What is the length of the crayon below?
The answer is 3 inches, but many children will say 4 inches. We tend to teach measurement as a procedure: Line up the object with the zero on the ruler and find where the end of object is. This approach skips over the underlying concepts of measurement, causing children to make mistakes such as this one.
In this post, we’ll dig into the concept underlying this common misconception: length measurement goes hand in hand with distance.
Length Measurement as Accumulation of Distance
Distance is the measurement between two points. When we measure the length of an object, we’re measuring the distance between one end of the object and the other end. The actual practice of measuring involves repeating a unit, end to end, for the entire length of the object. As we iterate the unit (or place it end to end), we are accumulating distance. The number of repeated units is the total distance, or the length.
Let’s apply this to our crayon example. We’ve chosen the unit of inches. We repeat the inch end to end for the length of the crayon. The total distance from the end of the crayon to the tip of the crayon is the number of units, which is 3 inches!
You can also think about this in terms of the number line, where the end of the crayon is our starting position and the tip of the crayon is the ending position.
Thinking about length measurement as distance helps us understand what the hashmarks on the ruler actually mean. The 4 on the ruler does not mean “4 hashmarks.” Instead, it means that this position is 4 equal units from zero.
Strategies to Support At Home
Measuring real world objects is a great way to support your child as they learn measurement skills. While you and your child play, use these tips and questions to maximize your child’s learning:
- When using a ruler, pay close attention to how your child is measuring. Are they counting the hashmarks or the spaces? If they’re counting the hashmarks, model how to count the spaces instead: I measured it like this, one inch, two inches, three inches…
- If you have a broken ruler, don’t throw it away. Have your child explore measurement with it.
- When your child says an object has a length of 5, ask, “5 what? What does the 5 mean?”
- Give your child physical units to measure with (blocks, paperclips, etc.). Make sure they are equally-sized! When measuring, help your child place the units end to end with no spaces.
Measurement Scavenger Hunt
Send your child on a quest to find five objects in their room that have the same length, perhaps 6 inches. You can make it more like a game by rolling 1-2 die to determine the target measurement. When they have found the five objects, have them prove to you that each object is 6 inches long. While your child is explaining, pay close attention to how they measure. You can extend the activity by asking, “Is there another way to show that two objects are the same length without measuring them?”
Read and Measure Inch by Inch
Inch by Inch by Leo Linni is a wonderful picture book that tells the story of an inchworm that measures objects to avoid being eaten. The book’s beautiful illustrations are perfect for talking about measurement!
Give your child a physical unit that is close to an inch long (paperclip, block, linking cube). Have them pretend to be the inch worm working its way across the toucan’s beak. Be careful to put the unit end to end and not leave any spaces.
The illustrations are especially interesting because the measurable objects aren’t completely straight. What a great discussion topic! Ask, “Could you use a ruler to measure the toucan’s beak? Why? How else could we measure it?“
Create a Ruler
Have your child create their own ruler by iterating a standard unit and marking it on a piece of paper. For an inch ruler, cut a strip of paper that is one inch long or use a cube with one inch sides. The experience of building their own ruler will help your child understand what the numbers on the ruler actually mean.
- Play the Measurement Scavenger Hunt on a rainy day this week.
- Check out the previous post on measurement: Early Measurement Part 1: Unit
- Get excited for the next post on measurement: Early Measurement Part 3: Unit Size Matters
Feikes, David., Schwingendorf, Keith. and Gregg, Jeff. (2018) Children’s Mathematical Learning. Retrieved from this website.
Goldenberg, et al. (2014). Developing Essential Understanding of Geometry and Measurement: Pre-K-Grade 2. National Council of Teachers of Mathematics.