Simon, a year 3 student, was able to do single-digit multiplication but was always very slow at finishing his work. The teacher suspected he did not understand the idea of equal groups.
She gave him the following patterning tasks in an individual interview.
- Count by threes and show the numbers on a number line.
- Draw a 3 \(\times\) 4 rectangular array of dots and tell me how many dots there are.
On both tasks Simon obtained correct answers by counting by ones.
The teacher deduced that Simon did in fact have a sound conception of multiplication in terms of equal groups but that he had not learnt to skip count.
The teacher therefore gave Simon some further patterning tasks.
- Count rhythmically (1, 2, 3; 4, 5, 6; etc) and mark the emphasised numbers on a number line.
- Count a 3 \(\times\) 4 array in threes or fours.
After several such tasks with different numbers, she helped Simon to learn to skip count by twos, threes, fours, fives and tens.
Simon could now do single-digit multiplication much more quickly and accurately.