Stage 4: Supported Column Method
This method will be taught as an introduction to a columnar method for recording addition from Year 2 onwards although children will become more familiar with the vertical layout in Year 3. 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 development of this more formal columnar method begins by encouraging the representation of TU numbers in a variety of ways, e.g as pictoral representations.
The formal recording with the columnar layout mirrors the practical use of the Dienes apparatus and is recorded alongside the practical procedure.
Vocabulary:
“start with the units”, "regroup"
Example without regrouping:
Step 1:
Dienes apparatus is used to represent both numbers in the calculation, set out on the place value mat in the correct columns.
Step 2:
“Starting with the units”, the digit representations in each place value column are combined upwards to form a total.
The resulting totals of “units” and “tens” are written simultaneously in the column layout to reinforce what is happening.
Example using regrouping:
Step 1:
Dienes apparatus is again used to represent both numbers in the calculation, set out on the place value mat in the correct columns.
Step 2:
“Starting with the units”, the digit representations in each place value column are combined upwards to form a total.
Combining the units gives us too many for the units column, “we can’t have more than nine in the units”.
Ten of the units cubes must be regrouped into a ten stick.
Step 3:
This leaves six cubes in the units column to be recorded in the written method. The one regrouped ten stick is now placed underneath the tens column; this is mirrored in the recording of the one ten under the line in the written calculation.
Step 4:
Finally, the tens are combined upwards (including the regrouped ten) to give a resulting total of tens which is recorded in the written calculation.
