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Making number sequences real

There are many ways in which investigations with objects or shapes lead to number sequences.

  • Building a block pattern by repeatedly adding the same unit of repeat leads to a sequence of multiples (see Introducing number sequences).
  • Building a staircase leads to a sequence of even numbers (see Making a Staircase).
  • Some problem situations lead to interesting number sequences (see Let's have a Party!).
  • The number of objects in a growing square array leads to a sequence of square numbers (see Find a rule).
  • Hops of a fixed length along a number line give a number sequence linked to addition (or subtraction if the jumps are backwards). For example, starting at 2 and repeatedly adding 3 gives the sequence 2, 5, 8, 11, 14, 17, 20…
A number line from 0 to 20, with every number marked and labelled in multiples of 5. Arrows show forward jumps of 3, starting at 2 and ending at 20.

A number sequence on a number line.

It can be a valuable exercise to reverse this process.

Give students a simple number sequence (one which increases or decreases at a fixed rate) and ask them to come up with a familiar situation which would yield the given sequence.

A hundred square

A wide variety of number sequences can be found on a hundred square or chart. Exploring them helps students strengthen their knowledge of place value and their addition skills.

Folding patterns

Number sequences can also be linked to fractions through this folding activity.

Curriculum links

Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction

Year 2: Describe patterns with numbers and identify missing elements

Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects