Last week I wrote about how I use a 100 bead string as a decimal number line. If you haven't already read it, you may want to
start there.
In grade 4, I have been working hard with my students on decimals and fractions. We have talked a great deal about number line models for whole numbers and fractions and done a bit of work with a decimal number line that goes from 0 to 1. Today, I wanted to make some strong connections for my students and decided to use a meter stick (actually 2 meter sticks) as a decimal number line. I find that kids need to start doing number lines on something that has a scale given. Only after they have had some experience with number lines with scale can they make the jump to an open number line.
I started by writing some lists of decimals and fractions on the board. I put them in three different colors so that we could tackle this job one step at a time. I had them start with the numbers written in green (see picture below) I put the kids into groups of 3 and had them use their base 10 pieces to build each number. Then they used scraps of paper to label the collections and put their collections in order from smallest to largest.
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| These are the 3 sets of numbers we started with. Kids first built and placed the green numbers followed by the blue and then finally the black. |
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| Part of a collection. Students labeled the collections with at least one decimal and one fraction name |
Then after the collections were built, I had each group put one of the numbers where they thought it belonged on the decimal number line. They had to show us where they put it and convince us they were right. The kids did a great job with this and it brought out a lot of great connections between fractions and decimals. Very cool!
We then moved onto the next set of numbers (the blue ones in picture 1) and built and ordered them at table groups before placing them on the number line and finally did the same with the black numbers. Check out the pictures to get a good idea of what the number line looked like
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| This is the full number line after we were done with all the follow up questions. To attach the meter sticks to the board, I used the little magnetic men. If you don't have a magnetic board, you may have to use tape or suspend with string. |
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| A close up of the left side of the number line (0-1) |
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| A close up of the right side of the number line 1-2 |
You can see some numbers in the pictures above that did not appear on the board originally. That is because we got into some extension questions. The first thing that I knew I wanted to address at this stage going into the lesson was the idea of density on the number line. So I had kids find 1.3 and 1.4 on the number line and then asked them to tell me a number that was between those two numbers on the number line.
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| I used the <, > symbols and words to ask kids to find a number between 1.3 and 1.4 . 1.32 was one of the numbers they identified. They also identified a few others before I asked the next questions |
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| I asked this questions to get at the big idea!!!! The kids were so funny because when I asked for answers, they were convinced that there were either 9 or 10 numbers between 1.3 and 1.4. Then one kid got really close to the number line and said, "what about those tiny lines between the hundredths?" This question sparked great thoughts and ideas from the rest of the kids and they took off from there. |
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| Some of the numbers kids found between 1.3 and 1.4. Notice the millimeter lines are visible this close up and think about how they could help your students with thousandths. |
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| A "zoomed in" part of the number line a kid created to prove to his classmates that there are an infinite number of numbers between 1.3 and 1.4. Notice the multiple colored partitioning happening between 1.38 and 1.381. In the students' words "you can just keep cutting the sections into tenths but you will need a microscope" |
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| This was another idea that kids were inventing as we did this activity. They were thinking about what fractions or decimals added up to a given number as a way to prove that they had placed it in the right position. |
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| We had a few minutes of follow up time before the end of our math block so I had kids grab their math journals and wrote a few questions on the board for them to answer in their journals. They did a great job! |
How do you use number lines in your classroom?
Looking for more ideas for modeling decimals? Check out this post about
5 different models for decimals. You can grab a
great set of task cards for fourth and fifth grade decimal ideas here!
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