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We can add numbers using the expanded column method
Year 3 Unit 12b
What we are learning:
- A written method is generally needed for the addition 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 add 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.
- The expanded column method allows us to begin using columns, whilst ensuring our children understand what each digit represents by keeping it in the correct column. This is particularly important as we are now working with higher numbers
- This is an example of how to set out the expanded column method for addition:
We always begin the addition sum in the units, 2 plus 4 equals 6, which we write underneath. Then the tens, 30 plus 10 equals 40. Then we add the 6 to the 40 to give the answer as 46.
This is an example of addition with numbers that add up to more than 10:
Once again begin the addition sum in the units, 8 add 4 equals 12, too many for the units column, so we exchange 10 units for 1 ten which we put into the tens column and 2 in the units column.
Then we add the 50 to the 30 which gives us 80. Then we add the 12 to the 80 giving us the answer of 92.
- 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.
- If your child is confident working in tens and units then we use exactly the same process for three-digit numbers, once again always starting in the units column:
8 plus 7 equals 15, 1 ten and 5 units.
40 add 60 equals 100 (1 in the hundreds column, 0 in the tens column and the units column)
200 plus 100 equals 300 (3 in the hundreds column, 0 in the tens column and the units column)
Then add up the three numbers, the final answer is therefore 415
Activities you can do at home:
Activity sheet 1 has some examples of column addition for you to work through with your child.
Activity sheet 2 has some sums that your child will need to set out in columns before completing.
Good questions to ask
How do we set out this addition?
Which digits need to go underneath each other?
Why is this the case?
What would happen if the numbers were in the wrong position?
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 cannot add units to tens in the same column.