Recently a number of parents have told me how strange they find some of the methods their children use in maths. Two of the big queries are ‘chunking’ – more about that one later- and ‘exchanging’.

Some of our tutors are available for daytime sessions to help parents learn these different methods, but below is a whistle-stop explanation of how we ‘exchange’.

 

Imagine I have 32 children in my class and I decide to buy them all a mars bar. Unfortunately, my local shop only stocks packs of 10 so I buy 4 packs.

When I give the mars bars out, I have to open the packs of 10 so I have individual bars.

That’s what decomposition, or ‘exchanging’ (the method your child uses for subtraction) does – it breaks tens in more useful units.

To take 5 away from 21 I’d lay the calculation out like this:

       

  T   U

2      1-  

        5                                                                                                                             

You can see I don’t have enough in the units column to take 5 away, so I exchange the 10 for ten units – in other words I break open one of the packs of 10 to make 10 units and I put them in the unit column. Now I have 11 in the units column  but I only have 1 pack of 10 left in the tens column :

      T   U

    ¹ 2  ¹ 1-

            5

      1   6        

 

Let’s look at another example.   

 T   U                                                                                                                   

⁶7   ¹2

 3     7

 3    5           

         

Sometimes we might need to exchange more than once.

Let’s take a look at how we can do that.                                             

H   T   U

2   0   1 –

     2   5        

 

We don’t have anything to exchange in the 10s column so we need to go to the 100s column and exchange 1 pack of 100 for 10 lots of 10:

H   T   U

¹2  ¹ 0   1 –

      2   5       

 

Now we can exchange from the 10s column:

H   T   U

¹2  ₉ ¹ 0   ¹1 –

          2    5

1      7     6