← Back to the activity

Year 5 Maths — Number patterns

Work out the rule behind a pattern of numbers and carry the pattern on.

Name: ________________________

Before you start

This line starts at 1 and every mark along it is 4 further on. Move from mark to mark and see which numbers the pattern lands on.

1917253341

Once you know what happens between two neighbouring marks you know every number on the line, however far along it you go. Finding the rule is the work; the next number then costs nothing.

  1. 1.What is the rule for 2, 5, 8, 11, 14?

    • a) Multiply by 2
    • b) Add 4
    • c) Add 3
    • d) Add 2

  2. 2.What comes next? 1, 4, 9, 16, ?

  3. 3.What comes next? 100, 90, 81, 73, ?

  4. 4.What comes next? 3, 7, 11, 15, ?

  5. 5.Sort each pattern by what its rule does.

    Groups: Adds the same amount each time · Doubles each time

    • 1, 2, 4, 8
    • 4, 8, 16, 32
    • 2, 4, 6, 8
    • 3, 6, 12, 24
    • 7, 12, 17, 22
    • 5, 10, 15, 20

  6. 6.Match each pattern to its rule.

    • 2, 4, 6, 8
    • 10, 20, 30, 40
    • 1, 3, 9, 27
    • 20, 17, 14, 11
    • 1, 2, 4, 8
    • Subtract 3
    • Multiply by 2
    • Add 2
    • Multiply by 3
    • Add 10

  7. 7.What comes next? 1, 1, 2, 3, 5, 8, ?

  8. 8.A pattern of squares grows: 1 square, then 4, then 9. How many squares are in the next step?

    • a) 12
    • b) 16
    • c) 20
    • d) 14

Answer key — Year 5 Maths — Number patterns

  1. 1. c) Add 3
  2. 2. 25
  3. 3. 66
  4. 4. 19
  5. 5. 2, 4, 6, 8 → Adds the same amount each time; 3, 6, 12, 24 → Doubles each time; 5, 10, 15, 20 → Adds the same amount each time; 1, 2, 4, 8 → Doubles each time; 7, 12, 17, 22 → Adds the same amount each time; 4, 8, 16, 32 → Doubles each time
  6. 6. 2, 4, 6, 8 → Add 2; 10, 20, 30, 40 → Add 10; 1, 3, 9, 27 → Multiply by 3; 20, 17, 14, 11 → Subtract 3; 1, 2, 4, 8 → Multiply by 2
  7. 7. 13
  8. 8. b) 16