Linear Measurement

So, aside from the question about standard versus nonstandard measurement units and the need to keep the same units throughout the task, are there other issues that a learner must face while learning about linear measurement? If the measurement task involves placing a tool such as a ruler repeatedly onto the distance being measured, then a major issue is placement of the ruler at the exact spot where the previous placement ended. If a person is measuring the length of a room with a 12-inch ruler, he must have a way to mark the place where the ruler ends so that he can place the ruler at that exact spot for the next step. Any slight error in placement, if it is repeated each time the ruler is moved, is multiplied as the measurement task unfolds. On a wall twenty feet long, a small overlap or gap of even a quarter-inch, multiplied by the twenty times the ruler is moved, turns into a rather substantial error of five inches by the time the measurements are completed.

Figure A
Measuring a Padlock

Another component of the set of skills involved in linear measurement is the ability to read the ruler in real-world situations. The question becomes one of precision. In Figure A, which mark on the ruler is closest to the end of the lock? Would an answer of 3 inches be close enough? Do we need to look more closely and report the answer as 2 ³⁄₄ inches? Should we place a straightedge against the lock and the ruler to be more precise, giving an answer of 2 ⁵⁄₈ inches? Would it be correct to say that it is exactly 2 ¹¹⁄₁₆ inches? There are two aspects involved in answering these questions: (1) our ability to read the fractions, and (2) our ability to decide how much precision is necessary for the situation we are dealing with. Experience with the "typical" ruler (as shown in Figure B) will equip a person to know that the smallest fractional parts of an inch shown are usually sixteenths-of-an-inch. These markings limit us to a level of precision to the nearest sixteenth-of-an-inch, but they do not dictate that we must attend to that level of precision. If we simply need to know whether the lock will fit into our 3-inch wide case, then a precision level of the nearest inch will be enough. We can ignore the fractional-inch marks on the ruler. On the other hand, if we are trying to create a custom-fit case for the lock, we probably want to create one that fits snugly. For that, we probably want to use the smallest marks available on this ruler. For other purposes we can ignore the smallest marks and attend only to the eighth-inch marks, or the quarter-inch marks, or even the half-inch marks. On most rulers these different increments are marked with progressively shorter lines. As seen in this enlargement of the ruler, the inch marks are the longest, the half-inch marks are shorter and are all the same as each other, the quarter-inch marks are shorter still, the eighth-inch marks are even shorter, and the sixteenth-inch marks are the shortest of all.

Figure B
An Inch Ruler

One final issue needs to be addressed in relation to precision of measurement with a ruler. On some wooden or plastic rulers the markings begin at the very edge of the wooden or plastic material. This is the case in the ruler shown in the figure. On such a ruler, whose measured inch begins with the edge of the material, it is possible for that ruler to get worn down over time, making the ruler a bit shorter than it was when it was new. This would cause measurements taken from the edge of the ruler to be inaccurate. Many teachers used to recommend to their students that they develop a habit of using the one-inch mark as the start-point for all measurements and then subtracting 1 from the results. This practice ensures that all inaccuracies connected to the ruler edge are eliminated. On the other hand, on some rulers there is a long, inch mark near the left edge of the wood. This indicates that the measured inch begins at that mark rather than at the edge of the wood. If a person uses the edge of the wood as the beginning of the measured inch, the measurement will be about inch longer than it should be. This sort of ruler is constructed in this way so that age and wear do not affect the accuracy of the measurements. It is important for children to learn to examine the edge of their rulers to find out which type they have and measure accordingly.

Further enhance your math curriculum with more Professional Development Resources for Teaching Measurement, Grades K-5.