Addition Wheels

This accessible island could be used to practise 3-digit addition, estimation and ordering of numbers. It also helps build the concept of place value through the impact each ring has on the sums and the careful placement of digits. Whilst it only uses 3-digit numbers, the thinking and problem-solving skills that are required provide plenty of challenge.

In an Addition Wheel, the digits 0-9 are arranged in three rings in ascending order clockwise as can be seen below. The zero is placed in a different place in each ring.

This creates five lines of addition which are colour coded. The direction of the addition is important as it shows the order of the digits. In the above example, we have: 960 + 514, 859 + 403, 748 + 392, 637 + 281 and 526 + 170.

Across these 5 additions, an Addition Wheel scores a point for each addition that is over 1000. This Addition Wheel scores 3 points.

What if we rotated one or more of the rings?

In the above Addition Wheel, we have rotated the outer ring. What impact does it have on the score? Why?

We can use a blank Addition Wheels to try and score from 0 to 5. Are they are possible?

What if one or more of the rings went counter-clockwise?

This possibility should change things but how much? Which scores are attainable now?

What if we had four rings?

This extension in reality will make little difference as the extra ring in the middle will have no impact. However, children might not realise that at first and so it might be worth them investigating it.

What if we tried to make every sum as close to 1000 as possible?

What would be the smallest difference from 1000 possible? I think this is a really nice follow up to each sum being over 1000 as it requires a lot more thought to arrange the digits to achieve this goal.

What if we found the difference between the numbers?

This is interesting in its own right. The results might surprise you and the children.

Children’s possible use of reasoning skills:

Search
Search inquiry reasoning skill in maths

The placement of the inner and outer rings are the most important aspects of this island. To achieve the extreme ends of the scores, children must think about how they can ‘hide’ either low or high digits. This is possible because on one half of the wheel, the inner ring is the first digit of the number. With the other half, it is the outer ring. They need to realise and play with this.

Organise

There is not necessarily a lot of need for organisation other than to record their score values. Having the Wheels with different score values side-by-side as above allows for the noticing of patterns and why they score the values they do by looking at what is the same and what is different.

Discover

Discoveries are possible in terms of discovering wheels that have a particular score and the patterns that are noticeable across different wheels.

Children will hopefully notice that the middle ring is largely irrelevant. The only way that they might prove important is if the opposite digits in them total over ten and that nudges the number into the thousands.

Investigate
Investigate inquiry reasoning skill in maths

In essence, the whole island is investigating the possibility of scores of 0 to 5.

There is the possibility for showing them an example of finding a counter example if they say that the middle ring is irrelevant. In rare cases, the middle ring could cause the sum of a line to total over 1000.

Argue

There is a lot of potential here for the children to use their Arguing skills. This will be through the constant reflection of why they have placed the rings as they have done.

This is best done before they start totalling the sums of each line. Get them to come up with a justification for their placement. This then leads to more thoughtful placing of digits and better outcomes.

Explore

There is the potential for various ideas and expansions here. If a child has discovered wheels for all possible values, the ‘what if…?’ question about getting each value as close to 1000 possible is a more challenging extension.

If you want them to have something to ponder, they could look at finding the difference between the numbers instead. There is definitely some curious treasure that they will discover as a result.

Of course, they might also come up with their own ‘what if…?’ question to explore as well.

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