Fractions on a Number Line

Kids tend to do really well understanding the concept of a number line and using it to count whole numbers.  And they also are usually able to understand basic fraction concepts.  But when it comes to putting the two concepts together- fractions on a number line- things can get tricky.  Here’s  a look at why and how we can help.

Why are fractions on a number line tough to understand? There are three models for understanding fractions.

-There’s the area model, which is what we are asking kids to understand when they are shading 1/8 of a pizza or 2/3 of a chocolate bar.  This usually goes over pretty well, because students are able to see that the top number is the number of shaded pieces, and the bottom number is the total.  No problem.

-There’s also the set model, which is what we use when we say we ate half of a batch of 12 cupcakes.  This is a little more complicated.  But it’s also basically division, so if your students understand division concepts, they’ll be alright.  

-The linear model is, in my experience, where kids tend to struggle.  It’s hard for them to understand why 3 marks on a number line creates halves.  (Because it takes 3 lines to divide the line into 2 spaces!)  Students sometimes have a hard time switching back and forth between looking at the spaces between the lines (like the area model) and looking at one point on the line (in the linear model). 

Here are some ideas for helping students understand the linear model and fractions on a number line:

-Build on their understanding of the area model.  Use visuals or concrete models to help students connect the idea of the spaces between the lines to the area model that they already know.  

-Relate it to measurement.  Start with finding the point that is half an inch, or half a meter, or half of a liter even.  Once your students develop the concept of a certain point being halfway, start working on fourths and other fractional parts. 

-Use a clothesline.  Hang the different fractions with clothespins or paperclips.  It’s interactive because you can add more fractions, move them, or take them away as your class explores and develops the concepts.  

-Use tons of visuals.  Connect the fractional number line to the whole number line by showing a magnification of the space between 0 and 1.  

-Use the number line to… count.  Just like with whole numbers, practice counting on the fractional number line.  0, 1/4, 2/4, 3/4, 1.  Have students point to each spot on the number line as they count.  

-Act it out.  Draw fraction number lines on the playground (with chalk).  Have the kids step or jump from one point on the line to the next as they count in fractions.  Have them figure out how many points they need to draw to have thirds, how many to make eighths, etc.  (They’ll soon see that it’s a lot harder to jump halfway than it is to jump 1/10th of the way, and they’ll start developing concepts about fractional size as they play!)

-Extend whole number line activities to fraction number lines.  Ask your Kindergarten colleagues how they teach kids the number line  (or check Pinterest!!).  Do that, but with fractions!

Happy (Number Line) Teaching!!
Christine Cadalzo

Here’s a FREE Fractions on a Number Line teamwork challenge…