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Word Problems to Equations: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Word Problems to Equations is a free printable algebra worksheet for Year 7 (ages 11 to 12), in Key Stage 3. Children read short "I think of a number" stories and turn each one into an equation, using n for the number they do not know. Then they solve it and check that the answer fits the story. It 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 meet short stories about a number someone is thinking of. Each story gives a clue, such as adding to the number, multiplying it, or dividing it, and then tells them the answer. Some stories need more than one step. For each one, children write an equation using n, solve it, and write their answer in the space provided.
- I think of a number and add 7. The answer is 15.
- I think of a number, then multiply it by 4. The answer is 36.
- I think of a number, double it and subtract 3. The answer is 11.
- A number divided by 5 is 6.
A worked example
I think of a number and add 12. The answer is 25. What is my number?
This example uses different numbers from the sheet. It shows two ways to think about the same equation.
Method 1: write it, then undo it- Call the number n. The story says n plus 12 makes 25.
- Write the equation: n + 12 = 25.
- Adding 12 is undone by taking away 12. Do that to the 25.
- 25 take away 12 is 13, so n = 13.
- Check: 13 + 12 = 25. It matches the story.
- Draw one long bar for the answer, 25.
- Split it into two parts: one part is n and the other part is 12.
- The unknown part is what is left when 12 is taken from the whole bar.
- 25 take away 12 is 13, so n = 13.
Turning a story into an equation
Find the unknown
Ask what the story does not tell you. Call that number n. Write down what n stands for, so you do not lose track of it.
Spot the operations
Look for words that tell you what happens to the number, such as add, multiply, double, subtract or divided by. Put them in the order the story gives them.
Write the equation
Build the equation from left to right as you read. Put n first, then each action in turn. The final amount goes after the equals sign.
Solve and check
Undo each action, working backwards. Then put your answer back into the story and read it aloud. It should make sense.
Why do we use letters in maths?
In algebra, a letter stands for a number. Sometimes we do not know the number yet, as in these stories. Sometimes the number can change. Any letter would work, but n is a popular choice because it reminds us of number. The important thing is to say clearly what your letter means before you start.
Word problems are where algebra becomes useful. A story is just a set of instructions written in words. An equation is the same instructions written in symbols. Once children can move between the two, they can solve problems that are too hard to guess. This skill underpins much of the algebra they will meet in Key Stage 3 and beyond.
Skills and curriculum link
- Forming equations
- Algebra
- Using n for an unknown
- Solving equations
- Problem solving
- 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 | Algebra | Year 7 |
What children will be able to do
- I can use n for the number I do not know.
- I can write an equation for a short story.
- I can solve the equation and check my answer.
Ideas that help with equations
- Words become symbolsEach action word in a story matches a symbol. Add matches plus, multiply matches times, and divided by matches the division sign. Learning these pairs makes equations quicker to write.
- Undo to solveEvery operation has an inverse that undoes it. Adding and taking away undo each other. Multiplying and dividing undo each other. To find n, undo what was done to it.
- Work backwardsIf a story has two steps, undo the last step first, then the one before. Backwards order is the reverse of the order in the story.
- Check by substitutingPut your answer in place of n and work through the story again. If you land on the number the story gave, your answer is right.
Key words
- EquationA statement that two things are equal, written with an equals sign. For example, n + 9 = 20.
- UnknownA number we do not know yet and are trying to find.
- VariableA letter that stands for a number, such as n.
- Inverse operationAn operation that undoes another. Adding and taking away undo each other.
- SolveFind the value that makes an equation true.
- SubstituteReplace a letter with a number, usually to check an answer.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
- Ask your child to read each story twice and underline the key numbers.
- Work through the first story together. Talk about what n stands for and how each word becomes a symbol.
- Let your child write and solve the rest. Ask them to check each answer against the story, then check with page 2.
- Come back to it another day. Repeating a familiar activity builds confidence.
Help, stretch and game ideas
If it feels too hard
Say the story as a sentence with a gap. For example, "I think of a number and add 9. The answer is 20" becomes "gap plus 9 makes 20". Then replace the gap with n. Do one story at a time and use a drawn bar to show the unknown.
To stretch confident children
Write two stories of your own for a partner to turn into equations. Try to make one of them need two steps. Keep your own answers on a separate piece of paper, so you can check your partner's work afterwards.
Make it a game
Swap sheets and mark each other's equations. Give one point for a correct equation and one point for a correct solution. Then each player writes a new story and the other races to write its equation.
Mistakes to watch for
Watch forA child writes the numbers from the story but leaves out n, so there is no equation.
Try thisAsk, "What number do we not know?" Write n for it first, then build the equation around it.
Watch forA child solves by repeating the action in the story, for example adding again when they should undo the adding.
Try thisRemind them that to find n they must undo what was done. Use a bar drawing to show the unknown part.
Watch forA child writes a division the wrong way round, for example the number on top and n underneath.
Try thisRead the story aloud, slowly. Ask which number is being shared out. That number goes first, then divided by, then the divisor.
Talk about it
- What does n stand for in this story?
- Which word in the story tells you what to do to the number?
- How do you know which operation to use to undo the step?
- Can you write the same equation in a different way?
- How could you check your answer without looking at page 2?
- Can you make up a story that matches an equation of your own?
Take it off the page
Number thinking game
Take turns to think of a number and give clues in words. The other person writes an equation on paper, then solves it. Check by saying the story back.
Balance scales
Use a kitchen balance or draw one. Put unknown weights in a bag and show how taking the same from both sides keeps the balance. This is a good picture for equations.
Story to equation cards
Write stories on small pieces of paper and equations on others. Mix them up and match each story to its equation. Make sure each match is checked aloud.
Who it is for
Parents
Sit beside your child for the first story, then let them lead. Ask them to explain their equation in their own words. If they get stuck, return to the sentence with a gap and swap in n.
Teachers
Use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing. Listen for reasoning, not just answers. Page 2 supports mixed ability groups with help, stretch and answers.
Home educators
Print it as part of a wider maths plan. It works well after work on number operations and before more complex equations. You can print it again for brothers and sisters or use it later for revision.
Where this fits in maths
Before this, children work with missing number problems and learn that a letter can stand for an unknown. They also learn that operations have inverses, so adding and taking away undo each other. Confident number facts make equations much easier to solve.
After this, children solve equations with more than one step and meet unknowns on both sides. They then use equations to model more complex situations and work with formulae. The habit of defining n, writing the equation and checking the answer carries through all of it.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- What does n stand for in your equation?
- How did you turn the words into an equation?
- How can you check that your answer fits the story?
Questions parents and teachers ask
- What age is Word Problems to Equations for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. It suits children who have met the idea of a letter standing for a number and are ready to use it in short problems.
- What will children practise?
They write and solve simple equations for short stories, using n for the unknown. They practise reading carefully, choosing the right operations and checking that their answer fits the story.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or revision, and share it with a class.
- What if my child finds it hard?
Try saying the story as a sentence with a gap, then replace the gap with n. Work on one story at a time and use a bar drawing to show the unknown. Page 2 has more help.
- Is it suitable for teachers to use 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, stretch and answers.
- Is this a screen free activity?
Yes. It is a printable that needs only paper and a pencil. That makes it useful for quiet time after school, rainy days and school holidays.
- Do I need to print in colour?
No. It prints well in black and white on plain A4 paper. Print both pages and keep page 2 for the grown up.
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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.