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Rates and Ratios Cipher: Free Printable Worksheet for Year 9
- ForYear 9
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Rates and Ratios Cipher is a free printable maths worksheet for Year 9 (ages 13 to 14), in Key Stage 3. Pupils solve a set of case files on speed, unit rates, best buys and sharing in a ratio. Each answer is found in a key row, and its letter goes into a box to reveal a hidden codeword. It needs only a pencil, and page 2 gives the grown-up notes, help, a stretch idea 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 the pupil and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children play the part of an agent working through case files. Each file is a rate, ratio or best buy problem, such as finding an average speed, scaling a recipe or sharing money in a ratio. The sheet has a table to fill in and numbered questions with space to answer. Each answer is matched to a number in the key row, which gives a letter. The letters spell the codeword.
- A car travels 150 km in 3 hours. What is its average speed in km/h?
- 4 people need 200 g of flour. How many grams do 6 people need?
- Share £84 in the ratio 2:5. How many pounds is the larger share?
- A train travels at 40 km/h for 2.5 hours. How many km does it go?
- 8
- 35
- 50
- 60
- 100
- 300
- Q1
- Q2
A worked example with different numbers
Share £63 in the ratio 3:4. How much is each share?
This is a different question from the ones on the sheet. It shows two ways to think about sharing in a ratio.
Method 1: find the value of one part- Add the parts of the ratio: 3 + 4 = 7 parts altogether.
- Divide the total by the number of parts: £63 ÷ 7 = £9 for one part.
- Multiply for each share: 3 × £9 = £27 and 4 × £9 = £36.
- Draw one bar and split it into 7 equal blocks.
- Label the whole bar £63. Each block is £63 ÷ 7 = £9.
- Shade 3 blocks for the first share and 4 blocks for the second. Count up the pounds in each.
What the case files ask pupils to do
Work out a speed
Speed links distance and time. Pupils find an average speed from a distance and a time, or use a speed and a time to find a distance. The units tell them which way round the division goes.
Scale a quantity
Some problems give an amount for one group and ask for another group. Pupils find the amount for one, then scale up. This is a rate in action.
Share in a ratio
Pupils turn a ratio into equal parts, find what one part is worth, then work out a share. A quick check is that the shares must add back to the whole.
Compare best buys
Pupils compare prices fairly by working out the cost of the same amount of each item. A calculator is allowed for the best buy question.
Why rates and ratios matter
Rates and ratios appear in everyday decisions. A journey time depends on speed. A recipe changes with the number of people. Prices in a shop are easier to compare when each is turned into a cost for one unit. Pupils meet these ideas long before Year 9, so this sheet gives them a chance to use them together in one place.
In Key Stage 3, the National Curriculum for England groups these ideas under ratio, proportion and rates of change. Pupils move from simple sharing to choosing their own method and explaining it. Finding the value of one part or one unit is a strong habit. It works for speed, scaling and ratio problems alike, and it makes checking easier too.
The cipher adds a reason to be accurate. If an answer does not appear in the key row, the pupil knows to look again. That gives instant feedback without a grown-up having to say a word.
Skills and curriculum link
- Calculating speed
- Unit rates
- Sharing in a ratio
- Comparing best buys
- Checking answers
- Decoding a cipher
Ideas that help with rates and ratios
- Find one firstFor many rate problems, work out the amount for one person, one hour or one item. Then scale up to the amount you need.
- Speed, distance and timeThese three are linked. If you know two of them, you can find the third. Check that the units match before you calculate.
- Add the parts of a ratioBefore sharing, find how many equal parts there are altogether. Then find the value of one part.
- Check by adding backWhen you share a total in a ratio, the shares should add up to the original total. If they do not, look for a slip.
Key words
- RateA comparison of two different kinds of amount, such as distance and time, or cost and weight.
- Average speedThe total distance travelled divided by the total time taken.
- Unit rateA rate for exactly one unit, such as the cost of one item or the distance in one hour.
- RatioA way to compare amounts. In 2:5, the first amount has 2 parts for every 5 parts of the second.
- Best buyThe option that gives the lowest cost for the same amount, or the most for the same cost.
- CipherA secret code where each letter is swapped for something else, here a number from the key.
How to use it
- Print both pages. Page 1 is for the pupil. Keep page 2, which has the notes and answers.
- Read the first case file together. Ask the pupil what is being asked for and what units the answer needs.
