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Substitution: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Substitution is a free printable maths worksheet for Year 7 (ages 11 to 12) in Key Stage 3. Children swap letters for values in simple algebraic expressions, then work out the answer. It takes about 15 minutes, 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 meet numbered questions with space to write each answer. The expressions use the letters a and b. Some ask for a sum or a difference, some for a multiple like 2a, some for a product, and one asks for a squared. A few combine two steps, such as a multiple and then an add or take away. Children replace each letter with its value, then work out the result.
- a + b
- 2a
- b - a
- 3b
- a x b
- 2a + b
- 4a - b
- a squared
A worked example
Work out 5m + 7 when m = 6.
This example uses a different letter and different numbers from the sheet. It shows two ways to think about the same substitution.
Method 1: write the numbers in place- Replace m with 6. Write 5 x 6 + 7.
- Multiply before you add: 5 x 6 = 30.
- Now add: 30 + 7 = 37.
- 5m means 5 lots of m.
- m is 6, so 5 lots of 6 is 30.
- Then add the 7 that is left in the expression: 30 + 7 = 37.
What is substitution?
In algebra, a letter stands for a number. Substitution means replacing the letter with a given value, then working out the answer. If a is 4, then every a in the expression becomes 4. The expression stays the same. Only the letter changes. This is one of the first algebra skills children use, and it comes up again and again in later maths.
Expressions are read in a set order. Multiplication and powers are done before adding and taking away, unless brackets say otherwise. A number written next to a letter, like 2a, means multiply. Writing the numbers in place first helps children see the sum clearly. It also makes it easier to spot where an error crept in.
Skills and curriculum link
- Substituting into expressions
- Understanding algebra notation
- Order of operations
- Multiplying and squaring
- 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 substitute numbers into a simple expression.
- I can work out the value.
- I can check my answer.
Ideas that help with substitution
- Letters are numbersA letter in an expression stands for a number. The question tells you which number to use.
- Next to means timesA number written right next to a letter means multiply. It does not mean the two digits sit side by side.
- Multiply before addWhen an expression has more than one step, do multiplication first. Then add or take away.
- Squared means times itselfA number squared is that number multiplied by itself. It is not the number doubled.
Key words
- VariableA letter that stands for a number that can change.
- ExpressionA group of numbers and letters with operations, like 3n + 2. It has no equals sign.
- SubstituteSwap a letter for its value.
- EvaluateWork out the value of an expression.
- TermOne part of an expression. In 3n + 2, the terms are 3n and 2.
- SquaredMultiplied by itself. 5 squared is 5 x 5.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
- Remind your child that a number next to a letter means times, so 2a means 2 times a.
- Work through the first question together. Talk about each choice, then let your child try the rest alone for about 15 minutes.
- Check the work against page 2. Ask, "How did you work that out?" The reasoning matters as much as the answer.
- Come back another day. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Write the sum with the numbers in place before working it out. For 3a when a is 7, write 3 x 7 first. Then calculate. Do the first few questions together, and say each step out loud as you write it.
To stretch confident children
Choose your own values for a and b. Write three expressions for a partner to solve, including one with two steps. Then swap back and mark each other's work. Try to write one expression that gives the same answer for two different pairs of values.
Make it a game
Swap values with a partner and race to find the answers. One player picks values for a and b. Both work out the same expression. The first to finish with the correct answer scores a point. Swap roles each round.
Mistakes to watch for
Watch forA child reads 6c as 6 and c side by side, so with c = 2 they write 62.
Try thisSay it as "6 times c". Write 6 x 2 and work out 12. Remind them that a number next to a letter means multiply.
Watch forA child adds before multiplying in 5m + 7 with m = 6, and works out 5 x 13 = 65.
Try thisWrite the numbers in place: 5 x 6 + 7. Do the multiplication first to get 30, then add 7 to make 37.
Watch forA child doubles instead of squaring, so n squared with n = 5 becomes 10.
Try thisSay that squared means times itself. Write 5 x 5 and work out 25.
Talk about it
- What does the letter stand for in this question?
- How do you know 2a is a multiplication?
- Why do we write the numbers in place before we work it out?
- What would change if a was a different number?
- Which question was trickiest, and why?
- How could you check your answer is sensible?
Take it off the page
Mystery value cards
Write a number from 1 to 10 on small pieces of paper and turn them face down. Pick one for a, write an expression and work it out. Pick a new card and see how the answer changes.
Shop price rule
Pretend each pencil costs p pence. Write expressions for 3 pencils, or 4 pencils and a rubber costing 10 pence. Then choose a value for p and work out each total.
Number machine
Draw a machine with a rule such as times 3, then add 2. Feed numbers in and write the results. Then write the rule as an expression, like 3n + 2.
Who it is for
Parents
Sit beside your child for the first question, then let them lead. About 15 minutes is plenty. If they get stuck, ask them to write the sum with the numbers in place before working it out.
Teachers
Use it as a starter, plenary, early finisher task, homework or table activity after teaching substitution. It needs no preparation beyond printing. Page 2 gives support, stretch and answers for mixed ability groups.
Home educators
Print it as part of a wider maths plan, or for revision a few weeks later. It pairs well with number puzzles and everyday talk about rules and patterns. It is free to print again for brothers and sisters.
Where substitution fits
Before this, children learn that letters can stand for unknown numbers, and they practise the four operations and the order in which to do them. Confident number work makes substitution much easier.
After this, children use substitution to work with formulae, simplify expressions and solve equations. Being able to swap in values quickly and accurately is a skill they will use throughout Key Stage 3 and beyond.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- What do you do when you see 3a and a is 4?
- How did you work out the value?
- What changes if a is a different number?
Questions parents and teachers ask
- What age is Substitution for?
It is written for Year 7 (ages 11 to 12) in Key Stage 3. It suits children who have met letters standing for numbers and are practising the first steps of algebra.
- What does 2a mean?
It means 2 times a. A number next to a letter means multiply. If a is given a value, replace the a with that value and multiply, so the number and value are not written side by side.
- How long does it take?
The sheet is designed for about 15 minutes of work alone. Working through the first question together at the start helps children settle into the method.
- Does the sheet include answers?
Yes. Page 2 is for the grown-up and includes notes on how to use the sheet, help for children who find it hard, a stretch idea and the answers.
- What if my child finds it hard?
Ask them to write the sum with the numbers in place first, such as 3 x 7, before working it out. Do the first questions together and say each step out loud.
- Is it a screen free activity?
Yes. It needs only paper and a pencil, so it works well for quiet time, rainy days and school holidays. Children read, think and write by hand.
- Can teachers use it in class?
Yes. It works as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and black and white printing works well on plain A4 paper.
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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.