# Teaching Area Concepts, part 1

Area and Perimeter are classic math concepts that kids learn in elementary school. As teachers, all of that content can be really overwhelming to teach. In this series, I’m breaking down the area and perimeter standards into manageable chunks.

This is part 1, Teaching Area Concepts. 3.MD.5-6

Part 2: Measuring Area & Multiplication 3.MD.7a-b

Section 3: Composing & Decomposing Area and The Distributive Property 3.MD.7c-d (coming soon)

Part 4: Teaching Perimeter 3.MD.8 (half)

Part 5: Area & Perimeter Relationships and Problem Solving 3.MD.8 (half)

## Common Core Area Standards:

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

5. Recognize area as an attribute of plane figures and understand concepts of area measurement.

a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

We’re going to leave the multiplication for part 2, but we’ll cover the rest of these concepts in this post.

Overwhelmed?? I’ve spent hours and hours thinking about this and creating a whole math unit so you don’t have to. Get my Understanding Area math unit here.

## Concept: 3 ways of measuring space.

This part is technically addressed in  standard 3.MD.8, but I think it’s necessary to tackle it first, before we even try to teach any other area concepts. It’s one of those concepts that seems super intuitive to us adults, but can be super confusing for kids if it’s not taught directly.

There are 3 ways of measuring space:

##### 1: length

This is measurement with a ruler. It’s sometimes referred to as linear measurement. It’s measurement in 1D/ one dimension (length). When we give distances, like 3mm or 12 inches or 350 miles, these are measurements of length. Students should be very familiar with measuring length if they’ve had exposure to the Common Core in grades K-2.

##### 2: area

These are measurements of flat space. It’s sometimes talked about with plane (flat) figures or shapes. This is measurement in 2D/ two dimensions (length and width). When we give measurements of how big a house is, or how big a field is or how much paint we need to cover a flat wall, these are measurements of area (or surface area). When measuring area, we use square units, such as 5000 square feet or 8 square miles. If your students have been taught the Common Core standards in grades K-2, they should have had some exposure to measuring area, but it would have been called ‘arrays,’ or they might have seen it in the context of geometry.

##### 3: volume

These are measurements of cubic space. This is measurement in 3D/ three dimensions (length and width and height). It’s what we talk about when we say how much volume a storage unit holds or how much is in a box or how much air is in a room. We use cubic units to measure volume. In the Common Core, volume is taught in the fifth grade, so we are just introducing the concept here so they can see the difference between the three kinds of measurements.

## Concept: Square units

This one is deceptively difficult to teach. I feel like this is a concept that kids develop better by interacting with it, instead of through direct instruction.

I introduced the concept of a unit square by making him into a cute character. First, I explained why his name had both ‘unit’ and ‘square’ in it and showed how to use the unit square to measure area. Then, I gave the kids a whole sheet of unit squares to color and cut out, so they have their own paper unit square manipulatives.

We had plenty of time to explore working with the unit squares and to measure things like our notebook covers and desks and other flat surfaces. Plus, we did some guided questions and had some good conversations about tips and tricks for measuring with unit square, and what mistakes to avoid. (It’s always better when the kids give each other a heads up on what not to do!)

I feel like the goal of this one is just to introduce the concepts and make sure that kids are using the correct language. But really, this is a concept that will grow as we go through the rest of the area math unit.

## Concept: Measuring area by counting squares.

I always felt like this one was pretty straightforward and the kids were able to grasp it relatively easily. In teaching measuring area, I found it was more about avoiding errors, because the students generally understood the concept.

Some common errors to watch out for:

-not making even squares (being rectangles)

-not making all the squares the same size

-having gaps between the squares

-having overlaps between the squares

-not having even rows or columns

-counting incorrectly, losing count, etc.

-not checking to see if the answer makes sense (getting an odd number when all the rows are evens, etc.)

## Concept: Area & Addition

This one is really a review of concepts from second grade, so you might not have to spend any time at all here if you’re teaching third grade. However, this concept is a crucial building block for moving on to multiplication concepts, so if you do need to stop and make sure everyone is solid on this, then definitely do that! The concepts in 3.MD.7 directly rely on kids being able to use repeated addition to find the total number of squares, so make sure they are able to do that confidently before moving on.

If your students spend enough time exploring and finding the area of things with square units, they’ll naturally start to look for ‘shortcuts’ for counting all of those squares. Sooner or later, they will realize on their own that you can just add the rows instead of counting every single square. For example, if you have a rectangle that’s 3 rows of 5, the students will almost always figure out on their own that they can add 5 + 5 + 5 instead of counting every single square.

##### What if my students don’t figure out addition and area on their own?

If your kids don’t figure this out on their own, or they don’t all figure it out, you can give them little nudges to help them get there. Ask things like, Is there a faster way to count all of these? Or give them an array with way too many squares to count (a base 10 hundreds block is perfect here!). Give them lots of time to come up with a strategy and to share their ideas with each other.

If your kids are stuck here or you feel like maybe they need more of a review, go back to standard 2.OA.4 for resources and ideas. In that standards, students need to add the rows in an array of up to 5×5 to find the total number of squares.

## Concept: Different units for measuring area

Once kids are used to measuring with the square units, you can start to introduce different units. If the length of one side of the square is an inch, then we are measuring square inches. If it’s a meter, we’re measuring square meters.

Here’s where we have a chance to get creative as teachers. The more real we can make these units, the more practice and interaction we can give the kids with them, the more likely they are to internalize the concepts and be able to use the correctly.

It’s hard to understand a square kilometer if you don’t really know what a kilometer is. In my class, we worked in groups to make paper versions of the smaller units: cm, m, inch, foot, yard.

We used Google maps to map out the larger units to mark a space around our houses or school. One thing we did was to draw out a square km and mile. It was so helpful for kids to see those as a reference connected to something they were familiar with, instead of some abstract words.

In third grade, kids should also be able to use improvised units for area. This one is super fun and creative! I had kids measuring their desk in square Cheez-its, measuring the SmartBoard in square Post-its, whatever you can think of. It just has to be a square is the only requirement!

Overwhelmed?? I’ve spent hours and hours thinking about this and creating a whole math unit so you don’t have to. Get my Understanding Area math unit here.