Fractions on a Number Line with Cuisenaire Rods

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

A couple of days ago, I blogged about equivalent fractions, and I promised a follow-up post about fractions on the number line.

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We’ve been using lots of different representations for fractions, including pattern blocks, Cuisenaire rods, and fraction tiles to explore fractions. To introduce fractions on a number line, I wanted to use a familiar manipulative, Cuisenaire rods, to help the students make a connection between fractions as parts of a whole and fractions on a number line. I wanted to introduce an element of problem-solving, so I didn’t want to directly teach the concept. Instead, I wanted to see if the students could use what they already knew about fractions to develop their own understanding of fractions on a number line.

Students were given the reproducible shown below and a set of rods to work with. First, I asked them to talk with another mathematician about the first number line and to make some observations.

Some students noticed that the number line showed 0, 1, and 2, but that A was between 0 and 1. Still others noted that the A was in the middle between 0 and 1. One student even commented that the A split the space between 0 and 1 into equal parts [smile!]. I referred the class to the number line on the wall and explained that the number line we were looking at was just a small part of the big number line–just the space between 0 and 2. I then gave them a few minutes to work with a partner, using the Cuisenaire rods, to see if they could identify the number represented by the letter A. It was really fun to see them work and hear the great math conversations! It actually wasn’t too long before a couple of partnerships came up with one half. That’s all you need!! I selected one pair of students to come up to the interactive whiteboard and use the Notebook file, which has the same number lines as the reproducible, and the infinite clone Cuisenaire rods to show how they arrived at their solution. I love it when the kids can teach a lesson instead of me.

We went through the same process with each of the other number lines. First students worked in pairs to try to solve the problem and then a pair of students were asked to present. The kids definitely had a much more difficult time with the second number line than the first, but that’s called problem-solving, right?

This is a screenshot of the Notebook file and how we showed our work for the second number line.

Grab your copy of the Notebook file here and the reproducible here.  Comments?

Do your students need more practice?  Check out my Fractions on a Number Line Scoot game.


  1. TinaMarie

    Love this!! Thank you for sharing…I can’t wait to use it with my students.

    • Donna Boucher

      My pleasure! 🙂

  2. TheElementary MathManiac

    I love how you took advantage of the linear aspect of the cuisenaire rod to move into thinking about number lines.

    The Math Maniac

    • Donna Boucher

      It’s a great model for fractions, Tara!

  3. Beth

    Donna, I can’t open the Notebook file

  4. Anonymous

    Love this!!!!

  5. April

    Thank you so much for the idea! I too downloaded the notebook file but it doesn’t recognize the file type. What did you open and use it in? You are a blessing to so many!! Thanks for all you do!

    • Donna Boucher

      It’s SMART Notebook, April. It’s the software used for SMART boards.

  6. Anonymous

    I have been a huge advocate of using Cuisenaire rods in the classrooms to model practically everything we do, but I didn’t understand how to use them for fractions since I was envisioning the whole being the 10 rod. I love your idea of the numberlines which allow the 2 rod to be use as 1/4 and the purple to be 1/2. How do you then use the other rods, though? Does your whole keep changing to accomodate the rods? How do your students who become really familiar with them being the numbers 1-10 do when presented to think of them in another way like this?
    Ann Elise

    • Anna

      I think the brown works well as a whole rod. I saw a lesson on the NCTM website that showed brown as 1 whole, pink as 1/2, red as 1/4 and white as 1/8. This doesn’t give you full range, but it will accommodate the most common equivalent fractions. Also, you can tell them that the whole is 1 10 rod and 2 1 rods. that way you can use the number 12 to break down into fractions. (1= 1/12, 2=1/6, 3=1/4, 4=1/3, 6=1/2)
      Just an idea, I’m on my fractions unit in January too.

  7. Karen Winford

    I don’t have a Smartboard – is there a way to convert the notepad file to Google-something? Thanks for the reproducibles – planning to do this next week, and these will be a great help.

  8. Jane L. Feldhausen

    Can you make the notebook file a pdf? I don’t have the app to open it, but would love to use it.

    • Donna Boucher

      Here’s the link to a PDF file. 🙂


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