Which row of flowers is longer?

If you’re wondering if this is a trick question, you’re right. The three rows are all the same length. However, many children will say that the top row is the longest because it has the most flowers.

While incorrect, this mistake makes sense. Children have spent a lot of time learning about counting and quantity. They know that when you compare two groups, the group with the most objects is the largest. It makes sense that the row with the most units is the longest.

This common misunderstanding points to an important difference between counting and measurement: Measurement is counting *with units*.

## Unit Size and Measurement

What happens when we measure a crayon with inches and then with centimeters?

The same object can have different measurements! Take a moment to imagine discovering this for the first time. What makes this possible, you ask? It all has to do with **unit size. **

Think about when you see a big dog and small dog walking together. They’re walking the same distance, but the number of steps is comically different. Due to its little legs, the small dog has to take lots of small steps. On the other hand, the big dog has longer legs and takes fewer big steps. Smaller step size, more steps. Bigger step size, fewer steps.

Let’s take a look back at our crayon example. An inch is bigger than a centimeter. This means that it takes fewer iterations (or repeating the inch end to end) to reach the end of the crayon. On the other hand, a centimeter is shorter than an inch, so it takes more iterations to reach the end of the crayon.

This demonstrates two important understandings in measurement. First, you can measure objects with a **variety of units**. Second, there is an **inverse relationship** between unit size and measurement: The larger the unit, the smaller the measurement, and the smaller the unit, the larger the measurement.

## Measurement Learning Trajectory

This understanding is one of the more advanced measurement concepts. Children need a strong understanding of unit and its relationship to measurement before comparing units of different length.

According to the Common Core State Standards, children learn about the relationship between unit size and measurement in **second grade**.

## Strategies and Activities

The relationship between unit size and measurement is not intuitive. Simply telling your child that smaller units have larger measurements won’t stick. In order to grasp this concept, your child needs to *experience *it in a hands-on way. They need to explore this idea with multiple opportunities to measure and discuss.

Have your child measure the length of an object with two different units. These units can be standard units, like inches and centimeters, or non-standard units, like paperclips, blocks, or pretzel sticks. Then, talk about it! In order for your child to develop this idea, they need opportunities to explain their thinking and put it into words.

**Discussion Questions**

- What do you notice about the two measurements?
- What do you notice about the two units you used? How are they different?
- What do you think would happen if we measured the length with a bigger unit?
- What do you think would happen if we measured the length with a smaller unit?

#### Encourage Exploration

Ask open ended questions about the real world.

- How many cereal boxes does it take to reach the end of the table? What if we turned the box sideways? Will that change our measurement?
- This cookie sheet is 13 inches long. If we measure in centimeters, will that change our measurement?
- When cooking, use a measuring cup with multiple measurements. How many cups of oil do we need? What is our measurement in milliliters? Why is the measurement different?

#### Make it a Game

Give your child an object to measure and 3-5 units to choose from. Ask, “Which unit will have the largest measurement? Which will have the smallest?” Then, have them test their answer.

## Further Reading

This is the third post in a series on measurement. Check out the first two posts here:

## References

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.