Monday, January 5, 2015

Oh, it's a number line!

I have a confession.  This post has been written and unwritten and rewritten many times.  It is the reason I have not written a blog post for an entire quarter.  This project was adapted from a combination of ideas from training sessions, math coaches and friends input.  It was fabulous, but nothing I have written about it has turned out to be as fabulous as it actually was when I did it in class.  I'm sharing anyway.  Hopefully, someone will glean something from it.  Here goes...

In my classroom I have a number line.  It's not any old number line.  It's different.  The first day my students saw my number line it looked like this:

On this day our number talk went something like this:

Do you notice anything new in our classroom? What do you notice about it?

There is a whiteboard, there is purple duct tape, there are three strings, there is an orange piece of paper, there are many rectangles.  

Tell me more about the string and the piece of orange paper.

The string is long, the paper is short, there is only one paper, there are three strings, the paper is folded over the string, the string is longer.

What do you mean the string is longer?  How do you know?

Because there is only one piece of paper, but there could be more.  More papers could fit on the string so that makes the string longer than the paper.

How many papers could fit on the string?

End day one.  Day 2 picked up with that very question, "How many orange papers of the same size could fit on one of the strings?  First I took guesses from the students, there was a wide range, then I allowed them time to try different measurement techniques.  Some students tried finding other objects that were the same size to lay across the floor, some tried what I like to call "air measuring" with their fingers and their eyes (that was fun because we got all sorts of different "reasonable" answers), some tried moving the paper and marking the white board.  After a discussion about what technique seemed to be the most accurate and precise, I "accidentally" dropped my folder which contained many more orange papers.  One of my students immediately had the idea that we could just place more orange papers on the string to find out how many would fit.  So we did.  It looked like this:

Ten orange papers could fit.  I asked the students,

How many units wide do you think one of the orange papers is?  

They looked confused.  5? Maybe 10? Could be 1,000,000!

Oh wait, I forgot something:

Oh, it's a number line!  

After some guesses, and some skip counting and some discussion, we finally figured out that each piece of paper must be 100 units.  So we labeled them and it looked like this:

The next day our discussion started with this question:

If there are 10 hundreds in 1,000, then how many tens are in 1,000?

Our discussion ended with this:

On day four I asked the students if they could write a number sentence to represent the orange pieces of paper.  We had a fabulous number talk revolving around equivalent number sentences and equality.  Ultimately, one of my students very excitedly suggested 10 x 10 x 10 and we modified our number line to look like this:

The number line still lives in my classroom and we have referenced it several times.  We've used it for rounding, grouping, division and much more.  Soon I will remove the original papers and the number line will be used for fractions.  I can't wait!

One more confession:  It took me three tries to build a number line that could survive in a classroom of 3rd graders.  On my first attempt I used string.  It sagged the top row of papers overlapped the middle row.  It was ugly, I took it down and tried again.  My second attempt was using 20 gauge wire.  Extremely pliable.  It also sagged, and broke easily.  The kids bumped it with their knees and the wire fell many times.  This third attempt was built with 16 gauge wire.  Not as easy to work with but much sturdier.  I also used flat head nails hammered into the shelving unit through the shower board to hold the wire in place.  I think this number line will last through the remainder of the school year.  


  1. Great visual for students Leandra and love the fact that you tied in some estimation at the beginning.

    Because this is 3rd grade and students need to begin exploring division what would happen if you placed 0 and 72 on respective ends of the number line and hung 8 pieces of orange paper (instead of 10). Then ask the students the value of each piece of paper. Some students might automatically jump to 9, while others might internally begin partitioning out 5 to each card, then 2 to each card, and so on until there is none left. What a slick way to introduce partial quotients in 3rd grade. If you try it I'd love to hear how it goes!

    Keep up the great work and thanks for making us all a little smarter!

    1. Seriously Graham! Great minds think alike! I did that yesterday! My best friend and math collaborator and I were brainstorming ideas for a division number talk that would tie into this week's project based learning task and we came up with changing the end points on my number line. I did 0 to 48 with 8 slips of paper. It was fabulous! They started with finding the midpoint and then one said, "I counted by 5s to 20 then I went back and added 1 to each one and they turned into sixes." A fabulous discussion ensued.

      By the way, I'm using one of your 3-Act Tasks next week! Thanks yourself for making us all a little smarter!