The elusive number line. Students have seen a number line since they first entered the kindergarten classroom. That famous border that goes around the room. What really is the number line? Why do we ask students to use it? Why should we as teachers use it?
I will admit that until I saw my mentor teacher use and explicitly teach the number line, I did not see it as valuable. I saw it like most of our students, a line with two arrows and some dashes. It didn’t really matter if one-half was closer to zero. If students could order fractions or a list of rational numbers, did it really matter where they placed them on the number line?
- Is five-sixths closer to one or one-half?
- Could three-tenths be closer to zero than one-third?
- Is -12.5% greater or less than -12%
All of these questions can be answered by using a number line.
By explicitly teaching students how to use the number line we are teaching them to think. Thinking is good, right?
It’s in the standards. “They” tell us to teach it. Common Core Mathematical Practice 1, “They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.” and Common Core Mathematical Practice 2, “Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.” The TEKS also mention reasoning, using tools appropriately, and number sense to solve problems.
It gives a concrete experience to an abstract concept. What do you think of when you see -180%? Not a lot. Our students don’t have a lot of experience with sales forecasts or quarterly business reports. They mostly think, that’s a lot and it must be bad because its negative. It is much like looking at the pieces of a puzzle without the box. A number line helps to give a number context.
It will lead to stronger number sense. As an adult there are few times outside of the classroom that I have ordered a list of rational numbers. However, I have been known to do a little bargain shopping at J.Crew and calculated a sale price. The cute dress is only 40% off, but the shorts are 30% off. Thirty percent is the same as three 10%s off. Or that is pretty close to 25%, which is a quarter. And 40% off is a little less than 50%, which means I will pay a little more than half. Which means I should buy them both! If we can teach students how the numbers are related, their bargain hunting future will be brighter.
It will support negative rational number thinking. Let’s be for real, ordering negative rational numbers can be a challenge. It is counter-intuitive. You count down, but then you count up. You write them in order, but then you reverse the order. Que head banging against wall. For the love of all the sixth grade math teachers in the world, let’s teach students how to use the number line.
Teaching students to use a number line can impact their reasoning skills, their number sense, and of course their shopping skills. Need a few number line resources? Check them out here.
What ways do you explicitly teach students to use the number line? Leave your great ideas in the comments, it could be featured in an upcoming post.