you make up a proportion problem of your own?
Questions parents and teachers ask
- What age is Proportion Word Problems for?
It is written for Year 6 (ages 10 to 11) in Key Stage 2. It practises the ratio and proportion strand of the National Curriculum for England through short, everyday word problems.
- How long does the worksheet take?
It takes about 20 minutes. Children who find scaling hard may need a little longer, and confident children may finish sooner and move on to the stretch idea on page 2.
- Does it include answers?
Yes. Page 2 is for the grown up and includes the answers, along with notes on how to use the sheet, help for children who find it hard and a stretch idea.
- Can children use a calculator?
Yes, a calculator can help check answers. Ask children to work the problem out first and then check, so the thinking comes before the button pressing.
- What if my child finds it too hard?
Ask them to draw a bar to show one share, then repeat it for each share needed. Working on the first few problems and returning to the rest later also helps.
- Is it suitable for classroom use?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and black and white printing works well.
- Is it free and screen free?
Yes to both. It is free to print for home and classroom use, and needs only paper and a pencil. It suits quiet time, rainy days, school holidays and home education.
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Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.