Measuring Area with Unit Squares

Section 1

Why Do We Measure Area?

Have you ever helped paint a wall, put tiles on a floor, or covered a book with paper? If so, you already know something about area! People have been measuring flat spaces for thousands of years. Let's look at how this idea started.

Ancient Egypt 🏛️

Long, long ago, farmers in Egypt needed to measure their fields after the Nile River flooded. They used ropes and sticks to figure out how much land they had.

Ancient Greece 📐

Greek thinkers, like a man named Euclid, wrote rules about shapes. They figured out how to compare the sizes of flat shapes by breaking them into smaller pieces.

Building Homes 🏠

When people build houses, they need to know the area of floors to buy the right amount of carpet. They need the area of walls to buy enough paint. Area helps us every day!

Today 🎒

Now, in 3rd grade math, you get to learn the same big idea that helped those ancient farmers. You will measure area by counting little squares!

Here is the question we are going to answer: How can we measure how much space a flat shape covers? The answer is simpler than you might think. We use unit squares!

Section 2

Key Ideas to Know

Before we start counting squares, let's learn four important words and ideas. These are the building blocks of understanding area.

Plane Figure

A plane figure is any flat shape. Think of a rectangle, a square, or an L-shape drawn on paper. It is flat — not a ball or a box.

Unit Square

A unit square is a small square where each side is exactly 1 unit long. It could be 1 inch, 1 centimeter, or 1 foot on each side.

No Gaps, No Overlaps

When you fill a shape with unit squares, every spot must be covered. No empty holes (gaps) and no squares stacked on top of each other (overlaps).

Area

The area is the number of unit squares that fill the shape. If 12 unit squares fit, the area is 12 square units!

✦ ✦ Key Takeaway

Think of area like covering a floor with square tiles. If your bedroom floor needs 20 tiles and each tile is one square foot, then your floor has an area of 20 square feet. No tile can be missing (no gaps), and no tile can sit on top of another (no overlaps). Count the tiles, and you have the area!

Section 3

See It: Covering a Shape with Squares

Let's look at a picture! Below you can see a rectangle that is 5 units wide and 3 units tall. We have filled it with unit squares. Count every square — there are no gaps and no overlaps.

A rectangle that is 5 units wide and 3 units tall, filled with 15 unit squares.

Did you count them all? There are 15 unit squares inside. That means the area of this rectangle is 15 square units. Every part of the rectangle is covered. There are no gaps and no overlaps. That's how area works!

Notice that the rectangle has 5 squares across each row and 3 rows going down. That's 5 + 5 + 5 = 15, or you can think of it as 5 × 3 = 15. Counting rows of squares is a handy trick!

Section 4

How It Works: Counting Square Units

Here is the big rule we are learning:

THE AREA RULE

Area = number of unit squares that fit inside

Count every square. No gaps. No overlaps. That number is the area!

You can find area in two ways. The first way is to count every single square, one by one. The second way works great for rectangles: you can count the rows and columns.

RECTANGLE SHORTCUT

Area = rows × columns

For rectangles, multiply the number of rows by the number of squares in each row.

But remember — the shortcut only works for rectangles. For odd shapes (like an L-shape or a T-shape), you still need to count each square. Let's look at an example of a tricky shape.

An L-shaped figure made of 6 unit squares.

This L-shape is not a rectangle, so we can't just multiply. We count each unit square: 1, 2, 3, 4, 5, 6. The area is 6 square units. Every piece is covered, with no gaps and no overlaps.

Section 5

Different Shapes, Same Idea

The area rule works for any flat shape, not just rectangles. Let's compare a few shapes and their areas. Notice how different shapes can even have the same area!

Shape	What It Looks Like	Unit Squares	Area
Small Square	2 squares across, 2 rows	4	4 square units
Long Rectangle	4 squares across, 1 row	4	4 square units
Big Rectangle	6 squares across, 3 rows	18	18 square units
T-Shape	Looks like the letter T	5	5 square units
L-Shape	Looks like the letter L	6	6 square units

Look at the small square and the long rectangle. They look very different, but they both have an area of 4 square units! That is because the same number of unit squares fits inside each one. Area is about how many squares fit, not what the shape looks like.

