Number Line with Intervals of 1

The basic measurement strategy introduced in the previous post can be used to build a number line from scratch.

Below is a set of directions for building a line with intervals of 1.

1. Getting started requires a blank number line and a standard unit of measure. Let’s say a bar or a rectangular strip of paper.
2. Decide what number is represented by the length of the bar. Let’s say that the bar represents a length of 1.
3. Draw a tick mark near the left end of the line and label it 0.
4. Line up the left end of the bar to the right of the 0 tick mark and measure off a distance of 1 by making a tick mark at the right end of the bar. Because 0 + 1 is 1, label the new tick mark with a 1.
5. Slide the bar just to the right of the tick mark for 1 and then make a new tick mark for 2.
6. Repeat to measure tick marks for 3, 4, 5, and so on.

 

Intervals Other than 1

The process above can be repeated with the initial length of the bar set to a number other than one. If that number is 4, then the next five tick marks would be labeled 4, 8, 12, 16, and 20.

Naturally, the next question might be, “Where would we locate 2, 1, or 7 on this line?” To locate these points, the bar of length 4 could be folded in half to measure 2 and that length could be folded in half to measure 1. A more formal version of this “splitting” strategy will be investigated in a series of future posts. But note that justifying why the halving strategy works requires invoking the basic measurement strategy.

 

Start Somewhere Other than 0

The process above can be repeated with a start point of 500 and an initial length of 20. The tick marks on this number line will be labeled 500, 520, 540, 560, 580, and 600.

 

Why Make Students Build Number Lines from Scratch?

Good question. If you want, try it with a set of your students and see how it goes. Then ask yourself, what questions would you or your students ask. For example, on the number line that starts with 500, “Where would zero go?”.

So, instead of me spouting off on this question, head over to the comments section and tell us what you think or what you found when you tried out this task with students. In the next post, I will pull together what we’ve come up with.