Resources For Teachers For Tutors For Students & Parents AI New Pricing
Create Free Account
Year 5 Maths Patterns & Rules

Describe & continue number patterns

20 practice questions 0 video lessons Theory + worked examples
Practice 20 questions
Practice questions

Every question with a fully worked solution.

Start practising
Create a free accountTrack your progress and save your work as you go.
Create free account

Theory

A number pattern follows a rule, such as "add \(6\) each time" or "double each time". This Year 5 maths page shows how to find the rule by looking at the change from term to term, how to continue a pattern and fill gaps, and how to use patterns to solve problems.

Each number in a pattern is a term. The rule tells you how to get from one term to the next.

If the gap between terms is always the same, the rule is add (pattern goes up) or subtract (pattern goes down) that amount.

If the gaps keep growing (or shrinking), try multiply or divide: check whether each term is the one before times \(2\), times \(3\), or halved.

A pattern that adds an even number keeps every term odd or every term even, so you can tell whether a number will ever appear.

Pattern adding 6 Boxes 7, 13, 19, 25 and a dashed box with a question mark. Each arrow between boxes is labelled plus 6. 7 13 19 25 ? +6 +6 +6 +6
The gaps are all \(6\), so the rule is "add \(6\)". Next: \(25 + 6 = 31\).
Pattern doubling Boxes 7, 14, 28, 56 and a dashed box with a question mark. Each arrow is labelled times 2. 7 14 28 56 ? ×2 ×2 ×2 ×2
The gaps grow (\(7, 14, 28\)), so look for multiplying: the rule is "double". Next: \(56 \times 2 = 112\).
Pattern subtracting 8 on a number line A number line from 55 to 95 with marks at 55, 63, 71, 79, 87 and 95. Jumps of minus 8 go from 95 down to 63. 556371798795 −8 −8 −8 −8
\(95, 87, 79, 71, \ldots\) goes down by \(8\) each time.

Kinds of rules:

PatternWhat you seeRule
\(7, 13, 19, 25\)same gap, going upadd \(6\)
\(95, 87, 79, 71\)same gap, going downsubtract \(8\)
\(7, 14, 28, 56\)gaps growingmultiply by \(2\)
\(240, 120, 60, 30\)gaps shrinkingdivide by \(2\)
Check every step. A rule must work for every pair of terms, not just the first two.
Gaps growing? Then it is not an adding pattern. Try multiplying.

Finding and using the rule

  1. Find the change from each term to the next.
  2. Same change: the rule is add or subtract it.
  3. Changing gaps: test multiply or divide by the same number.
  4. Check the rule on every term, then use it to continue the pattern.

Missing terms

  1. Find the rule from the terms you know.
  2. Apply it forwards into the gap, then check the next term still works.
Example 1 — Add pattern
Find the rule and the next two terms: \(7, 13, 19, 25, \ldots\)
Solution
\(25 + 6\)\(=\)\(31\)
\(31 + 6\)\(=\)\(37\)
25+6=31,31+6=37

Rule: add \(6\). Next terms \(31\) and \(37\).

Example 2 — Subtract pattern
Find the rule and the next two terms: \(95, 87, 79, 71, \ldots\)
Solution
\(71 - 8\)\(=\)\(63\)
\(63 - 8\)\(=\)\(55\)
71−8=63,63−8=55

Rule: subtract \(8\). Next terms \(63\) and \(55\).

Example 3 — Multiply pattern
Find the next term: \(4, 12, 36, \ldots\)
Solution
\(36 \times 3\)\(=\)\(108\)
36×3=108

Rule: multiply by \(3\). Next term \(108\).

Example 4 — Halving pattern
Find the rule and the next term: \(240, 120, 60, 30, \ldots\)
Solution
\(30 \div 2\)\(=\)\(15\)
30÷2=15

Rule: halve (divide by \(2\)). Next term \(15\).

Example 5 — Missing term
Find the missing term: \(9, 16, \square, 30\)
Solution
\(16 - 9\)\(=\)\(7\)
\(16 + 7\)\(=\)\(23\)
16+7=23

\(23\). Check: \(23 + 7 = 30\).

Example 6 — Will it appear?
Will \(50\) appear in the pattern \(3, 7, 11, 15, \ldots\)?
Solution

No. The pattern starts odd and adds \(4\) (even), so every term is odd, and \(50\) is even.

Example 7 — Savings
Kim has \(\$15\) in week 1 and saves \(\$8\) more each week. How much does she have in week 4?
Solution
\(15 + 3 \times 8\)\(=\)\(39\)
15+3×8=39

\(\$39\) (week 2: \(\$23\), week 3: \(\$31\), week 4: \(\$39\)).

Example 8 — Water used
A tank holds \(200\) L and \(12\) L is used each day. How much is left after \(4\) days?
Solution
\(200 - 4 \times 12\)\(=\)\(152\text{ L}\)
200−4×12=152 L

\(152\) L.

Common pitfalls

Using only the first gap. In \(7, 14, 28\) the first gap is \(7\) but the next is \(14\), so it is not "add \(7\)".
Wrong direction. If the pattern goes down, the rule subtracts or divides.
Counting weeks wrongly. From week 1 to week 4 there are \(3\) jumps, not \(4\).
Not checking the rule. Test the rule on every term before using it.

Frequently asked questions

What is the rule of a pattern?

The instruction that gets you from one term to the next, like "add 6" or "double".

How do I find the rule?

Look at the change between terms. Same change: add or subtract. Growing changes: try multiplying.

How do I find a missing term?

Find the rule from the other terms and apply it: \(16 + 7 = 23\).

How can I tell if a number is in a pattern?

Continue the pattern past the number, or look for a property such as every term being odd.

What is a doubling pattern?

Each term is two times the one before: \(7, 14, 28, 56\).

More in Patterns & Rules