Weekly challenge

Addition and Partitioning

The first stage of arithmetic is usually learning to put numbers together and take them apart. There are actually 2 main ways to put numbers together. We can do it with addition or multiplication. Here we’re using addition.

This is most commonly learnt as number bonds and generally, we learn our number bonds to 10 and then 20 to begin with. This is an important step because if we learn these tricks with numbers, we can extend our brain’s limited ability to cope with numbers. With out these tricks (remembering addition and subtraction facts), we wouldn’t be able to deal with numbers much beyond 20 probably or we would need a specialised profession of people who do all the counting for us (like actual bean counters).

It’s a really good idea to keep the link between the number representation (numerals and digits) and the idea of an amount. This is done well with Numicon for example. Dominoes, dice and cards are also useful for helping us maintain awareness of the numbers behind the numerals.

This week’s challenge gets you to find dominoes that add up to a certain amount. It allows you to practise adding and subtracting in a playful way.

We start by laying dominoes out in some way. We’ve chosen the layout shown which takes 10 dominoes and produces a shape that has 6 sides. The goal is to get the dots on each side to add up to a specific number.

This shows a square in the middle of each side. The dots on each side should add up to a square number. What’s the largest square number possible? What’s the smallest?

To start getting into the challenge see if you can get the sides to add up to a square number. The square numbers are 1, 4, 9, 16, 25, 36 and so on. There are six sides on this shape. You could ask what the largest square number it would be possible to fit in might be. The top row has 3 and a half dominoes or 7 numbers that would fit into it. What’s the largest of the square numbers that a standard set of dominoes (with numbers zero to 6 on them) could produce there?

Each side showing a particular square number. Can you do this with just doubles and blanks? Any more solutions?

Here’s an example of a layout with just square numbers that you could try to get to first.

To make this more challenging, you can introduce more constraints. Can you make this shape with these numbers using a subset of dominoes such as only doubles and ones with blanks or zero?

Once you’ve had a go at these, see if you can get children to come up with their own puzzle. How can they make the puzzle more or less challenging? Is it just bigger numbers or are there some puzzles that have less solutions? See who can come up with the easiest or most difficult challenge.

Here’s the download with templates for you to use to make your own puzzles. Or come up with your own arrangements of dominoes.

I’ll post an answer to this week’s arrangement later in the week. Please email or tweet any solutions that you come up with. If tweeting, please include #momentofmaths or @mathsexplorers so we can share it.

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