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We can subtract numbers using the formal (efficient) written method
Year 4 Unit 11d
What we are learning:
A written method is generally needed for the addition and subtraction of two-digit, three-digit and four-digit numbers as there may be several parts to each calculation. This can be too much to hold in our memory.
The column method (where numbers are written in hundreds, tens and units columns) is referred to as a FORMAL written method or an EFFICIENT written method.
Children will be introduced to the column method at the stage in their maths education when the teacher feels it is appropriate according to their ability to understand and use this method. Remember that progressing to a different method is not a race, and introducing your child to a concept that they are not ready for can knock confidence.
This is an example of how to set out the formal written method for subtraction:
When we start this subtraction we realise that we cannot take 9 units away from 4 as there are not enough units in the top number. We therefore take a ten from the tens column, changing 7 tens down to 6 tens and move the ten we have taken into the units column to make 14 altogether. This is called ‘decomposition’ as we break up, or partition the top number and move value from one column to another. Note that we have not changed the overall value of the top number, we started with 74 and now we have 60 + 14 which is still 74. Now we can subtract each column.
We can do this with three-digit numbers in the same way
We do not have enough units to take 7 away from 4 so we try to partition the tens column. However, there is only a zero in the tens column so we can’t move value across from there. We go to the hundreds column and partition the 900 into nine groups of ten in the tens column, and one group of ten in the units column. Since 800+90+14 = 904 we have not changed the value of the top number, we have only partitioned it. Now we can complete the subtraction.
When children start using this method it may still help them to use equipment e.g. bundles of ten straws and single straws so they can see what is happening
Activities you can do at home:
Have a go at the examples on the Activity Sheet together. Remember to talk through the method – this is just as important as getting the answer right.
Good questions to ask:
What do we do if we cannot take the bottom number away from the top number?
Where can we get more value from?
Have we changed the value of this number?
How do we know that we have not changed it?
If your child:
Tries to take away a larger digit from a smaller digit, e.g. tries to take 4 away from 3 instead of partitioning the tens
Ask them to look at what they are trying to do and whether there are ‘enough’ to subtract. Once they recognise that they do not have enough value they will start to look for where they can get more value by partitioning.