Mathematics

Preschool numerical patterns: Numberblocks and number bonds


“Daisy, how many toes have you got on this foot?”

I was sitting in the back of the car with my granddaughter Daisy as we travelled home from another afternoon spent rock-pooling at the beach, and Daisy had cast off her wellies and socks.

Daisy looked at the foot I was drying and quickly answered “Five!”

“What about your other foot?”

“Five!” She paused for a moment before announcing, “And five and five are ten!” 

We continued our analysis: Daisy confirmed that she had five fingers on each hand – which added up to another ten.

Then Daisy surprised me and told me that 10 and 10 made 20, and that if we had another five we could have 25 and then we could have a “number five square”.

This delightful and spontaneous conversation, during a routine moment, provided an opportunity for Daisy to explore a numerical pattern, and to do so in a different context to the fun she has when exploring numbers with her Numberblocks toys

A square constructed from multicoloured 36 Mathlink cubes
Daisy made a 6×6 square of 36 cubes

Daisy’s curiosity about numbers (from odds and evens to big numbers) is well documented by now. One of her favourite episodes of the Numberblocks TV show is ‘We’re Going on a Square Hunt’. After watching the episode, together we used her Mathlink cubes to construct the squares for 1, 4, 9, 16 and 25. We talked about the pattern of square numbers and the Numberblocks Square Club motto: even though we’re different sizes, you can always recognise us: we’re as tall as we are wide; we’re the same turned on each side!

We stood the number squares on their sides, turned them around and talked about their sizes (bigger, biggest, smallest). Exploring the number squares, we stacked them on top of each other to create a pyramid and talked about their different sizes and the shape of the pyramid. 

Number bonds

This interaction with Daisy got me thinking about number bonds. Put simply, a number bond is a pair of numbers which, when added together make, another number. The number bonds for 10 are: 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5 (these are reversed as 9 and 1, 8 and 2, 7 and 3, 6 and 4 – it’s worth bearing in mind that this is something a young child might not instantly recognise).

As adults, we naturally (and usually unthinkingly) use number bonds in any simple calculation we make. For a child, number bonds provide the foundation for them to be able to do addition and subtraction as well as more complex mathematics. 

Our conversation in the car made me realise that Daisy had started to use number bonds. Now that she is aware that her two hands of five fingers make 10 fingers we can start to build on this and introduce the other number bonds for 10, simply by playing with fingers – in the car, on the park bench, or after watching the ‘Ten, Again’ Numberblocks episode.

Granny Smith says…

  • When a preschool child is able to play and use manipulatives to visualise patterns, they’re ready for you to introduce number bonds, number patterns and square numbers.
  • You can create square numbers with a matching set of wooden cubes, coloured counters or even use a set of same size milk bottle lids – you can then talk about number patterns and the sizes of the squares.
  • Once you’ve introduced the concept, you might use 10 of the same counters, bottle lids or brick cubes to explore the number bonds for 10.

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