# Algebra, Geometry, Desmos, and the number line…

Number lines are wonderful tools. Simple, elegant, and useful to everything from beginning to count, to categorizing number groups, to helping students make sense of irrational numbers.

So, naturally my mind started racing when my daughter handed me this.

I think she intended for me to throw it away, but, sticking to the old adage “One man’s trash is another man opportunity to integrate several pieces of instructional tech to create a delicious opportunity for young people to learn mathematics” (Paraphrased), I decided that this was just to powerful a tool to chuck.

So, I thought 3-Act. The problem is, unless I’m extremely resourceful, I don’t have enough for an Act III here, so I switched to a different number line.

And trimmed it.

There we go!

Okay, so let’s start estimating the locations of some missing values. To give it a bit of context, I placed the number line scrap on a grid on Desmos.

Then, to collect the data, I created a Google Form for the students to enter their estimated coordinates at points 100 and at 55 in the missing portions of the number line.

Once you get all of the student data entered, you can simply copy the x and y columns in the Google Sheet…

… and paste it into a new line in your Desmos graph.

Then, the second part of the lesson becomes the teacher facilitating a conversation about the different ways we could either hone down our estimates, or calculate EXACTLY where the 100 point would be. (The two ideas I had were modeling the number line as a linear function or as a hypotenuse of a right triangle. Both scream for proportional reasoning, which my experience suggests is a useful activity anytime it can be fit into the curriculum.)

Then, once they feel like they’ve come up with answer they like a bunch, you can reveal to them the answer.

You may also choose to re-paste their estimate points so they can see how well they did as a group.

I like activities like this because it provides ample opportunity for focused guessing, collaboration, and a variety of solution processes. It also asks a pretty simple question at the beginning, which helps to include everyone, regardless of level.

It just seems the longer I’m involved in math education, the more and more functional uses I’m seeing for the number line.