Split a Measurement in Half

An extension of the basic measurement strategy involves another basic mathematical concept, splitting something in half to get two equal parts.

Fortunately, most students come to school with this concept. Why, because most students have been in the situation where they and someone else want to share something and “you can’t have more than me.” So what do they do, they split the shared item into two equal parts.

Students can combine the halving and measurement strategies to halve even-valued distances on a number line. To start with, students can fold a bar (strip of paper) representing 4 in half. When the bar is unfolded, there are two equal parts. Students can then show that a bar of length 2 plus a bar of length 2 is equal to a bar of length 4. These steps can then be repeated to halve a bar of length 2 to get a bar of length 1.

It’s important to note that this halving technique applies the basic measurement strategy to justify the length of two equal parts that are created. One way to challenge students is to ask them if it would be okay to label one of the equal parts 1 and the other equal part 3. The point here is to emphasize a fundamental rule that governs how a number line works: two distances that measure the same length on a given number line have to be represented by the same number.

 

Measure to Locate Points

The bars of length 4, 2 and 1 can now be used to locate points on a number line that is marked off in intervals of 4.

The strategy demonstrated in the animation uses a given measurement to add or subtract from existing points on a number line. After the fact, the results are double-checked by using the given measurements to show that the distance from 0 is correct. For younger or less experienced students, you may want to build the distance from 0 first and then show that the distances from existing points are also correct.

 

Common Placement Errors

Students with a weak understanding of number lines often do not use measurement strategies when locating points on a number line. For example, to locate 2 on a number line with intervals of 4, these students move “just to the right” of 0 and make a point for 1. Then, they will move a little farther to the right and make a point for 2. In this case, the placement of the point for 2 is based on being a little more than 0 and ignores the placement of the tick mark for 4. A basic measurement strategy can be used to challenge this incorrect strategy by measuring the distance between 0 and 2 and then showing that a distance of 2 + 2 on the line does not line up with 4.

A similar misconception may be masked by students stating that “2 is between 0 and 4” and not clearly stating that it is halfway between. Be sure to push back when a student gives this response. For example, purposely misinterpret their directions by placing the point for 2 clearly closer to 0 or 4. Students that meant halfway will quickly restate their directions. For students that don’t object, more work with the basic measurement strategy is needed.