In my day job, I work with elementary students to help develop their number sense. Sometimes, I like to share when something works really well.
I am reading Choral Counting and Counting Collections by Megan Franke and this counting progression caught my eye. I tried it out with 2nd, 3rd, and 5th grade intervention students and it really sparked some great mathematical discussion.
First, we decided how we wanted to skip count and then I recorded the numbers down the first column. I let them continue to 24. I stopped there because I wanted to know if they could determine the horizontal pattern. The students noticed that the numbers increased by 10 when moving across to the right. I had a student come up and record the row of 2s in the ones place. I really wanted to hear if anyone would talk about place value and I am glad to say that they did!
We looked at the diagonal pattern and figured out that it increased by 12.
My fifth graders chose to skip count by 3s. My students scrambled to get paper and pencil to figure out the patterns across and diagonally. They even came up with the fact that the diagonal difference was the same as horizontal plus vertical movements. The numbers increased by 3 working downward and 15 horizontally an diagonal was 15 + 3. We really could have gone on longer talking about the number patterns. Nobody discovered that the bottom number of the first column will tell you how much the numbers increase horizontally. Maybe they will notice it next time.
Another tool to use for skip-counting are the five frame, ten frame, and dot cards. Skip counting lays a solid foundation for multiplication. You can also use Unifix cubes linked into 2s, 3s, 5s, 10s, etc. for skip counting.