Most kids learn, in kindergarten or first grade, to count by 2’s, 5’s, 10’s. By rote. This has its uses, but going beyond that level of skip-counting can make great numeracy practice, and it seems to be quite under-used.
In our school, we have the primary kids skip-count by 2’s starting from numbers other than 2. Then they practice skip-counting by other numbers, again starting at arbitrary places. Forward and eventually backward. This is an easy one to differentiate, because you can have some kids counting up by 2’s and others counting backward by 7’s at the same time. 
Eventually skip counting is used to introduce multiplication.
Today I asked the intermediate group (approx 3rd – 5th grade math levels) to do some skip-counting for me, forward and backward by 2, 3, 5, 10, 20, 25, 50, 100 and 99! Boy that last one was a doozie! (“Can we use calculators?”) But all of it was clearly good practice even for these “big kids”. For counting (up) by 99’s, they quickly realized that they could add 100 and then subtract one. But a LOT of them got stuck crossing the 1000 boundary (going from something like 987 to 1086). I didn’t think of it at the time, but now I think that pointing out that 1000 is really the same as “ten hundred” might be helpful for a lot of them. Now backward by 99’s was really tricky! So… you first subtract 100 and then… what? Only one of the 6 kids I was working with today (only half of the usual group) really understood that you would then have to ADD 1 back. “I’m taking away a little LESS than 100, so should the answer be a little more or a little less than what we got by taking away a whole hundred?” This is not intuitive for a lot of kids!
So, if you’re working with elementary school aged kids, skip count! Regularly! I think it’s a key skill for developing number sense.
April 16, 2008 at 10:35 am |
Wonderful idea about skipping count. I was trying to find ideas to interest the students on multiplication. Seems like this is one of the activity I can put in. I was also thinking of dot-to-dot picture drawing but with numbers running up by 2, or 3, … times table in mind. Yes, number sense is one fundamental area we need to put in effort as it sets the foundation for advance math.
April 27, 2008 at 4:38 pm |
I wonder what would happen if I asked (older) kids to skip ‘count’ by fractions: two-thirds or three-fifths or something like that.
Starting at “other” places? (ex, starting at one half, count up by two-thirds, or, if I were mean, starting two thirds, count up by three-quarters)
Maybe I’ll try…
(I love your skip counting…)
Jonathan
April 27, 2008 at 4:57 pm |
Sounds like fun, Jonathan. (Or at least, an evil math teacher’s vision of fun… ) I think once they got started (figured out the right denominator to work with), they’d be ok, if they were reasonably comfortable with fractions. I should do that next with my middle schoolers.
I did have my middle schoolers do a little of the skip counting after trying it with the intermediate kids, and even some of the younger ones there got hung up on backwards by 99’s.
We did some other mental math practice as well. It’s been a while since I explicitly worked on numeracy stuff with them (as opposed to just building it into the problems I have them work on) and that was worthwhile.
September 18, 2008 at 6:22 am |
Skip-counting is especially important in the lower grades as well when children begin trying to count money. The concept of counting 10, 20, 30, 35, 40, 41, 42 is a difficult one to handle. If the child has a good grasp on skip-counting, however, this is a much easier task to complete.
September 30, 2008 at 3:13 pm |
I have a question for the group. When you say “skip count by 2″, I take it to mean a number sequence of 1,4,7,10,etc., so that we are skipping 2 numbers when counting. If instead one is asked to “count by 2s”, then the sequence becomes 1,3,5,7, etc., meaning every second number is counted.
However, my son (3rd grader) insists that skip count by 2 should also generate 1,3,5,7. I asked him what “skip count by 1″ would mean then – certainly it should not mean 1,2,3,4… as that would be not skipping at all.
What does the group think? I am assuming there is a difference between “skip count by 2″ and “count by 2″. Is this a real difference or is it semantics, ie. “skip count by 2″ really means “count by 2″?
September 30, 2008 at 3:39 pm |
My children’s school uses your son’s definition — “skip counting” by 2’s (or any other number) is the same as counting by that number. Which is why, in my post above, skip-counting by 99 was a bigger challenging than by 100.
October 1, 2008 at 7:04 pm |
Skip counting can be so much fun. Today we counted the number of eyes in our classroom by 2’s, the number of fingers by 5’s, and then took off our shoes to count our toes by 10’s.
We then started to talk about things that normally come in 2’s, 3’s, 4’s etc. and will start making art projects with those number of objects. I plan to take pictures of the art projects and then turn them into class books.