Subitizing With Third Graders

Estimates of the number of items that humans can discern without counting – subitizing - vary from four to about seven.  I conducted a Quick Images lesson with four third graders at Highland Elementary and found the results support this statement.  I also learned that it is the number of groups, not the number of pips in each group, that determine the difficulty of the array.

My first Quick Image array was five groups of four pips each.  Each of my four students used a different strategy (multiply four times five groups, adding groups of four, counting on by fours, etc.) to determine the total number of pips and all four gave the right answer. 

The second array was six rows of three.  This time the students again used various strategies (three times three times two, counting by threes, etc.).  One student saw twenty four pips instead of eighteen.  He said he saw four rows of six. 

The last array was nine groups of two pips.  One saw ten groups of two.  Two saw nine groups of three.  Only one student correctly determined there were eighteen pips in total.  He counted by twos.

I noticed that the number of pips per group was reduced in each subsequent test – presumably making the test easier, while the number of groups in the array increased in each subsequent test – presumably making it more difficult.  So it seems the number of groups is more important than the number of pips in each group.

I thought all the strategies the students used were valid.  Two students understood that multiplication could speed up their processing.  The greatest difficulty they had seemed to be in visualizing the number of groups – subitizing – as the number of groups increased.