✦ ✦ Key Takeaway

Imagine you have 4 square crackers. You can line them up in a row to make a long rectangle, or you can put them in a 2-by-2 group to make a bigger square. Either way, you still have 4 crackers. The area is the same because the number of squares did not change — only the arrangement did!

Section 6

Worked Example: Finding the Area

Finding the Area of Emma's Picture

ProblemEmma is making a picture with square stickers. Her picture is a rectangle that is 4 stickers across and 3 stickers tall. What is the area of her picture in square units?

Step 1 — Draw It OutLet's imagine Emma's rectangle. It has 4 stickers in each row and 3 rows going down. Every sticker is one unit square.

Step 2 — Count by RowsRow 1 has 4 stickers. Row 2 has 4 stickers. Row 3 has 4 stickers. That's 4 + 4 + 4 = 12.

Step 3 — Or Use the ShortcutSince it's a rectangle, we can multiply: 4 × 3 = 12. We get the same answer!

Step 4 — Write the AnswerThe area of Emma's picture is 12 square units. That means 12 unit squares cover her picture with no gaps and no overlaps. Great job, Emma!

Section 7

Tips, Tricks, and Things to Watch Out For

Area can be easy and fun, but there are a few things that can be tricky. Let's look at what helps and what to be careful about.

✅ HELPFUL TIPS	⚠️ WATCH OUT FOR
For rectangles, use rows × columns as a shortcut.	Don't use the shortcut on shapes that are NOT rectangles.
Count carefully — touch each square as you count it.	Don't count a square twice! Mark each one as you go.
Always use the same size square for every part of the shape.	Don't mix big squares and small squares — they must all be unit squares.
Write "square units" after your number so people know it's area.	Don't forget the word "square" — just writing "15 units" is not complete.
Area measures the inside of a shape.	Don't mix up area (inside) with perimeter (the border around the outside).

✦ ✦ Key Takeaway

Area and perimeter are not the same thing! Think of it this way: if you build a fence around a garden, the fence is the perimeter. The dirt inside the fence where flowers grow is the area. Area counts the squares that fill the inside.

Section 8

What Comes Next?

Right now, you are learning to count unit squares to find area. This is a really important first step! As you grow in math, you will learn even more cool things about area.

WHAT YOU LEARN NOW	WHAT YOU'LL LEARN LATER
Count unit squares one by one to find area.	Use formulas like length × width to find area faster.
Area is measured in square units.	You'll learn specific units like square inches (in²), square feet (ft²), and square centimeters (cm²).
Measure rectangles and simple shapes.	Find the area of triangles, circles, and more!
All your unit squares are whole squares.	Sometimes you'll count half-squares too.

Everything you learn today is the foundation for those bigger ideas. Just like building blocks, you need the first layer before you can build higher. Counting unit squares is your first layer — and it's a strong one!

Section 9

Practice Problems

Now it's your turn! Try these five problems. Click "Show Answer" when you're ready to check your work.

PROBLEM 1 — WHAT DOES AREA MEAN?

In your own words, what is the area of a flat shape? What do you use to measure it?

PROBLEM 2 — COUNT THE SQUARES

A rectangle is 3 squares across and 2 squares tall. What is its area?

PROBLEM 3 — A BIGGER SHAPE

A rectangle is 7 squares across and 4 squares tall. What is its area in square units?

PROBLEM 4 — REAL-LIFE AREA

Mr. Garcia is putting square tiles on his kitchen floor. The floor is 5 tiles across and 6 tiles from front to back. Each tile is one square foot. How many tiles does he need? What is the area of the kitchen floor?

PROBLEM 5 — THINK ABOUT IT

Maya makes a rectangle that is 2 squares across and 6 squares tall. Ben makes a rectangle that is 4 squares across and 3 squares tall. Do their shapes have the same area? How do you know?

Summary

What We Learned

Today you learned that area is the amount of space inside a flat shape, called a plane figure. We measure area by filling the shape with unit squares — little squares that are each 1 unit on every side. The squares must fit perfectly with no gaps (empty spots) and no overlaps (squares stacked on each other). The number of unit squares that fit is the area, and we write it as square units.

For rectangles, you can use a shortcut: count the squares in one row and multiply by the number of rows. For other shapes, count each square one by one. Remember, different shapes can have the same area if the same number of unit squares fit inside them. Area tells us about the inside of a shape — not the border around it. Keep practicing, and you'll be an area expert in no time!