Making Sense of Decimals in 5th Grade, Pt. 1

A fifth grade teacher shared with me last month her concerns about her students that were struggling with decimals. They didn’t understand place value. They had trouble identifying greater than or less than. They confused the tenths with the hundredths.

One of the ideas she was interested in pursuing was Choral Counting. We had done work in the past on various talk routines, including Number Talks and Which One Doesn’t Belong. I consulted another coach (remember how I get by with a little help from my friends?) and made sure I was clear on the strategy.

So we started simple. A choral count by 0.25. I used this planning tool my coach colleague suggested to think ahead about what I would scribe on the board.

I planned to stop and look at patterns, but I realized that my structure didn’t lend itself as well for beginning choral counters. So, I changed the number of rows.

That made more sense. A pattern of increasing by one in each column was easily distinguishable with four rows. We could look at why that happens (0.25 is equivalent to 1/4, and our numbers are grouped in 4’s.) Hmm…

They picked up on this pretty quickly. All I had to do was ask:

  • What do you notice?
  • Do you notice any patterns?
  • Can you predict what would be ____? (I put that blank space in the 3rd row of the next column).
  • How could you prove it without counting?

The teacher liked this strategy, but still felt like her students were struggling with the idea of greater than, less than, and the concept of decimals as compared to whole numbers. She wanted to explore the clothesline number line.

It was a couple of weeks later, and I wanted to see if the students remembered the choral counting. I remembered that they thought it was pretty easy, and they were engaged with it, so I thought we’d warm up with a choral count. So, we counted by 0.03. This made for some fascinating conversations that went a little longer than I planned. I wrote 0.03, 0.06, 0.09, and then asked:

  • What number comes next? How do you know? – That elicited 1.2 and 0.12. So I wrote them both up there.
  • Convince me that one of these is correct. – They practiced with their partners first.

Once the group was convinced that it was 0.12 (one of the students had said, well, there are 12 hundredths and that is the same as one tenth and 2 hundredths), then we kept going on. Eventually the count looked like this (without the fourth column):

So I asked if there were any patterns. I waited (did I wait 10 seconds? I need to work on that), then gave them partner talk time so they could orally rehearse. Sometimes I pull sticks after this but this time I preselected a volunteer. He can be a reluctant student, but he noticed a pattern of 12’s with his partner, which he explained to the class that at the bottom he sees 12 x 1, 12 x 2, 12 x 3. So I wrote that on our count, purposefully leaving the misconception on the board. I asked, if that is true, what comes next? A student volunteered 48. So I wrote that on the board, then asked the students, what do we think? Does that make sense?

Discussion ensued, and I noticed it got more lively as they started to realize what happened. I listened in to conversations, and once I was comfortable that the partnerships were prepared, I pulled a stick. The student explained that it should be 0.48. I asked, “Why?” Another student explained the pattern was counting by 12 hundredths, not twelves. So, I changed 48 to 0.48. I again asked if it made sense. They looked around at each other. This time I remembered my wait time! Eventually the partner talk picked up, I called a volunteer, and the student explained that the 12 x 1 and so on should have been 0.12 and so on. Aha! We spoke for a minute about the importance of precision in math (SMP 6), and then moved on.

How long did this routine take? About 10 minutes. Lots of partner talk and making sense of math, with a very easy to implement routine. In part 2 I’ll talk about the number line.

Author:

I'm a K-6 Instructional Coach, supporting school sites in ELA and Math.

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