A few posts ago (December 13, 2016 and February 21, 2017), I discussed the importance of skip counting with meaning. If you are teaching particular grade levels, you may have students who skip count to solve problems already. So, how can we tell if skip counting is meaningful to them?
Often times, a student will be able to skip count up to a certain point. For example, they may be able to count by threes up until 9 or even 12. Giving them a problem that goes beyond their memorized sequence can help to determine if they have conceptual understanding of their actions. You could have the child determine how many blocks there would be in 6 rows of three. There are different possible reactions from the student, and I’ll focus on two.
A child who does not have a meaningful skip counting procedure may not be able to continue to count beyond 3, 6, 9. Once they realize this is not enough counts, they will not know how to proceed.
Contrast this behavior with a student who counts in this way: 3, 6, 9… 10, 11, 12… 13, 14, 15… 16, 17, 18. These actions imply that the student knows that when they “skip count”, they are truly counting three ones. So continuing to count by one is an obvious choice for them if they haven’t memorized their sequence of 3’s beyond 9.
The first example shows a child who has memorized a sequence of number words, similar to memorizing the alphabet or a song. What this child has not done is connect that sequence to the concept of increasing by three units. For them, the words 3, 6, and 9 do not contain three units within their count. The second example shows that the student understands that there are units contained within the counting by three, and therefore can fluidly move between counting by three or counting by one.
There are many other ways that students may approach these problems, but watching the behaviors of students and attempting to infer about what they understand will help to decide what the best next steps for the student may be.
In what ways have you seen children use skip counting? Could you tell if it was meaningful to them? Why or why not? Leave me a note below and tell me how you use skip counting with your children.