Chunking for Addition

The chunking method is based on separating the numbers of an addition into their place-value components and dealing with them separately. In the example shown in the diagram, the number 36 is chunked into two parts, 30 and 6, while 45 is chunked into 40 and 5. The tens and units are added separately, and if necessary the process is repeated leaving a final step of joining the tens and units to form the answer.

As children become more familiar with the addition of a number such as 11 to a tens number, the step in which 11 is chunked into 10 and 1 will be omitted. The key difference between chunking and the vertical algorithm is that in chunking, the digit 3 in 36 and the digit 4 in 45 are immediately seen as representing 30 and 40 and the place-value representation of the numbers 36 and 45 are interpreted correctly. This process cannot happen unless the student has a solid grasp of place value, which is not the case when the vertical algorithm is used. Indeed the very language of the vertical addition, where the carry digit is referred to as a 1 and not as the 10 that it actually represents, ignores the place-value aspect of number representation.

In England, once students have developed sufficient number sense through chunking as shown above, they are encouraged to use what is termed number splitting. Again, for 36 + 45, students would split the 36 into two parts in such a way that the parts they are dealing with contain only friendly numbers such as 35 and 45. These are then added before the remaining 1 is combined with the subtotal to give the answer. Of course, what happens is that students choose their own friendly numbers and this leads to discussion about alternative ways of proceeding with an addition question, a discussion that is both meaningful and productive.

Chunking for Subtraction

A Year 2 child in a class where I was trying to introduce chunking for subtraction interrupted me before I had even begun and told me that I needed minus numbers. She came to the board and demonstrated that if I had 3 things (drew 3 strokes on the board) and I wanted to take 8 away (she crossed off the three strokes as she counted to 3 and then continued drawing strokes below it until she reached 8 in her counting. She then said so you are short five so you must 'minus' it. This has understanding has become very popular with children who seem to have very little difficulty with it and it forms the basis for chunking with subtraction.

The diagram shows the steps that students would typically take in response to being asked to find 73 - 28. As with chunking for addition, the tens and units are dealt with separately, and it is quite acceptable to find that a negative number can occur in the intermediate steps. In this example, 20 is subtracted from 70 leaving 50, while 8 is subtracted from 3 leaving -5. The 50 and -5 are then combined to give the answer of 45.

Number splitting has its place too in this process. Once the students have become confident with chunking the tens and units separately, they can be encouraged to look at the subtraction form a strategic point of view, and to decide that perhaps it would be a good idea to split the 28 into two parts, 23 and 5, leaving a one-step subtraction of 73 - 23 with the final step being to subtract 5 from 50.