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Broadbent Maths - creative primary maths

Using mobiles to explore complements of numbers

Monday, 5 June 2017
The visual representation of balanced mobiles is a great way to explore the complements of sets of numbers. Children need to be able to quickly recall the complements of 10, 100 and 1000 as well as the decade numbers to give them mental agility when calculating. Mobiles are also useful for practicing complementary addition to work out the difference between two numbers. This challenge to balance the mobile is open ended and is a great starting point that can be accessed by all abilities before progressing in complexity.  
The complements of 10 are particularly important and should be recalled immediately (0, 10) (1, 9) (2, 8) (3, 7) (4, 6) (5, 5). Once these are mastered children can go on to learn the complements of 20 then other decade numbers to 100.
simple mobile copy

Designing mobiles

You could make a mobile using card shapes, wooden dowels (or straws) and cotton to demonstrate how they balance. However, to show how they work with the complementary pairs of numbers it is helpful to draw a simple shape mobile like this on the board.

Starting point
Write a number in the triangle, for example 20.
KS1 can find complements to 10 and 20, KS2 can find complements of 100 and1000 as well as all the decade numbers to 100.

Explain that:
Shapes that are the same contain the same number.
Each side of a balance must have the same total.

Ask for different possible solutions.

simple mobile

Extending the activity
Extend the activity by increasing the complexity of the mobile. Keep the rules the same and encourage the children to use complementary addition to make up to each total. Remind them that each side of each balance must have the same total to stay balanced.

mobile 1
mobile 2
Here are a few more examples to try with your class. Once they have had a go at these they can try to make up their own. Designing the mobiles is a good challenge and involves many mental process, so encourage them to start off with a simple mobile before progressing in complexity.
mobile 3
mobile 4

Practising complementary pairs
‘Show me…’ type activities with children using sets of arrow cards or fan numbers to hold up the answers are useful for practicing these skills:

The total is 20. Show me the number that must be added to 12, 9, 16, 5…
The total is 80. Show me the number that must be added to 50, 20, 72, 25…
The total is 100. Show me the number that must be added to 30, 60, 45, 76…

Complementary addition

Complementary addition is often used to find the difference between two numbers by counting up from the smaller number.

Using a number line for this helps children to visualise the jumps that the complementary addition involves.

It is an important way for children to represent their mental process, the step before children progress on to formal written methods of subtraction.

counting on
For example, this is the counting on method that could be used to work out the difference between 26 and 70. The process using complementary addition is to identify the complements for each step:

26 + __  = 30
30 + __  = 70

If we unpick this skill a little more, it is clear that children need to have quick recall of the complements of 10, 100 and 1000 as well as the decade numbers.

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