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We can subtract numbers using the expanded column method using partitioning with exchange
Year 3 Unit 12d
What we are learning:
- A written method is generally needed for the subtraction of two-digit and three-digit numbers as there can be several parts to each calculation. This can be too much to hold in the memory.
- The column method (where numbers are written in hundreds, tens and units columns) is referred to as a FORMAL written method.
- We are now learning how to use our knowledge of partitioning numbers into tens and units to enable us to subtract larger numbers using the column 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.
First we partition each number into tens and units, so 53 becomes 50 + 3, and
35 becomes 30 + 5.
When we start this subtraction we realise that we cannot take 5 units away from 3 as there are not enough units in the top number. We therefore take a ten from the tens column, changing 50 down to 40 and move the ten we have
taken into the units column to make 13 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 53 and now we have 40 + 13 which is still 53. Now we can subtract each column.
We can use exactly the same process for three-digit numbers. If your child is confident try the examples in the Extension Activity.
- 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:
The Activity sheet has some subtractions that your child will need to set out in columns before completing
Good questions to ask
Which digits need to go underneath each other?
Why is this the case?
What would happen if the numbers were in the wrong position?
Are there enough units to subtract in the top number?
If there are not, what will we need to do?
Have we changed the value of this number? How can you show me it is still the same?
If your child:
Sets out the calculation incorrectly (in the wrong columns)
Ask them to read each number and to say what each digit represents in it.
Do this for each number and ask them to compare to make sure the units are underneath each other, as are the tens etc. We are aiming to get them to see that the place value has to be consistent as we can only subtract units
from units and tens from tens.
Inverts the subtraction because there are not enough units, e.g. in the example above says 5 – 3 = 2 for the units column
Ask them to look at the subtraction carefully and ask them to confirm which number they are taking away from which.
If they are not sure, ask them to read both numbers to see which is the biggest – confirm that the biggest number has to be at the top of a subtraction. Look again and ask them to say the subtraction out loud for the units column – here they should say ‘three take away five’.
They should now see that there are not enough units to subtract from, so they need to get some more from the tens column.
If they are still unsure use some straws or similar objects to help demonstrate the exchange of a ten for ten units.