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…
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.
