Mini Minds Hub · Free printable
Solving One Step Equations: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Solving One Step Equations is a free printable maths worksheet for Year 7 (ages 11 to 12), in Key Stage 3. Children use the balance method to find the value of x. They meet equations that need adding, subtracting, multiplying or dividing to solve. 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 your child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children work through numbered equations, each with space to write their answer. Some have a number added to x, some have a number taken away, some have x multiplied by a number and some have x divided by a number. For each one, children choose the inverse operation, apply it to both sides and find x. They can then check by putting the answer back in.
- x + 7 = 15
- x - 4 = 9
- 3x = 21
- x / 5 = 4
- x + 12 = 30
- 6x = 48
- x - 9 = 11
- x / 3 = 7
A worked example
Solve x + 16 = 40
This is a different equation from the ones on the sheet. It shows two ways to think about the same step.
Method 1: the balance method- Think of the equals sign as the middle of a set of scales. Both sides must stay equal.
- Adding 16 is the operation we want to undo. Its inverse is subtracting 16.
- Subtract 16 from both sides. On the left, x + 16 becomes x. On the right, 40 minus 16 is 24.
- Write x = 24.
- Draw a pair of scales. Put x and 16 on the left pan and 40 on the right pan.
- Cross out 16 from the left pan. To keep the scales level, take 16 away from the right pan too.
- The left pan now holds only x. The right pan holds 24.
What is an equation?
An equation is a statement that two amounts are equal. It has an equals sign in the middle. In algebra, a letter such as x stands for a number we do not know yet. Solving the equation means finding the number that makes the statement true. A one step equation needs just one operation to get x on its own.
The balance method is a reliable way to think about this. Whatever you do to one side of the equals sign, you must do to the other, or the two sides stop being equal. To undo an operation, use its inverse. Adding and subtracting are inverses. So are multiplying and dividing. Putting the answer back in is a quick check.
Skills and curriculum link
- Solving one step equations
- Inverse operations
- Using the balance method
- Finding the value of a letter
- Checking answers by substitution
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 an inverse operation to solve an equation.
- I can find the value of the letter.
- I can check my answer by putting it back in.
Ideas that help with equations
- Keep the balanceThe equals sign means both sides have the same value. Do the same thing to both sides and they stay equal.
- Pair up the inversesAdding undoes subtracting, and subtracting undoes adding. Multiplying undoes dividing, and dividing undoes multiplying.
- Write every stepWrite what you do on each side, one line at a time. It makes mistakes easy to spot.
- Always checkPut your answer in place of x in the original equation. If both sides match, the answer works.
Key words
- EquationA statement that two amounts are equal, with an equals sign between them.
- UnknownA number we do not know yet. In algebra it is often shown by a letter such as x.
- Inverse operationAn operation that undoes another. Subtracting is the inverse of adding.
- Balance methodDoing the same to both sides of an equation so that it stays equal.
- SolveFind the value of the unknown that makes the equation true.
- SubstitutePut a number in place of a letter. We do this 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.
- Work through the first equation together. Say out loud what you do to both sides.
- Let your child finish the rest alone. Ask them to write each step, not just the answer.
- Check against the answers on page 2. Ask, "How did you find x?" and listen for the reasoning.
- Come back to it another day and redo any that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Draw a pair of scales for each equation. Put the equation on the scales, then show taking the same amount from both sides. Seeing the scales stay level helps children trust the method. Start with the adding equations before moving on to the others.
To stretch confident children
Write three more equations of your own and swap them with someone to solve. Make one for each of adding, multiplying and dividing. Then try writing an equation where the answer for x is a number you choose in advance.
Make it a game
Play equation swap. Each player secretly picks a number for x, then writes an equation that has that number as its answer. Swap papers and solve. Score a point for each correct solution, and check by substituting.
Mistakes to watch for
Watch forA child does the operation to one side only, so the two sides are no longer equal.
Try thisUse the scales picture. Ask, "If I take something off one side, what happens to the balance?" Then do the same to both sides.
Watch forA child sees x + 2 = 10 and adds 2 to get 12, using the same operation instead of the inverse.
Try thisAsk what has been done to x, then what undoes it. Adding 2 is undone by taking 2 away.
Watch forA child sees 5x = 20 and takes 5 away from 20, because 5x looks like an addition.
Try thisExplain that 5x means 5 times x. Its inverse is dividing by 5. Check by multiplying the answer by 5.
Talk about it
- What is the inverse of adding a number?
- Why must we do the same thing to both sides?
- How can you tell which operation to use first?
- What does 3x mean? Is it the same as 3 + x?
- How can you check that your answer is right?
- Can you make up an equation that you think is tricky?
Take it off the page
Scales at home
Use kitchen scales or a homemade balance with a coin and some weights. Talk about how adding or removing the same amount keeps things level. An adult should help with any sharp or heavy items.
Mystery number cards
Write an equation on a card with the answer on the back. Shuffle the cards, solve each one and flip to check.
Inverse pairs
Write the four operations on paper and draw arrows linking each one to its inverse. Keep it by your desk while you work.
Who it is for
Parents
Sit beside your child for the first equation, then let them lead. You do not need to be an algebra expert. Ask them to explain each step, and use the answers on page 2 to check.
Teachers
Use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing. Ask pupils to show the step on both sides, then check by substituting.
Home educators
Print it as part of a wider maths plan. It pairs well with other algebra and number work, and you can reuse it for brothers and sisters or for revision a few weeks later.
Where this fits
Before this, children practise the four operations and work with missing number problems. Knowing that adding and subtracting undo each other, and so do multiplying and dividing, makes one step equations feel natural.
After this, children move on to equations that need more than one step, then to equations with letters on both sides and with brackets. The balance method and the habit of checking by substitution carry through all of these.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- What is the inverse of adding 5?
- How did you find the value of x?
- How can you check that your answer is right?
Questions parents and teachers ask
- What age is Solving One Step Equations for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. It also works as revision for older pupils, or as a stretch task for confident younger children who already know their inverse operations.
- What will children practise?
They practise using inverse operations to solve one step equations. They find the value of the letter using the balance method, then check their answer by putting it back into the equation.
- How do I use it?
Work through the first equation together and say what you do to both sides. Then let your child finish alone. Check against the answers on page 2 and ask them to explain their method.
- What if it feels too hard?
Draw a pair of scales for each equation and show taking the same amount from both sides. Start with the adding equations before trying the others. Come back to the sheet on another day.
- 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 costs very little to use.
- 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 help and a stretch idea for mixed ability groups.
- Does the sheet 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.
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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.