Open Number Lines

Subtraction on the open number line can be problematic.  Depending on the prompt question or teacher direction, it can be displayed as adding up or take away.  For this reason, some teachers are hesitant to approach this.

Let’s take 83 – 37 as an example.  If we start at 82, we can record the jumps as we take away 37, and end up at the answer.

If we look at adding up, it could also look like the following.  We start at 37, and make the jumps needed to end up at 82.  The jumps total the answer in this case.

I actually like to use a third approach that once again stresses subtraction as the difference or distance between two numbers.  It’s really the second method, but presented a little different conceptually.  I’ll break it down a little more as it’s the one I like best.

Mark the two numbers on a number line. How far apart are the two numbers?
Mark two anchors or decade numbers that are close to the two end numbers.
Mark down the distance between the various chunks that you have broken the distance into. The total is how far apart the numbers are.

This approach also fits very well with timelines, which are a required part of the grade 4 curriculum.

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