A note about count-by-ones strategies

Students need opportunities to develop skills in a variety of counting-on-and- back strategies to solve number problems.

Count-up-from

This strategy is typical of additive tasks involving two screened collections, such as six and three. The student typically says: “Six....seven, eight, nine. There are nine counters.” The essential feature is that the student counts on from “six”. Inherent in this strategy is keeping track of three counts. This may involve explicit double counting, e.g. seven is one, eight is two, nine is three, etc., or may involve sequentially raising three fingers in coordination with saying the number words from “seven” to “nine”. Alternatively the student has and uses a concept of three number words in temporal sequence. In this case saying “seven, eight, nine” is recognised as three words. The student anticipates that he or she can make three counts after “six”.

Count-up-to

This strategy is typical of missing addend tasks. For example, 6 plus some equals 9.

The student says: “Six,... seven, eight, nine. I need three more.” The essential feature is that the student counts on from “six”. As before, this strategy involved keeping track of counts but the students does not know in advance the number of counts. Rather, the student knows in advance where he or she is counting to. This may involve explicit double counting similar to, but differing from, that in the previous case. The difference may not be apparent to the observer. As before, the student may sequentially raise three fingers or may use a concept of three number words in temporal sequence.

Count-down-from

This strategy is typical of the removed items task. Example: 9 remove 3.

The student says: “Nine,...eight, seven, six. There are six left.” This strategy involves keeping track of backward rather than forward counts and the student knows in advance the number of counts.

Count-down-to

This strategy is typical of missing subtrahend tasks. Example: 9 remove some equals 6.

The student says: “Nine,...eight, seven, six. Three, there are three that have been taken away.” This strategy involves keeping track of backward counts. The student knows in advance where he or she is counting to.