Mini Minds Hub · Free printable
Solving Two Step Equations: Free Printable Worksheet for Year 8
- ForYear 8
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Solving Two Step Equations is a free printable algebra worksheet for Year 8 (ages 12 to 13) in Key Stage 3. Children solve equations such as 2x + 3 = 11 by undoing each step in the right order. It takes about 15 minutes, needs only a pencil, and page 2 gives the grown-up notes, help and stretch ideas 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 solve a set of equations, each with an unknown x. Some have a number multiplying x with a number added or taken away. Others have x divided by a number, then a number added or taken away. Each one takes two steps to undo. There is space under every question to show working and write the answer. Children then check by putting their answer back into the equation.
- 2x + 3 = 11
- 3x - 5 = 16
- 5x + 2 = 27
- 4x - 7 = 17
- x/2 + 3 = 9
- x/3 - 1 = 4
- 6x + 5 = 29
- 2x - 5 = 9
Worked example with different numbers
Solve 10x + 14 = 94
This equation uses different numbers from the sheet. It shows two ways to think about the same job.
Method 1: keep the balance- Write the equation: 10x + 14 = 94.
- Take 14 from both sides. Now 10x = 80.
- Divide both sides by 10. Now x = 8.
- Check: 10 × 8 = 80, and 80 + 14 = 94. It matches.
- Read the steps forwards. Start with x, multiply by 10, then add 14 to reach 94.
- Go backwards. The last step was add 14, so take 14 from 94 to get 80.
- The step before was multiply by 10, so divide 80 by 10 to get 8.
Four habits for two step equations
Spot the two steps
Look at the side with x. Name what has been done to x, and in what order. For example, x may have been multiplied, then something added.
Undo the last step first
Start with the step that happened last. This is usually the number added or taken away. Do the opposite operation.
Do the same to both sides
Whatever you do to one side of the equals sign, do to the other. This keeps the equation true.
Check every answer
Put your answer in place of x in the original equation. If both sides match, you can be confident it is right.
Why undo in a set order?
An equation says two things are equal. In a two step equation, the unknown has had two operations done to it. To find it, we undo those operations. The key idea is that they must be undone in reverse order, starting with the one that happened last.
Think about getting dressed. You put on socks, then shoes. To undo that, you take off shoes first, then socks. Equations work the same way. Each undoing step uses an inverse operation, such as addition against subtraction, or multiplication against division. Doing the same to both sides keeps the equation balanced.
Skills and curriculum link
- Solving equations
- Inverse operations
- Working in reverse order
- Keeping an equation balanced
- Checking answers
Ideas that help with equations
- Inverse pairsAddition and subtraction undo each other. Multiplication and division undo each other. Match each step to its opposite.
- Reverse orderUndo the operations backwards, like taking off shoes before socks. The last thing done is the first thing undone.
- BalanceAn equals sign means both sides have the same value. Doing the same thing to both sides keeps them equal.
- SubstitutionReplacing x with a number tests an answer. If both sides give the same value, the answer works.
Key words
- EquationA statement that two things are equal, with an equals sign between them.
- UnknownA letter, such as x, that stands for a number we need to find.
- SolveFind the value of the unknown that makes the equation true.
- Inverse operationAn operation that undoes another. Adding undoes subtracting, and dividing undoes multiplying.
- TermA part of an expression, such as 3x or 7, separated by plus or minus signs.
- SubstituteReplace a letter with a number, often 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.
- Read the first equation together. Ask your child to say what has been done to x, and in which order.
- Let them work through the questions on their own for about 15 minutes. Ask them to write each step on a new line.
- Mark together using page 2. Ask, "How did you decide which step to undo first?" The reasoning matters as much as the answer.
- Come back another day to redo any tricky questions. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Draw a balance with the equation on it. Take the same amount off both sides, one step at a time. Say each step aloud, such as "take away the number added", then "divide both sides". Try the first few questions with an adult first.
To stretch confident children
Write three two step equations that all have the same answer, and choose that answer yourself. Swap with a partner and solve each other's. Then write one equation where x is divided first, and explain how you would undo it.
Make it a game
Play Guess My Number. One player secretly picks a number, then multiplies it and adds or takes away something. They say only the result. Their partner writes an equation and solves it to find the number. Swap roles after each round.
Mistakes to watch for
Watch forA child undoes the multiplying or dividing first, so the added or subtracted number gets left out or mixed up.
Try thisGo backwards through the steps. Undo the number added or taken away first, then deal with the multiplying or dividing.
Watch forA child does an operation to one side only, such as taking a number from the left but not the right.
Try thisDraw a balance. Remind them that whatever happens on one side must happen on the other to keep it level.
Watch forA child sees x divided by a number and divides again instead of multiplying.
Try thisAsk what undoes dividing. Test it with a simple number: 12 divided by 3 is 4, and 4 times 3 gets back to 12.
Talk about it
- How do you know which step to undo first?
- Why do we do the same thing to both sides of an equation?
- What is the inverse of adding? What is the inverse of dividing?
- How can you check an answer without looking at page 2?
- Can you make up a two step equation that is easy to solve? What makes it easy?
- Where else do we undo things in reverse order, in daily life?
Take it off the page
Balance scales
Use kitchen scales or a homemade balance with small objects. Show that taking the same amount from both sides keeps it level. This makes the idea of balance real.
Number machine
Draw a two step machine on paper, such as times a number then add a number. Give a partner the output and ask them to run the machine backwards.
Equation cards
Write equations on slips of paper and answers on others. Mix them up and match each equation to its answer by solving.
Who it is for
Parents
Sit beside your child for the first equation, then let them lead. Ask them to explain each step in their own words. Fifteen minutes is plenty. If they get stuck, try the balance drawing.
Teachers
Use it as practice after teaching inverse operations, as a starter or plenary, or as homework. Page 2 has the answers for quick marking, plus support and stretch ideas for mixed ability groups.
Home educators
This fits into a wider algebra plan after one step equations and inverse operations. It is free to print again for brothers, sisters or revision a few weeks later. Ask learners to talk through their method.
Where this fits in maths
Before this sheet, children meet inverse operations and solve one step equations. They also learn that a letter can stand for a number, and that an equals sign shows two sides with the same value.
After this sheet, children can move on to equations with the unknown on both sides, equations with brackets, and forming equations from word problems. These all build on the habit of keeping both sides balanced. Solving linear equations is a core part of the Key Stage 3 algebra strand.
Questions parents and teachers ask
- What age is Solving Two Step Equations for?
It is written for Year 8 (ages 12 to 13) in Key Stage 3. It suits children who already know inverse operations and are ready to apply them in two steps.
- What will children practise?
Children practise solving equations in two steps. They undo addition or subtraction first, then multiplication or division, and check each answer by putting it back into the equation.
- How long does it take?
It takes about 15 minutes. Children can work faster or slower, and you can split it over two sittings. Mark it together afterwards using page 2.
- What if it feels too hard?
Slow down and use a balance drawing. Write the equation, then take the same amount off both sides, one step at a time. Page 2 has more help ideas for the grown-up.
- 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 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 it prints well in black and white.
- Is it free, and is it screen free?
Yes to both. It is free to print for home and classroom use. It needs only paper and a pencil, so 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.