Maqqii A balanced network of maths skills for primary school children Maths practice

Number sequences

Number sequences practice, from 7, 11, 15 to 2, 3, 5, 8, 12: the same step every time first, then steps that change, then everything mixed.

Your child can only do the exercises here once they know the 3, 4 and 5 times tables. Spotting that 7, 11, 15 goes up by 4 each time, or that a row is counting in threes, is far quicker for a child who recognises those steps from the tables.

Usually taught in Year 1–3 in England and Wales, around ages 5 to 8. Every child goes at their own pace; this is a guide, not a requirement.

The same step every time
  • 8→10→12→14
  • 8→11→14→17

The first of 11 exercises in this topic. See them all

What it looks like for your child

With one exercise from this topic as the example: Adding on: fill in.

1 The topic's page has the next exercise ready.
The topic's page has the next exercise ready.
2 Your child plays a round of 10 sums.
Your child plays a round of 10 sums.
3 No mistakes and in time: the exercise is done, and it earns wood for the village.
No mistakes and in time: the exercise is done, and it earns wood for the village.
4 The same page, a round later: the next exercise is ready.
The same page, a round later: the next exercise is ready.

How it fits together

The arrows point to what can be done next. Whatever sits inside a box belongs to it.

Needed first

3 times table 4 times table 5 times table

Puzzles

Number sequences

The same step every time

Adding on
Adding on: fill inDoublingTaking away
HalvingTaking away: fill in

Changing steps

Growing stepsUp and down
Add the last twoShrinking steps

All together

Everything mixed

first this, then that belongs to

The same step every time

  • 8→10→12→14
  • 8→11→14→17

See how much is added each time.

  • 10→12→14→16
  • 20→25→30→35

Find the step between two neighbours first.

  • 4→8→16→32→64
  • 1→2→4→8→16

Each number is double the one before. Which number is missing?

  • 15→13→11→9
  • 13→10→7→4

See how much is taken away each time.

  • 48→24→12→6→3
  • 32→16→8→4→2

Each number is half the one before. Which number is missing?

  • 23→21→19→17
  • 13→11→9→7

Find the step between two neighbours first.

Changing steps

  • 5→8→13→20→29
  • 6→8→12→18→26

Each jump is a little bigger than the one before. Which number is missing?

  • 1→3→4→7→11→18
  • 2→4→6→10→16→26

Each number is the sum of the two before it. Which number is missing?

  • 29→20→13→8→5
  • 16→12→9→7→6

Each jump is a little smaller than the one before. Which number is missing?

  • 12→15→13→16→14→17
  • 9→14→12→17→15→20

The row steps up, then down, then up again. Which number is missing?

All together

  • 5→10→20→40→80
  • 19→12→7→4→3

40 sums in a row, everything mixed: the real test.

Why it matters

A sequence is a puzzle: the numbers are there, the rule isn't. To find the missing number, a child has to look for a pattern, test a hunch and check that it works all the way along. That is calculating and reasoning at the same time.

Along the way there is a lot of practice that doesn't feel like it: adding, subtracting, doubling and halving. And looking for a rule is exactly the way of thinking that comes back later in algebra.

How to approach it

Start with the neighbours: what is the difference between two numbers side by side? In 7, 11, 15 it is 4 each time, so 19 comes next. If that difference doesn't hold all the way along, see whether the numbers are being doubled or halved.

In the trickier sequences, the step itself changes. In 2, 3, 5, 8, 12 each jump is one bigger, +1, +2, +3, +4, so the next number is 17. Have your child write the jumps above or below the numbers; often the pattern suddenly becomes clear.

When is it secure?

All 10 right in one round, and no more than 50 seconds altogether. Around 5 seconds a sum shows your child is no longer counting.