Stage 5: Supported Column Method
This method will be taught to most children from the start of year 3 as an introduction to a columnar method for recording addition. The use of resources (Dienes base 10 apparatus and place value mats) are crucial to support this method. A sound knowledge of place value is necessary at this stage.
The formal recording with the columnar layout mirrors the practical use of the Dienes apparatus and is recorded alongside the practical procedure.
“start with the units”, “regroup”
Example without regrouping:
As with addition, Dienes apparatus is used to represent the calculation. However, for subtraction, only the larger number in the calculation is represented on the place value mat in the correct columns.
“Starting with the units”, the smaller number is physically taken away from the Dienes representation of the larger number.
The resulting totals of “units” and “tens” left on the mat are written simultaneously in the column layout to reinforce what is happening.
Example using regrouping:
Again, Dienes apparatus is used to represent only the larger calculation on the place value mat in the correct columns.
“Starting with the units”, the smaller number is physically taken away from the larger number. Here, children will recognise that we can’t subtract 8 from 3 as we don’t have enough units in the units column.
So we regroup one of the ten sticks from the tens column into ten unit cubes and move them into the units column. We now have 5 tens sticks in the tens column and 13 units in the units column. This is mirrored in the written calculation.
The 8 units can now be subtracted from the 13 units, leaving 5 in the units column. This is recorded in the written calculation.
Finally, the 4 tens are subtracted from the 5 tens in the tens column to leave a resulting total of tens which is recorded in the written calculation.
Most children will use this method from year 3 to subtract numbers with up to three digits. Regrouping hundreds into tens will be necessary when dealing with these larger calculations:
One hundred flat can be regrouped into ten ten sticks.