# Exploring Number Lines

One Saturday morning, I decided to try out an estimation task with my five year old daughter while we were eating pancakes. I gave her a piece of paper and drew a blank number line on it and labeled the ends with a 0 and 10.

I started by asking her to place where the 5 should go. I wanted to give her a landmark to see how that would shape her placement of the other numbers. Here’s what she did:

I was curious whether the number line would prompt her to connect that 5 is half of 10 and should therefore go in the center. It did not.

Then I asked her to fill in the 9. I was trying to be strategic about first asking her to place 5 and then 9, so she would be more inclined to space the numbers throughout the number line. From there, I asked her to fill in the rest of the numbers. Here’s what she did:

She quickly realized that her number line didn’t look right, and she wanted to fix it. So, she did another number line below and ran into trouble between 9 and 10.

I asked her to do a third number line, and this is what she did next:

You can see from this number line that she placed 5 at the midway point. She also corrected herself more than once to make the number line more accurate and linear.

Having kids experiment with number lines is an easy and fun way for them to think more deeply about number relations and estimation. There are some fascinating studies about how kids start with a logarithmic pattern of estimating (e.g. my daughter’s first number line, where the majority of the numbers lie towards the left of the number line) and with practice and age get more linear (evenly spaced).

Here’s a great research article by Dr. Robert Siegler (Carnegie Mellon Univ.) and Dr. Julie Booth (Temple Univ.) on children’s numerical estimation:  http://www.cs.cmu.edu/~jlbooth/sieglerbooth-cd04.pdf

Want to try this type of activity with your students? Here are some blank number lines you can cut out and give to your students.