Counting On/Counting Back

Counting on is an early strategy that can be used in addition. If a student used this strategy to solve 3 + 5, the student might say “three”, hold up five fingers, and then count onwards from the first addend. You might hear a student say “3…4, 5, 6, 7, 8.” They may model the counting by moving or putting down their fingers as they count.

Counting back is an early strategy that can be used in subtraction. If a student used this strategy to solve 8 - 3, the student might say “eight”, hold up three fingers and then count backwards from the minuend (i.e., 8) to find the difference (i.e., 5). You might hear the student say “8…7, 6, 5.” They may model the counting by moving or putting down their fingers as they count back.

As students transition from direct modelling and counting to counting more efficiently and tracking, educators will notice that students begin to keep track of their count rather than directly modelling the problem. If a student was tracking while adding 3 + 5, the student might say "3", and then count on 5 more, putting up one finger for each count and tracking the number of fingers raised until 5 fingers were up. You might hear the student say "3...4, 5, 6, 7, 8." If a student was tracking while subtracting 8 - 3, the student might say "8", and then count back 3, putting up one finger for each count and tracking the number until 3 fingers are up. You might hear the students say "8...7, 6, 5."