Maths Without Limits
Opening Young Minds to Endless Possibilities

First published on the Maths Investigations Website in April 2016.

Step 1: Adding and subtracting single-digit numbers

Did you know that children use different strategies for adding and subtracting, depending on their level of skill and understanding of numbers?  And you can bet that the strategies they choose will determine how quickly they can work things out.

The games in this section will help your child to become skilled in the most effective methods.

Counting on and Counting Back

When children first learn to add and subtract they will learn to count two groups of objects together, counting all the objects beginning at 1.

A quicker method is to count on or count back from the first number. For example, if you are adding 6 and 5 then you THINK 6 and BEGIN COUNTING from 7:

To do this accurately a child needs to be able to begin counting from any number (without starting from 1) and know not to count the number that you start on (in this case 6) but to begin counting from the next number (in this case 7).

The Envelope Game will help with this.

Number Bonds: Using Known Facts

Children who find it easy to learn number facts will discover that a much more efficient way to add and subtract is to learn the number bonds.

4 + 7 = 11
5 + 6 = 11
6 + 5 = 11

etc

Your child’s school will spend time teaching these during the early years in Primary School.

Some children are lucky in that they find it easy to commit facts to memory. Others find this more of a challenge. But even the most talented of us cannot learn all the possible number facts off by heart!  The secret of being good at maths is to learn certain key facts and to know how to use them to work out others.

6 + 6 = 12

so

6 + 7 = 13

etc

Number Stories

The most important addition and subtraction facts to learn by heart are the number pairs that add together to make 10.

 10 + 0 = 109 + 1 = 108 + 2 = 107 + 3 = 106 + 4 = 105 + 5 = 104 + 6 = 103 + 7 = 102 + 8 = 101 + 9 = 100 + 10 = 10 10 – 0 = 1010 – 1 = 910 – 2 = 810 – 3 = 710 – 4 = 610 – 5 = 510 – 6 = 410 – 7 = 310 – 8 = 210 – 9 = 110 – 10 = 0

The complete set of facts for 10 is know as the ‘Story of Ten’.

If you know these really well then you can use them to help you with other calculations:

2 + 8 = 10    so   20 + 80 = 100

4 + 6 = 10    so   10 – 6 = 4

Your child will also learn the stories of other numbers (story of 6, story of 11 etc).  These are useful, but the most important is the Story of 10.

Also very important are the ‘doubles’ and the ‘teens’ number facts.

 Doubles 0 + 0 = 01 + 1 = 22 + 2 = 43 + 3 = 64 + 4 = 85 + 5 = 106 + 6 = 127 + 7 = 148 + 8 = 169 + 9 = 1810 + 10 = 20 Teens Number Facts 10 + 0 = 1010 + 1 = 1110 + 2 = 1210 + 3 = 1310 + 4 = 1410 + 5 = 1510 + 6 = 1610 + 7 = 1710 + 8 = 1810 + 9 = 1910 + 10 = 20

Tap, Say, Turn Number Bonds is a good game for consolidating any facts that your child is finding difficult.

Missing Numbers

OK, so now we know how to add and subtract small numbers, we think!

And then we meet those nasty questions like

15  –  ?  =  7

or, worse still,

?  –  8  =  7

Number tracks, which show the numbers in order, can be really useful here.

Find the Treasure is an excellent game using number tracks which will REALLY help with these kinds of problems.  Do give it a go!