Updated: Apr 20, 2021
What does it mean to measure something? What decisions do we have to make when we measure something in the real world? The following questions and decisions are ones that we want children to ask and grapple with in math class:
What is being measured---length, angle, weight?
What is a good unit---tiles, cans, inches, squares, centimeters, ounces?
What is an appropriate procedure---covering, iterating, filling, counting?
Which instrument is needed to count the units---ruler, measuring cup, thermometer, protractor?
There is a difference between teaching students how to measure and what it means to measure. Modeling how to use a ruler, introducing standard and non-standard units of measurement, and teaching students how to figure the volume or area of an object is often a teacher centered activity. Giving students a measuring task and asking them to think about the decisions they have to make when measuring puts the student in the driver’s seat. Both approaches are necessary when teaching mathematics, but unfortunately, the student-centered approach often gets left to the wayside.
For Younger Students…
Using children’s literature is a great way to engage students in asking questions and making important decisions about measurement. Measuring Penny by Loreen Leedy is one that we recommend for young children. I got the idea for using this book from an article I read in NCTM’s Teaching Children Mathematics by Mi Yeon Lee and Dionne Cross Francis (Vol. 25, No. 4, 2019).
In Measuring Penny, the main character has a homework assignment. Her task is to go home and measure something. When it’s time to do her homework, she has a great idea---she can measure her Boston Terrier named Penny! The book goes on to tell the reader about standard and non-standard units of measure, and about the different ways that Penny can be measured. The main character can measure the length of Penny’s tail, the width of Penny’s pawprint, how tall Penny is, how much Penny weighs, and how big Penny is compared to other dogs.
Measuring Penny is a wonderful book about measurement, but I discovered that if I read the book first to students, it would rob them of the opportunity to ask questions and think about the important decisions we have to make when measuring. So, I decided to just read the first couple of pages and then stop and ask the class, “How would you go about measuring Penny? What would you measure? What would you measure it with? How would you measure it?”
Students invariably end up thinking, writing, and drawing about all the ways to measure Penny, and I get to find out what they already know about measurement. Children love the idea of drawing pictures of Penny (or their own pet) and illustrating different things they’d measure.
My friend and colleague Sharon Fargason read the first couple of pages of Measuring Penny to her primary grade students and then asked them how they would go about measuring Penny or their own dog. Most of Sharon’s students drew pictures that showed that they knew about measuring length, height, or width. They seemed to know about some measuring tools like rulers and yardsticks, but didn’t know the names of these tools. Here are some examples of students’ work:
This student “Measured with race cars.”
Notice how this student measured the dog’s length using numbered units.
Here a masked student shows that she knows about tools to measure her dog Coco.
Once I gather their ideas, we do a picture walk with Measuring Penny, and I let the students tell what they notice and wonder. Next, I read the book Measuring Penny aloud to the class. Finally, I present to students the following standards-based tasks, depending upon their age.
Choose an object and compare it with other objects in your house (or the classroom). Is your object longer or shorter? Heavier or lighter?
Compare objects with a straw. Is the object about the same length? Longer? Shorter?
Choose 3 objects and order them by length.
Using Non-Standard Units:
Estimate and measure the length of an object using toothpicks (or beans, paper clips, markers).
Using Standard Units:
Estimate and measure the length of an object using an appropriate tool (ruler, yardstick, meter stick). Figure out how much longer one object is from another.
For Older Students…
Measuring Penny could certainly be used as a context to help older students think about the decisions they have to make when measuring. But as students move through the grades, they must consider attributes beyond length, including area, perimeter, volume, mass, and weight. I’ve found the following lesson more appropriate for older students.
I begin by holding up a box (or showing a picture of one if teaching remotely).
I ask, “If you were to measure this box, what measurement decisions would you have to make?” This question is pretty open-ended, but I like to start with it to see what students know and what experiences they have had. If I need to provide more support, I ask questions that help students think about measurement tools and the attributes of the box.
“What if you wanted to fill the box? What unit of measurement would you use and why?”
“What if you wanted to measure the sides of the box? What unit would you use and why?
When we talk about units of measure, I want to make sure that students understand that the unit we use to measure should match with what we’re measuring. For example, if we are measuring the area of one of the sides of the box, the unit should be two-dimensional and rectangular. If we are measuring the volume of the box, the unit should be a three-dimensional rectangular prism. If we are measuring a linear attribute such as the length or width of the box, then the unit should be one-dimensional, such as an inch or centimeter.
After we brainstorm about the decisions we have to make when measuring a box, students get to measure their own box. They can work in groups or individually, and they get to choose from a variety of math tools (cubes, rulers, yardsticks or meter sticks, measuring tape, color tiles, inch-squared paper, and so on).
The purpose of the activity is for students to make measurement decisions and choose the tools that best fit the measurement task.
Putting Students in the Driver’s Seat
As students move through the grades, they go through different stages in their learning about measurement. They begin by making comparisons between objects. Then they compare objects first with non-standard units of measure and then with standard units. Students finally learn to choose suitable units and tools for specific measurements.
By posing real world situations and asking students to think about the decisions they have to make when measuring something, we are putting them in the driver’s seat and giving them opportunities to learn about what it means to measure. All you have to do is hold up a box or have students think about a dog and ask, “If you were to measure this, what decisions would you have to make?”