# Counting Objects by Twos

You might think this was a lone case–that’s certainly what I thought. So I decided to ask my other third grader to count the cubes by twos. Pretty much the same story. And then my three fourth graders. I think you can guess the result.

It’s just so interesting because we teach skip-counting by twos and we teach the concept of one more than a number, and those are the skills needed to count objects by twos. But somehow those skills don’t transfer to this application. Skip counting is also connected to multiplicative thinking, yet it’s often taught as simply a rote memorization process–saying the numbers without understanding what they mean.

I’ll wrap this up with a pitch for small group instruction. It’s really difficult to make this type of discovery using whole-group instruction. Working with small groups of students is like mining for treasure every day!

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1. Nancy Belkov says:

I think you pointed out a big part of the problem- counting by twos (and other numbers) “is often taught as simply a rote memorization processโsaying the numbers without understanding what they mean.” How can we teach counting by twos to develop deeper understanding. Do students have opportunities to discuss what happens when they count by twos starting at different even numbers, starting at odd numbers, counting odd amounts of objects. Do they create visuals in their heads that help them understand patterns that occur. #elemmathchat

1. Sandy says:

I agree, but I do not think skip counting is the same as understanding skip counting. I think skip counting can be learned by rote as early as pre/k. That once learned, it can be built upon to develop the number sense concepts at various intervals later on.. I appreciated my students having a background in skip counting when it came time to introduce multiplication. They could count an array or set more quickly, etc…..

2. Teri says:

I started my small group this week. With a class of 28 my small groups are 2 of 14. I know that’s not ideal, but it’s better than whole class. We just got 14 chrome books so I have the independent workers on that. Can you recommend any “free” math sites? I have them using FrontRow and I like that. The reports you get are good ( and a bit scary when I see 12 of my 3rd graders working in the 1st grade range!) I wonder how I could have so many in that range???

3. Jennifer says:

I was just talking to a teacher about this the other day before her class started a counting collections activity. I was with a little guy who had 120 chart and this day she wanted them to count by 10s. He said “I get it.” and counted by 10s using the hundred chart. He then progressed to counting his single pom poms by ten. It was a great teaching moment. I called her over because I had just mentioned to her why that rote counting might translate to this… I was like “Come see this!” It was great for the teacher to see too.

4. sharon says:

I’m going to put circles on the floor in pairs, counting to 20. Then the kids will “walk it out” by putting left foot on the odd number, right foot on the even number. Then progress to counting by 2’s. Thoughts?

1. Donna Boucher says:

I love it!