# Teaching Measuring Area & Multiplication, part 2

Area and Perimeter are difficult math concepts that kids usualy learn in upper elementary. As teachers, it can feel overwhelming to tackle all of that content. I’m breaking down the perimeter and area standards into manageable chunks in this blog post series.

Part 1:Teaching Area Concepts

This is part 2: Measuring Area & Multiplication

3: Composing & Decomposing Area and The Distributive Property (coming soon!)

Part 4: Teaching Perimeter

Part 5: Area & Perimeter Relationships and Problem Solving

Standards:

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

7. Relate area to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

We covered the basic area concepts and addition in part 1. Those concepts are building blocks for these standards, so make sure your kids have the foundation they need before moving forward.

Overwhelmed?? I’ve spent hours and hours (like soooo many hours) thinking about this and creating a math unit so you don’t have to. Get my Measuring Area math unit here.

## Concept: Area/ Arrays/ Products

Okay, so these are really all the same concept, if you ask me. (Or at least when dealing with the area of rectangles.) Arrays are just rectangles with the rows and columns and squares already drawn in. To find the total number of squares, you can do repeated addition or multiplication. That’s how you find the area of a square.

And any time we’re using multiplication, we’re using factors and products. So students can use these three related concepts to build their understanding.

If your students are struggling with multiplication concepts, or even their multiplication facts, I highly recommend using arrays to help them. Some students just take longer to convert the concept of repeated addition to the concept of multiplication, and that’s okay. Working with arrays and area should help them develop those concepts and make that jump. They’ll eventually get tired of counting the squares and start using the ‘shortcut’ of multiplying instead.

I used these Array Cards like alllllll the time while teaching area and multiplication.

## Concept: Multiply to find the area.

The key here is that the students MUST understand WHY we multiply to find the area of a rectangle. They need to ‘get’ how we all collectively know to multiply the length and width to find the area. Kids need to go on that journey and make that discovery for themselves, so that they truly understand the concept and can apply it and use it flexibly. Some kids will get there faster than others, and that’s okay. The important thing is that everyone understands why we multiply to find the area. So how do I make sure my students all get to that understanding?

Tiling. So. Much. Tiling. OMG, we tiled so much.

By ‘tiling,’ I mean making arrays out of squares. We made them in all one color, we made them with the rows different colors, we made them with the columns different colors. We tiled with plastic inch squares, with paper square units, with masking tape on the floor, with chalk outside on the blacktop. So much grid paper was colored in and labeled with rows, columns, totals, and formulas. We cut out array cards and sorted them and played ‘capture’ (war) and organized them from smallest to biggest and inevitable lost at least one array card each. Everything that was tile-able was tiled.

###### One of the key things about doing all of this tiling was writing the equations to go with the arrays we were building.

For me, this is the key step connecting the concrete tiles or drawings and the numbers we use in math.

For example, if we made a 3 by 5 array, we might write down some of these equations/ vocabulary:

3 + 3 + 3 + 3 + 3 = 15

5 + 5 + 5 = 15

3 x 5 = 15

5 x 3 = 15

Rows: 3

Columns: 5

Total Squares: 15

Factors: 3, 5

Product: 15

Length: 5 units

Width: 3 units

Area: 15 square units

### Questions for math talks/ assessment:

How many tiles/ squares do you have total here? What’s your strategy for finding the total?

How many tiles will you need to make a ____ by ____ array?

Which equation matches this array? How do you know?

Make an array to match this equation. How did you figure out how many rows & columns to use?

How many different arrays (rectangles) can you make with 24 total squares (an area of 24 square units)? (This one leads to being able to find the factors of a product, so your fourth grade colleagues will thank you for introducing this!)

***KEY IDEA: How did you know to multiply to find the area? (Or: Why does multiplying work to find the area?)

(Advanced) If you know the total squares and the number of rows, can you figure out how many columns?

### What if my students don’t know their multiplication facts?

Yeah, I mean, there will definitely be at least a few in every class who are struggling to memorize them. I do think it’s important for them to keep working on that, because they really do need to know the facts in order to tackle harder multiplication problems and concepts. Not knowing the multiplication facts will really slow them down, especially in the higher grades.

That being said, there’s no reason why not knowing their facts has to hold them back from understanding the area concepts at this level. They can continue to work on memorizing them AND be able to handle the same area concepts and problem solve at the same level as their peers.

There is a time and a place for supports, and I believe this is one of them. I provided my students with a multiplication fact table for this unit. It was available to anyone who wanted to use it, and I made sure no one felt bad about using it. Sometimes kids only needed it for a few facts, and sometimes they needed it for all of them. And that’s fine, because the concepts here are about understanding area and its relationship to multiplication concepts (not facts). And I found that the more they used the charts, the less they needed to use them. No one wants to do an extra step and look something up if they already know it. Laziness is a natural motivator in this case, so let’s use that to our advantage!

## Concept: Use multiplication to find the area in problem solving.

Once kids have internalized the concepts of area and multiplication, it’s time to apply that learning. After all, if you can’t use what you’ve learned, then how helpful is it, really?

Most teachers have their own problem solving tips and tricks that they teach, so I’ll leave that up to you. I always liked having the kids write their own word problems for each other. If they leave out info or their problem doesn’t make sense, the other kids will let them know, don’t worry!!  My other favorite strategy was having the kids draw the problem, so if they didn’t get enough practice drawing arrays yet, then here’s their chance!

Overwhelmed?? I’ve spent hours and hours (like soooo many hours) thinking about this and creating a math unit so you don’t have to. Get my Measuring Area math unit here.