Mini Minds Hub · Free printable
Equation Colour Mosaic: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Equation Colour Mosaic is a free printable algebra worksheet for Year 7 (ages 11 to 12), in Key Stage 3. Children solve the equation on each tile, find the answer in the colour key, then shade the tile. 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
Each tile holds a linear equation. Children solve it, then look up the answer in the key, where every value of x has its own colour. They shade the tile with that colour. There is working space on the sheet, and children check each answer by substituting it back into the equation. As the tiles fill in, the colours build into a repeating pattern.
- x = 2: Teal
- x = 3: Coral
- x = 4: Navy
- x = 5: Gold
- Tile A
- Tile B
- Tile C
- Tile D
A worked example with two steps
Solve 7x + 2 = 58
This example uses different numbers from the sheet. It shows two ways to think about a two step equation.
Method 1: keep the balance- The equation is balanced, so do the same to both sides.
- Subtract 2 from both sides. This leaves 7x = 56.
- Divide both sides by 7. This gives x = 8.
- Read the equation as a story. Start with x, multiply by 7, then add 2 to get 58.
- Undo the story from the end. Take away 2 from 58 to get 56.
- Undo the multiplying. 56 divided by 7 is 8.
Tips for solving equations
Read the equation as a story
Say what happens to x. For example, x is multiplied by 7, then 2 is added. Saying it aloud makes the steps clear before any working starts.
Undo with inverse operations
Adding and subtracting undo each other. Multiplying and dividing undo each other. Pick the inverse for each step.
Undo the steps in a sensible order
Work backwards through the story. In an equation like 7x + 2 = 58, the adding or subtracting is often undone first. If the equation has brackets or a division over the whole left side, the order can change, so read the story each time.
Check by substituting
Put your answer back in place of x. If both sides match, the answer is right. Do this before you reach for a colour.
Why equations are worth practising
An equation says that two things are equal. When a letter stands for a number we do not know, solving the equation means finding the number that makes it true. This is one of the main ideas in Key Stage 3 algebra. It moves children from finding answers by sight to using a method that works every time.
The key idea is balance. Whatever you do to one side of an equation, you must do to the other. Inverse operations are how children keep that balance while getting x on its own. Colouring tiles gives a reason to be accurate, because a wrong answer leads to the wrong colour.
Skills and curriculum link
- Solving linear equations
- Inverse operations
- Checking by substitution
- Working accurately
- Spotting patterns
Ways to help with equations
- Use the balance pictureDraw a pair of scales. Whatever you do to one side, do to the other. This shows why both sides change together.
- Write every stepPut each step on its own line, with the equals signs lined up. Clear working makes mistakes easier to find.
- Say the inverse aloudBefore writing, ask, "What is being done to x, and what undoes it?" Saying it first helps the working follow.
- Substitute to checkPut the answer back into the original equation. If the two sides match, it is right. This works on every question.
Key words
- EquationA statement that two things are equal, shown with an equals sign.
- UnknownA letter, such as x, that stands for a number we are trying to find.
- SolveFind the value of the unknown that makes the equation true.
- Inverse operationAn operation that undoes another. Adding undoes subtracting, and multiplying undoes dividing.
- SubstituteReplace a letter with a number.
- Linear equationAn equation where the unknown is not squared or raised to any power, such as 4x = 12.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
- Read the key together. Each value of x has its own colour.
- Solve each equation in the working space, then find the answer in the key and shade the tile.
- Check each answer by substituting it back into the equation before shading.
- Compare with page 2. Ask, "How did you work that out?" Then come back another day to repeat it.
Help, stretch and game ideas
If it feels too hard
Start with the equations that have one step, such as 4x = 12. Ask what operation is being done to x and what undoes it. Use the worked example on this page as a model for two step equations, and write each step on its own line.
To stretch confident children
Write your own four equations that give x = 6, then design a new colour key for them. Include at least one two step equation. Swap with a partner and check each other's work by substitution.
Make it a game
Swap sheets with a partner. Shade only half the tiles, then ask them to work out the missing colours. They must show the equation working for each tile. Swap back and check each other's answers by substituting.
Mistakes to watch for
Watch forA child changes one side of the equation but not the other.
Try thisDraw the balance scales. Remind them that both sides must change in the same way, or the equation is no longer equal.
Watch forA child divides first when the equation has an adding step, so 7x + 2 = 58 becomes 58 divided by 7.
Try thisRead the equation as a story. Ask what happened last, then undo that step first.
Watch forA child gets an answer that is not in the key.
Try thisSubstitute the answer back in. If the two sides do not match, go through each line of working and look for the slip.
Talk about it
- What is being done to x in this equation?
- Which inverse operation will undo that step?
- Why must we do the same thing to both sides?
- How could you check your answer without looking at page 2?
- Can you spot a pattern in the colours as you shade?
- What would you change to make an equation harder?
Take it off the page
Balance scales
Use a pair of kitchen scales or a drawn balance with small objects. Add the same weight to both sides and see that it stays balanced.
Think of a number
Ask a friend to think of a number, multiply it, add something and tell you the result. Work backwards to find their number.
Mosaic design
Draw a grid on squared paper. Write your own equations in the squares, make a colour key and swap with someone to solve.
Who it is for
Parents
Sit beside your child for the first tile, then let them lead. Ask them to explain each step in their own words. Praise careful checking, not only correct answers.
Teachers
Use it as a starter, plenary, early finisher task or homework. The key gives instant feedback, and page 2 offers support and stretch for mixed ability groups.
Home educators
Print it as part of a wider maths plan. It suits independent work, and you can print it again for brothers and sisters or for revision a few weeks later.
Where this fits
Before this, children have worked with number operations, missing number problems and simple one step equations. They also need to be confident with inverse operations, which are the heart of this sheet.
After this, children can move on to equations with brackets, equations with the unknown on both sides, and using formulae. Solving linear equations underpins much of later algebra, so secure, accurate habits now pay off.
Questions parents and teachers ask
- What age is Equation Colour Mosaic for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. Younger confident children and older learners who need to revisit equations may also find it useful.
- What will children practise?
Children practise solving one and two step linear equations in algebra. They use inverse operations, check answers by substitution, and use each answer to colour a tile in a repeating pattern.
- How do I use it?
Solve every equation, find the answer in the key, then shade the tile. Use the working space, and check each answer by substituting it back into the equation before shading.
- What if it feels too hard?
Start with the equations that have one step, such as 4x = 12. Use the worked example on this page as a model for two step equations, and write each step on its own line.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters, other pupils or revision.
- Do I need to print in colour?
No. It prints well in black and white on plain A4 paper. Children can shade with coloured pencils, or write the colour names or use patterns instead.
- 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 the answers and ideas for support and stretch.
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.