- Let them choose a method and write their working. Then find the answer in the key row and write its letter in the matching box.
- Reveal the codeword, then check with page 2. Ask, "How did you know where to start?" The reasoning matters as much as the answer.
- Come back another day and redo any case file that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Start by finding the amount for one person or one unit. Ask, "What does one cost?" or "How far in one hour?" Write that down, then scale up. A calculator is fine for the best buy question. Try one case file together first.
To stretch confident children
Write your own code of three problems for a partner. Choose the answers, give each one a letter, and build a key row with a few spare numbers as decoys. Swap and crack each other's codes. Check the working, not only the final word.
Make it a game
Play secret agents. Give each player a copy and time them. The first to decode the word correctly, with working shown, is promoted to Chief Agent. Swap roles, set a new code for a second round and see who holds the title.
Mistakes to watch for
Watch forA pupil divides time by distance when finding a speed, so the answer is far too small.
Try thisSay the units out loud. Km per hour means kilometres for each one hour. Ask which amount goes on top.
Watch forWhen sharing in a ratio, a pupil divides the total by each number in the ratio separately.
Try thisAdd the ratio numbers to count the equal parts. Divide the total by that count to find one part, then multiply.
Watch forA pupil treats a decimal time as hours and minutes, for example reading 1.5 hours as 1 hour 50 minutes.
Try thisRemind them that 1.5 hours is one and a half hours. Use a decimal calculation, or half an hour as 30 minutes.
Talk about it
- How did you decide which number to divide by?
- Why is it useful to find the amount for one first?
- How could you check that your shares are fair?
- When might a best buy not be the right choice?
- Where do you see speeds, rates or ratios in real life?
- How did the key row tell you whether your answer was sensible?
Take it off the page
Kitchen scaling
Pick a simple recipe and rewrite the amounts for a different number of people. Compare your new amounts with a partner. An adult does any cooking or use of hot items.
Shop price detective
Look at two sizes of the same product, on a receipt or a shelf list. Work out the cost for the same amount of each and decide which is better value.
Journey planner
Choose a trip you could take. Estimate a sensible average speed and the distance, then work out how long it might take. Say what could change the time.
Who it is for
Parents
Sit beside your teenager for the first case file, then let them lead. Ask about their method rather than the answer. Short bursts work better than a long session. If they are stuck, suggest finding the amount for one.
Teachers
Use it as a starter, a plenary, an early finisher task, homework or cover work. The cipher gives pupils quick feedback, so you can circulate and look at working. Page 2 has support and stretch ideas for mixed groups.
Home educators
Print it as part of a wider maths plan on ratio and proportion. Ask the learner to explain each method aloud. It works for revision a few weeks later, and it can be printed again for other learners.
Where this fits in maths learning
Before this sheet, pupils use multiplication and division, fractions and simple ratio sharing. They meet unit prices and speed in earlier years. This sheet brings these ideas together and asks pupils to choose a method rather than follow a set one.
After this, pupils move on to more formal work on proportion, scaling and rates of change. In Key Stage 4 they meet harder ratio problems and measures that combine two quantities. A secure habit of finding one part or one unit helps with all of them.
Questions parents and teachers ask
- What age is Rates and Ratios Cipher for?
It is written for Year 9 (ages 13 to 14), in Key Stage 3. It also works as revision for older pupils, or as a stretch task for confident Year 8 pupils who are comfortable with ratio.
- What will pupils practise?
Pupils practise rate, best buy and ratio problems, including speed, scaling an amount and sharing in a ratio. They then use a key to turn their answers into letters and decode a hidden word.
- How do I use it?
Pupils solve each question, find the answer in the key row, and write its letter in the matching box. The letters reveal the codeword. Page 2 has the notes and answers for the grown-up to check.
- What if it feels too hard?
Suggest finding the amount for one person or one unit first. Then scale up. A calculator is allowed for the best buy question. Working through the first case file together can also help.
- Is it free, and do I need colour?
Yes, it is free to print for home and classroom use. No colour is needed. It prints well in black and white on plain A4 paper, so it is cheap to use with a whole class.
- Can teachers use it in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 has support and stretch ideas for mixed groups.
- Is this a screen free activity?
Yes. It needs only paper and a pencil, plus a calculator for the best buy question if you allow one. It suits quiet time, rainy days, homework 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.