Making Sense of Decimals in 5th Grade, Pt.2

So about that number line I mentioned in part 1. I love clothesline math! I loved it before I knew there was a blog about it. I loved it when a colleague said, “Hey, did you see this?” There are so many possibilities with putting numbers on a number line, and discussing things like:

  • Convince me 7/4 is in the correct spot.
  • Why did Johnny put 1.2 on top of 12/10?
  • Do you agree that 1.25 belongs between 1.3 and 1.4? Why or why not?

The discussion with the partners is so interesting. And then putting numbers on your own white board. And the formative assessment that comes with that! And then magically having numbers in the correct order without having to stack them on top of each other with place values lined up.

Quite honestly, I’m not sure how you teach math without a number line at this point. I’ve had so much fun with it that it makes me want to be back in the classroom exploring it. But, I’m enjoying exploring it with my teachers as well.

So, my 5th grade teacher who was looking for strategies probably felt my excitement about doing the number line, so she agreed to try it. After warming up with some choral counting, we jumped right in. I had consulted Kristin Gray’s blog, KG Math Minds, and got some great ideas there. Check the post out here to get far better description of how I planned using many of her ideas. A couple of the ideas she reflected on were where to place the 0 and how many cards to give partners. I decided I’d start the conversation by putting the 0 in the middle of the number line. I asked the students if that was OK, and why. They agreed that the left was negative and the right was positive. Since that seemed clear, I moved the 0 to the left and told them we’d only be focusing on positive numbers today. Then I held up 1/2. Where should this go, I asked. The students were hesitant. Rightfully so, as there was no benchmark for the whole. A brave soul came up and placed it. We had a brief conversation about the choice, and the realization dawned that it didn’t really matter till we placed the 1. So, I tested the theory. Instead of a 1, I held up a 2. A brave volunteer came to place it. She placed it so that it the 1/2 was equidistant from the 0 and the 2.

Aha! Misconception. Keeping my poker face (isn’t that hard when you want to raise an eyebrow and say nope, try again?), I applauded her bravery and asked the class, how do we feel about the placement? Talk to your partner about why you agree or disagree. The students worked to find the words to say that 1/2 should be closer to 0 than 2. They eventually got there.

Now the cards were spread out, and we added in the 1 to help settle some disagreements. So, I handed out the decimal cards to pairs of students. Here is the end result:

First, don’t make fun. I know the cards are too small. I was anticipating bringing them to the carpet for a closer experience, and I thought my number line would be much smaller. I hated the overlap when I used full sized index cards in the past and was trying to avoid that. Plus, proper planning prevents poor performance – I should have planned this part out with the teacher but the time crunch got to me. So, I overthought this a bit and ended up with a problem. But, the kids assured me they could see it, and that my phone did not take an accurate picture (side note…why do iPhone pics look so much further away than the reality?)

Second, I took the picture at the very end when I realized I had no visuals to share with others about the clothesline. It didn’t start as well spaced out. Plus, there were some answers that needed more immediate revision, and we had to discuss those. Coaching note…take more pictures during lessons. Visualization is important!

One of my favorite events of the lesson was the partnership that had 7/4. During the questioning in choral counting and the beginning of the number line, I had noticed a couple partnerships talking at a pretty high level. So as I passed out the decimal cards, I handed out a couple of fractions that I figured would be a little more challenging at this stage in their learning. This partnership put 7/4 to the right of 2…suggesting it was more than 2. I let that go for a bit, as we debated a few of the other decimals (mainly spacing them accurately between 1 and 2.) Suddenly one of the partner’s hand went up. When I called on him, he asked if he could move the fraction. I agreed and he moved it to the left of 2. Why did he move it? Ensuing partner talk.

During the partner talk I chatted for a bit with the teacher. She was surprised at some of the discussions her kids were having, but also at some of the misconceptions that surfaced in the placement of the numbers. She realized that they needed to do some more work with placing numbers accurately on the number line.

In the debrief later on, the teacher shared with me that she had continued the number line work, and was using it as they considered comparison of decimals. She was interested in using it as they moved into fractions. I’m excited for her as she journeys on with the number line, and I’m excited for her students who begged me to stay and keep working with the number line. I’m excited for the student who discovered his own error and was willing to revise his work in front of the group.

In my own reflection, my math goal was really to seek information about their understanding of numbers on a number line. The difficult part about demos is that even though a teacher shares knowledge and data on where the children are at, there is still the reality of being in the room with students day in and day out, and the deep understanding that comes with knowing what you’ve taught, where they’ve struggled, and where that zone of achievable challenge is. The teacher and I both saw that moving forward they needed to work on the distance between numbers, justifying that distance, and understanding the link between fractions and decimals. Too often we rely on kids “understanding” as demonstrated by a conversion worksheet, but we discover in the number line that their “understanding” is limited to a procedure. I do wonder how much of this affects 5th grade SBAC scores. I look forward to seeing what they do with the number line over the next few weeks!

Any best practice ideas for implementing the clothesline in the classroom? Comment below!

Author:

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

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