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Simple Formulae: Free Printable Worksheet for Year 6
- ForYear 6
- StageKey Stage 2
- CostFree
- FormatPrintable PDF
Simple Formulae is a free printable maths worksheet for Year 6 (ages 10 to 11). Children put numbers into a rule written with letters and work out the answer. Some rules take one step. Others take two. The sheet also includes rules for the area and perimeter of a rectangle. It takes about 15 minutes and needs only a pencil.
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. It has notes, help, a stretch idea and the answers. Black and white printing works well.
What is on the sheet
Children read a rule written with letters, such as one that links b to a, and swap the letter for a number. Some rules need one step. Others need two, such as multiplying and then adding. The sheet also has rules for the area and perimeter of a rectangle, where two letters are swapped for numbers. There is space under each question to write the answer.
- b = a + 4. Find b when a = 6
- b = a x 3. Find b when a = 5
- b = a - 2. Find b when a = 9
- b = 2a + 1. Find b when a = 4
- b = 10 - a. Find b when a = 3
- b = 3a + 2. Find b when a = 5
- A = l x w. Find A when l = 7 and w = 4
- P = 2l + 2w. Find P when l = 6 and w = 3
A worked example
t = 8m + 12. Find t when m = 11
This is a different formula from the ones on the sheet. It shows two ways to set out the working.
Method 1: swap, then work in order- Write the formula with the number in place of the letter: t = 8 × 11 + 12.
- Multiply first: 8 × 11 = 88.
- Then add: 88 + 12 = 100.
- Read 8m as 8 times m. The rule says: multiply m by 8, then add 12.
- Start with 11. Multiply by 8 to get 88.
- Add 12 to get 100.
What is a formula?
A formula is a rule that uses letters to stand for numbers. Instead of writing a new sum every time, we write the rule once and put different numbers in. The letter is a place holder. The rule tells us what to do with whatever number takes its place. Builders, scientists and engineers all rely on formulae.
Swapping a letter for a number is called substitution. Two things help. First, a number written next to a letter, like 5n, means 5 times n. Second, multiplication is done before adding or subtracting. Area is the space inside a flat shape. Perimeter is the distance around its edge. Each has its own rule.
Skills and curriculum link
- Reading formulae
- Substitution
- Order of operations
- Multiplying and adding
- 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 6 |
What children will be able to do
- I can read a simple formula.
- I can swap a letter for a number.
- I can work out the answer step by step.
Useful things to know before you start
- Letters stand for numbersA letter is a place holder. Each question tells you which number to put in its place.
- A number next to a letter means timesWritten side by side, 6n means 6 times n. There is no hidden plus sign.
- Multiply before you addIn a two step rule, do the multiplying first. Then add or subtract the last number.
- Write the swap firstCopy the rule, then rewrite it with the number where the letter was. Work out the answer from there.
Key words
- FormulaA rule that uses letters and numbers to show how to work something out.
- SubstituteSwap a letter for a number.
- VariableA letter that stands for a number that can change.
- AreaThe space inside a flat shape, measured in square units.
- PerimeterThe distance all the way around the edge of a shape.
- Length and widthThe two side measurements of a rectangle.
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 formula aloud. Ask what the letters stand for and which number goes where.
- Let your child rewrite the rule with the number in place of the letter, then work it out step by step.
- Check together using page 2. Ask, "How did you work that out?" The reasoning matters as much as the answer.
- Come back another day and redo any questions that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Write the sum with the number in place of the letter first. Circle the number that replaces the letter. Say the rule in words, such as "times three, then add two". Try the shorter one step rules first and come back to the rest later.
To stretch confident children
Make up a formula of your own and swap it with a friend. Write a question for them to solve, with the number to put in. Check each other's answers. Then try a rule that needs two steps.
Make it a game
Make a function machine from a box. Choose a secret rule. One player posts in a number on a card, and the other works out the rule and writes the number that comes out. Swap roles, then test your formulae.
Mistakes to watch for
Watch forA child reads 2a as 2 plus a, or joins the digits so that 2a with a = 8 becomes 28.
Try thisRemind them that a number next to a letter means times. Write 2a as 2 × a, then swap in the number.
Watch forA child adds before multiplying. With 8m + 12 and m = 11, they work out 11 + 12 first.
Try thisSay the rule in words. Multiply first, then add. Underline the multiplication so it is done first.
Watch forA child mixes up the area rule and the perimeter rule for a rectangle.
Try thisAsk what each one measures. Area is the space inside. Perimeter is the distance around. Sketch the rectangle and label the sides.
Talk about it
- What does the letter stand for in this formula?
- How do you know which step to do first?
- What would change if the number in place of the letter were bigger?
- Why do we write a rule with letters instead of a new sum each time?
- How are area and perimeter different?
- Can you make up a formula of your own?
Take it off the page
Function machine
Use a box and some paper slips. Pick a rule, post a number in and write the number that comes out. Ask a family member to guess the rule.
Rectangle measuring
Measure the length and width of a book or table in centimetres. Use the area and perimeter rules from the sheet to work them out.
Rule cards
Write simple rules on cards, such as "times four, then add one". Draw a number card, apply the rule and write the result as a formula.
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 rewrite the rule with the number in place of the letter.
Teachers
Use it as a starter after teaching substitution, as an early finisher task or as a homework sheet. The rules move from one step to two steps, so it suits mixed ability groups. Page 2 has support, stretch and answers.
Home educators
Pair it with practical measuring around the house so the area and perimeter rules feel real. It can be repeated for revision a few weeks later or used again with brothers and sisters.
Where this fits in maths
Before this, children learn that a symbol or letter can stand for a missing number. They also learn to use the order of operations, so multiplying comes before adding. Practice with area and perimeter of rectangles gives them real rules to work with.
After this, children can go on to make up their own formulae, work with more than one letter and solve simple missing number problems. These skills lead into the algebra they meet in Key Stage 3.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- What does the letter stand for in this formula?
- How do you work out the answer when a = 5?
- Can you make up a formula of your own?
Questions parents and teachers ask
- What age is Simple Formulae for?
It is written for Year 6 (ages 10 to 11), in Key Stage 2. Some children in Year 5 may manage the one step rules, and some may need extra support with the two step rules.
- What will children practise?
They practise substituting numbers into simple formulae. That means reading a rule with letters, swapping each letter for a number and working out the answer in the right order.
- How long does it take?
It takes about 15 minutes. Children who like to talk through their working may take a little longer. You can stop after the first few questions and finish another day.
- What if it feels too hard?
Write the sum with the number in place of the letter first. Say the rule in words, and remember that a number next to a letter means times. Start with the one step rules.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or revision a few weeks later.
- 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 page 2 gives support and stretch ideas for mixed ability groups.
- Is this a screen free activity?
Yes. It needs only paper and a pencil, so it suits quiet time, rainy days and school holidays. It also prints well in black and white 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.