Maths topic
Patterns and algebra
What children learn in patterns and algebra, from their first year of school to the end of primary, and the lessons to watch together.
What's taught, year by year
The steps in patterns and algebra, in the order children usually meet them. Years are named as in Australia; the ages are a guide.
Before school ages 3–5
- Spot and talk about patterns. Notice patterns around us and say what repeats.
Foundation ages 5–6
- Copy and continue an AB pattern. Copy and extend a two-part repeating pattern with objects, colours or sounds.
- Make your own repeating pattern. Create a repeating pattern and explain what repeats.
Year 1 ages 6–7
- Repeating patterns with three parts. Continue ABC and AAB patterns and fill in a missing element.
- Find the repeating unit. Circle the part that repeats and use it to predict what comes later.
- Skip-counting patterns on a hundred grid. Colour counts of 2, 5 and 10 on a hundred grid and describe the pattern.
- The equals sign means 'the same as'. Decide whether number sentences like 5 = 3 + 2 or 4 + 1 = 2 + 3 are true.
- Missing numbers in addition and subtraction. Find the unknown in sentences like 8 + _ = 13 or _ - 4 = 6.
Year 2 ages 7–8
- Balance number sentences. Make both sides equal in sentences like 7 + 5 = _ + 6.
- Number patterns that go up or down by the same amount. Find the rule and the missing terms in a sequence like 3, 7, 11, _, 19.
- Growing shape patterns. Build the next step of a growing pattern and say how it grows.
Year 3 ages 8–9
- Missing numbers in multiplication and division. Find the unknown in sentences like 6 x _ = 42 or _ / 4 = 5.
- Patterns in addition and times tables. Find and explain patterns in an addition or multiplication table.
- Follow steps to make numbers (input-output machines). Put numbers through a one-step rule machine and record what comes out.
Year 4 ages 9–10
- Write a number sentence with a symbol for the unknown. Turn a word problem into a number sentence using a box or letter for the unknown.
- Make a pattern from a rule. Generate a number or shape pattern from a given rule and describe its features.
- Find the rule for a growing pattern with a table. Use a table of step number and amount to describe the rule in words.
Year 5 ages 10–11
- Number sentences with all four operations. Solve true/false and missing-number sentences using any operation.
- Write and read number expressions. Write calculations like 'add 8 then double' as (n + 8) x 2 without working them out.
- Compare two patterns and plot them. Make two related patterns, pair their terms and plot them on a grid.
- Patterns with fractions and decimals. Continue and find rules for sequences that step by fractions or decimals.
Year 6 ages 11–12
- Use letters for unknown numbers. Use a letter to stand for a number and write simple expressions like n + 5.
- Write expressions from words. Turn phrases like '3 more than twice a number' into algebra.
- Substitute values into a formula. Work out the value of an expression or formula when the letter is given.
- Linear sequences and the nth-term rule. Describe a sequence with a constant step using a rule linked to position.
- Solve one-step equations. Solve equations like x + 7 = 12 or 3x = 21 by undoing the operation.
- Equations with two unknowns. List number pairs that make an equation like a + b = 10 or 2a = b true.
- Simplify expressions. Collect like terms and use the distributive property, as in 2(x + 3) = 2x + 6.
- Inequalities on a number line. Show solutions to statements like x > 4 on a number line.
- Input, output and graphs of a rule. Use a table and graph to show how one quantity depends on another.