Measurement is often one of those lowest performing areas for kids. Yeah, it’s one of those areas that on those tests that we give our kids in elementary school, they tend to score the lowest in. That’s why today, we’re going to talk about the two things that you need to focus on to help kids learn measurement in the elementary grades.

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• Navigating Through Measurement in Prekindergarten-Grade 2 (Principles and Standards for School Mathematics Navigations)
• Navigating Through Measurement in Grades 3-5 (Principles and Standards for School Mathematics Navigations)

Now, a lot of what I have learned about measurement came from two books. They’re a lot the same book, just one is for pre-K to 2nd, and one is for 3rd through 5th. They’re kind of an old book, I guess you could say. It’s not new, but sometimes we have to be reminded of the basic essential things that we need to develop for kiddos. So these two books are from the NCTM series called Navigating Through. They had like Navigating Through Geometry and Navigating Through Number. We are going to focus on the Navigating Through Measurement series.

There is the pre-K through 2nd and there’s the 3rd through 5th one. These were published back in 2005, which seems like a long time ago. But they are full of wonderful information about how kids build their understanding of measurement, along with some great activities to do in those grade bands. So, if you’ve ever struggled with things to do for measurement, check out those two books.

Now there’s a line in that book that really struck me, and it was right in the introduction, first page. It says that, “Measurement is the assignment “of a numerical value to an attribute “or characteristic of an object.”

And, it’s very basic. I know that’s a basic form of what measurement is. But really, it’s just assigning a numerical value to something about an object. And that’s really all that we have to help kids understand, is to be able to do that one thing. But in these series, they talk about two big ideas that help do that and those are the two that I really want to focus in with you. Now, you have specific grade level standards. But each of those grade level standards comes back to these two big ideas.

Understand Measurable Attributes Of Objects And The Units, Systems, & Processes Of Measurement

The first big idea is to understand measurable attributes of objects and the units, systems, and processes of measurement. I want you to think about the typical type of measurement activity that you have in your textbook. It’ll have a picture of something, and things will be marked off, and it’ll say, how long is the pencil, or whatever it might be. So, are kids really paying attention to certain attributes? No, they’re being told which attribute to pay attention to, and saying, “Here, measure it” and it’s all lined out for them.

When it comes to measurement, one of the biggest things I want you to try to be doing is letting kids measure actual objects with other objects. In pre-K to 2nd, the biggest thing is having them measure with the informal and non-standard unit. So they’re not officially using rulers. They are using paper clips. They’re using their Unifix Cubes. They’re using their feet and talking about how many feet long their whatever is.

And then we start moving them in the upper grades into the idea of the standard units because your foot is different than my foot. And that’s the cool part, is that we’re measuring the same thing, yet you say it’s three and I say it’s five. How could that be? They get to have that disequilibrium, and when we are in that phase of disequilibrium we learn the most. We want kids to struggle and understand what should we be measuring, and with what kinds of tools? And why is it important that we have a standard process and standard units to measure?

Let’s take, for instance, just these two pens here, these markers.

Some kid might say that thicker marker is bigger. But, what specifically, how specifically is it bigger? Kids, as they start to investigate things, they have to become more precise with their language, number one. A kid who says it’s bigger might say it’s bigger because this one is wider, and this one is skinnier. They might still be using some informal language as they go along. But, another kid might say the thinner marker is bigger because it is taller. And so they have to pay attention to certain attributes to be able to describe the measurements that they are looking at. And then, maybe it’s not the height or width of this at all, maybe it’s the weight that they want to pay attention to. So those attributes of an object are what we need kids to really focus on.

I’m going to share with you one of the lines from the pre-K to 2nd book.

And it says, “By the end of the pre-K to two grade band, students should understand that the fundamental process of measurement is to identify a measurable attribute of an object, select a unit, compare that unit to the object, and then report the number of units.”

That is found on page 3 of the pre-K to 2nd-grade book. So all it boils down to is decide what attribute am I going to measure, what kind of thing am I going to use to measure it, what unit am I using. Then take that unit and compare it to the object, and report back how many of those units it takes. That’s the big thing that we need kids to be able to do by the end of 2nd grade. It’s all still really informal.

Now, I know some of that has changed because of state standards. You may have something a little bit more specific, but those are the big ideas. Then in 3rd through 5th grade, they start to become more precise. We start to become deeper in those attributes. We look at specific things. We look at comparing the different attributes and what we can do with those attributes, and how it impacts the measurement of an object.

Apply Appropriate Techniques, Tools, & Formulas To Determine Measurements

The second big idea that gets brought up in these books is that kids need to learn to apply appropriate techniques, tools, and formulas to determine measurements. Now again, in the earlier grades, that starts off very informal. But it’s the idea of being able to understand that you don’t leave any gaps when you’re measuring in the early grades. For example, if I’m using paperclips, I have to line them up, end-to-end, with no gaps, no overlays of those paperclips, that’s a big thing that can impact your measurement versus my measurement. And things like you have to have a consistent measurement tool.

So if you’re going to use paperclips, you can’t use small paperclips and big paperclips at the same time. You could measure it all using big, or all using small, but you need a consistent form of a unit that you are measuring. Now, again, in the early grades, it’s all still really informal, you’re using non-standard units of measurement. They’re starting to be able to estimate a little bit in those early grades. And they’re really looking at the comparison of lengths, heights, widths, weights, all of those kinds of things. So it’s all based upon the comparison, being able to see which one it might be without having to do formal measurements.

And then in the upper grades, is where things start becoming more formal, more precise. They start learning and using all of the standard units, being able to convert in between units, all of that kind of stuff. This is also when they start to build much more of a formal vocabulary around measurement. Because they aren’t just doing height and weight. Then we have things where we’re using our measurements to determine perimeter and circumference and area versus surface area versus volume. All of those different vocabulary terms become more important in the upper grades.

So yes, we have a ton of grade level standards around measurement that our textbooks are trying to have kids go through. But I really want you to pay attention to, are those coming back to these big ideas.

Are they helping develop these two big ideas? Or, are kids just going through the motions of measuring stuff? As you’re doing your grade level standards, I want you to think about which of these two big ideas is this really supposed to be helping my kids do. Is it helping them look at attributes and decide how they’re going to measure that attribute? It is helping them be able to select an appropriate tool? And be precise with those tools? And are the kids being able to actually do it hands-on?

Because so many of the tasks in our textbook think that they are addressing these two big things, but kids aren’t in that state of disequilibrium, wondering, “What should I measure about this pencil? What is the important attribute that I measure?”

Alright, I hope that this helped you build your math mind so that you can go build the math minds of your students.

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