Year 5

We can explain each step when we write subtraction calculations in columns using the compact method

Year 5 Unit 5a

What we are learning:

• Once your child understands the expanded method and can use it confidently the compact method can be introduced.
• If we have 567 – 234 we can write it down and subtract each column as follows:

In this case we can subtract each column because the number at the top is always bigger than the number below it.

• However, if we have 354 – 283 and we set it out in the compact method we get:

• We can subtract the units (4 – 3) but when we try to subtract the tens there are not enough in the top number (5 – 8). We have to partition the 300 into 200 and ten lots of 10, which we bring across into the tens column. We write it down like this. Now we can complete the subtraction in each column.

Now we can subtract all three columns to give the answer 71.

• When we have to partition the top number in a subtraction we call it decomposition, because we partition the number and change the way we write it, but we do not change its overall value.
  There is no ‘borrowing’ – we simply write the number in a different way.

We can do the same with four-digit numbers like this:

In this example we have to decompose, or partition the tens column to increase the value in the units column, then we have to partition the thousands column to increase the value in the hundreds column.

Activities you can do at home:

Try some examples using the compact method that do not require decomposition.

When your child is confident with these and can explain what they are doing try some examples that do require decomposition. This will take time and practice to master.
Some examples are:
291 – 148
639 – 292
827 – 696
382 – 249
555 – 237

Good questions to ask:

Do we have to use decomposition in this calculation?
If we do, how are we going to partition the top number?
Can you take it away now?

If your child:

Is not confident about partitioning a column to bring value across to another column
Talk together about the value in each column and how you can partition it.
Remind your child that partitioning does not change the value of a number; it simply allows us to write the number in a different way.
Do not be tempted to use the expression ‘borrow’ from the next column. We do not borrow in subtraction as we do not pay back.