Difference Daisies

In this island, we explore subtraction and the result comes out as somewhat magical. It is a great one for building a sense of wonder within maths. The construction that is created reminds me of petals, hence Difference Daisies. It is very similar to Diffy Squares. I quite like how in this version though, the same numbers appear in a line. I’ve uploaded templates that you can print if you want to use them.

We start with three numbers. You can choose any three numbers depending on the confidence of your children. In this example I’m using four-digit numbers which work well.

We then pair up the numbers, find the difference between them and as a result, we get three new numbers (2784, 5380 and 2596).

We carry this on. At this point, I encourage the children to choose their own three numbers and have a go.

This isn’t an island with lots of different directions. It’s about continuing on.

What they will notice is that the same numbers came up multiple times. I’ve got the same numbers in the same colour above. I normally get them to colour in the petals for the same number the same colour. Children often make the conjecture that each number will appear three times. It doesn’t prove to be true as 188 shows above but that’s fine. What is noticeable is how the same number appears in straight lines across the flower – it’s a truly wondrous part of the construction. This should work no matter what numbers they try. Sometimes, children will make mistakes in their calculations. Through comparing the patterns with each other, they can identify them and correct them. I’ve stopped where I have but sometimes, children want to carry on and on.

What if we tried with fractions?

This can be a nice extension for them to appreciate that fractions are numbers too.

Children’s possible use of reasoning skills (click on each heading):

This isn’t an island that focuses on a lot of skills but is more about the sense of wonder that they will get from the results.

Search
Search inquiry reasoning skill in maths

The children aren’t selecting their data in this example although through the collection of daisies that they create, they can see that it works for whatever numbers.

Organise

There isn’t much need for the children to organise as the flower has been organised for them.

Discover

The main discovery is that of how the numbers line up. If you used lower numbers, they would reach a repeating cycle of three numbers (1, 1 and 0) but I think there is more awe from the numbers being in a line.

Investigate
Investigate inquiry reasoning skill in maths

They can use the Investigate skill to check their fluency. If they aren’t getting a number they expected to get, it might be that they made a mistake in their subtraction.

Argue

It’s tricky to explain why this is happening in an accessible way to children but lower numbers can make it clearer.

Explore

This tends to be quite a linear exploration but it is still rewarding.

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