More or Less

When I showed young children how to use number lines, I used to take advantage of an old teacher trick and tell them to count "hops" on the line. This stopped them from counting one for the number they were already on  and getting an answer that was one less than the actual answer.

I don't do that anymore. I came to realize that this did not lead to deeper understanding. Instead I work with the children on the concept of more and less.

I start with objects. First we work with two groups of different sizes to identify which group has more objects and which has less (or fewer) objects. Then we work on adding one more, two more, three more, ect.

From this foundation we can move to the number line.  To use the number line to find 5 + 1, I say "Five and one more." Then I point to the number line as I say "Five, one more than five." We move on to two more than, three more than, ... Later I will compare the two ways of using the number line to add. I might show 5 + 4 and count one while pointing to the 5 and end landing on 8, and then do it counting one as I point to 6 and end landing on 9. I ask the students to think about which way of doing this is correct and why. After they have had some time to think, I call on a student to tell the class which way is correct and to explain why.

I do something similar with less than. This leads to a much deeper level of understanding than the old "Let's count hops" trick.