Year 6 maths · Key Stage 2 · Algebra

Year 6 algebra: formulae, sequences and missing numbers

Year 6 is the first year in which algebra appears as its own part of the maths curriculum. Children use letters and symbols to stand for numbers they don’t know yet or that can change, use simple formulae, describe number sequences, write missing number problems with letters, and find the pairs of numbers that fit an equation with two unknowns. The aim is to see algebra as a tidy way of describing patterns and puzzles they already understand.

Introduction to algebra, explained

In algebra, a letter stands for a number. Sometimes it is a number we want to find, as in a + 7 = 20, where a must be 13. Sometimes it is a number that can change, as in a formula. Children have been solving missing number questions with boxes since Year 1, such as ? + 7 = 20. Year 6 replaces the box with a letter and asks them to say what it means. Letters are used in familiar settings: missing numbers, lengths, coordinates and angles.

A formula is a rule written with letters that works for any numbers. Area of a rectangle is written A = l × w, so a rectangle 8 cm long and 3 cm wide has an area of 8 × 3 = 24 cm². Children substitute numbers into a formula and work out the answer. Other examples are a cost rule such as C = 3 × n + 2 (£3 per ticket plus a £2 booking fee) or a formula from science. Children also meet the idea that a + b = b + a, because addition can be done in either order, which is a first step to simplifying expressions.

A linear sequence goes up or down by the same amount each time. In 5, 9, 13, 17, … the rule is “add 4”, and the rule applies from term to term. Children generate sequences from a rule and describe them in words, and may link a term’s position to its value: multiply the position by 4 and add 1. Finding and using the nth term formally, written as 4n + 1, is Key Stage 3 work, so in Year 6 the rule is usually described in words.

Some problems have two unknowns. If a + b = 10, there are many pairs of whole numbers that work: 1 and 9, 2 and 8, 3 and 7, and so on. Children are taught to find them in an organised way, so none are missed, and to notice patterns: as a goes up by one, b goes down by one. Listing possibilities for two variables is the foundation of later work on solving equations and drawing graphs.

Many schools use bar models and number puzzles to make this concrete. A bar split into a and 7 with a total of 20 shows what is missing. Children are encouraged to explain their thinking in words as well as write the answer. You will often see a child check by substituting the answer back in: if a = 13, does 13 + 7 = 20? Yes, so the answer is right.

Words your child will hear

Variable: A letter that stands for a number that can change or is not yet known.
Unknown: A number we are trying to find, usually shown by a letter such as a or n.
Formula: A rule written with letters, such as A = l × w for the area of a rectangle.
Equation: A number sentence with an equals sign, where one side must be worth the same as the other.
Term: One number in a sequence.
Term-to-term rule: The rule for getting from one term in a sequence to the next, such as “add 4”.
Substitute: Replace a letter with a number.

What the National Curriculum says

In Year 6, pupils should be taught to:

Use simple formulae
Generate and describe linear number sequences
Express missing number problems algebraically
Find pairs of numbers that satisfy an equation with 2 unknowns
Enumerate possibilities of combinations of 2 variables

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Two positive whole numbers, a and b, satisfy a + 2 × b = 11. Find every possible pair.

Be clear what the rule says: a, plus two lots of b, makes 11. Because a and b must be positive whole numbers, b can’t be 0.
Work through the values of b in order, starting at 1. If b = 1, then 2 × b = 2, so a = 11 − 2 = 9. If b = 2, then 2 × b = 4, so a = 11 − 4 = 7.
```
b = 1  →  a = 11 − 2 = 9
b = 2  →  a = 11 − 4 = 7
```
Carry on in the same way. b = 3 gives a = 5, b = 4 gives a = 3 and b = 5 gives a = 1. If b = 6, then 2 × b = 12, which is more than 11, so there are no more pairs.
```
b = 3  →  a = 11 − 6 = 5
b = 4  →  a = 11 − 8 = 3
b = 5  →  a = 11 − 10 = 1
```
Check each pair by substituting it back in: 9 + 2 = 11, 7 + 4 = 11, 5 + 6 = 11, 3 + 8 = 11, 1 + 10 = 11. Notice the pattern: a goes down by 2 every time b goes up by 1.

The pairs (a, b) are (9, 1), (7, 2), (5, 3), (3, 4) and (1, 5).

Common mistakes and how to help

Treating a letter as a label or an object, not a number

In everyday life “a” can stand for apple, and “b” for banana. A child may read a + b as “an apple and a banana”, not as two numbers added.

What helps: Say “a is a number” whenever you read one. Swap the letter for a box or a question mark to show it is the same idea as the missing number puzzles they know.

Believing a letter always has the same value, or that different letters must have different values

If a was 3 in one question, the child keeps it as 3 in the next. And in a + b = 10, they think a and b can’t both be 5.

What helps: Explain that a letter takes its value from the question it is in. A letter can be 5 in one problem and 12 in another. Different letters can have the same value unless the question says otherwise.

Reading the equals sign as “the answer comes next”

Sums like 3 + 4 = ? teach the equals sign as a signal to give the answer, so 7 = 3 + 4 or 3 + 4 = 2 + 5 look wrong.

What helps: Describe the equals sign as a balance: both sides must be worth the same. Draw scales with 3 + 4 on one side and 2 + 5 on the other. Try missing numbers on the left: ? + 4 = 11.

Finding one pair and stopping, or finding pairs in a random order

Most maths questions have one answer, so when a question has two unknowns the child gives the first pair that works.

What helps: Ask “Are there any others?” and show how to be systematic: start with the smallest possible value for one letter and move up in steps, writing a table. It will show the complete list and the pattern.

How to help at home

Mystery number puzzles. Say “I’m thinking of a number. If I add 8, I get 21.” Then write it as n + 8 = 21 and check by substituting. Swap roles and let your child set puzzles for you with letters.
Sequence patterns around the house. Make a sequence with lolly sticks, straws or building blocks, such as a row of squares needing 4, 7, 10 … sticks. Ask how many for the next, what the rule is, and how many for the 10th.
Use a real formula. Use a rule like “cost = £4 × number of tickets + £3 booking fee”. Work out the cost for 2, 5 and 10 tickets, and ask what the cost would be if the fee were £5. Your child sees what a formula does.
All the pairs. Ask “Two numbers add up to 12. What could they be?” and encourage a full, ordered list. Then change the rule to “a and two lots of b make 12” and see how the list changes.
Talk about the equals sign. Write number sentences with the answer in different places, such as 15 = 9 + ? or 6 + 5 = 4 + ?, and let your child fill in the missing numbers. It builds the balance idea before more advanced algebra.

Leads on to

Key Stage 3: Algebraic notation and formulae
Key Stage 3: Solving linear equations
Key Stage 3: Graphs of linear and quadratic functions
Key Stage 3: Sequences and the nth term

Everything in Year 6 maths

Updated 20 October 2026.