3rd Grade · 3.MD.C.5 · 3.MD.D.6

What is area in 3rd grade?

What is area? Area is the amount of flat space a shape covers, like the space a rug covers on a floor. In 3rd grade, your child learns to measure area in square units and to find it by counting squares.

What the standards say

The official Common Core wording, quoted exactly. The plain version follows.

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

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

What it means, in plain words

Area and square units 3.MD.C.5

Area measures how much surface a shape covers. It is a different measure from length. Length tells how long a line or a side is. Area tells how much space is inside a flat shape.

To measure area, your child uses a unit square: a square with sides 1 unit long. One unit square covers 1 square unit of area. If 10 unit squares cover a shape with no gaps and no overlaps, the shape has an area of 10 square units. A gap is a space left uncovered, and an overlap is one square lying on top of another.

So what is area in 3rd grade? It is a count of the unit squares that fit inside a shape. The quick rule for rectangles, multiplying the two sides, comes later in the year and is built on this count.

Your child should be able to:

Explain that area is the amount of flat space a shape covers
Describe a unit square and 1 square unit
Cover a shape with unit squares, with no gaps and no overlaps

Example

Square sticky notes, each 1 inch long on every side, cover a card with no gaps and no overlaps. It takes 12 notes. What is the area of the card?

Each sticky note covers 1 square inch.
The notes cover the whole card with no gaps and no overlaps, so the count is the area.
The card has an area of 12 square inches.

Finding area by counting squares 3.MD.D.6

Area by counting squares is the main method in 3rd grade. The shape sits on a grid, or your child covers it with square tiles, and then counts every square inside it. Counting row by row keeps the count tidy, so no square gets counted twice.

The answer names the size of the square. A square centimeter is a square 1 centimeter on each side, about the size of a fingernail. Small shapes use square centimeters or square inches, and a rug or a floor uses square feet or square meters. Your child can also use made-up units, such as sticky notes, as long as every unit is the same size.

Your child should be able to:

Find area by counting squares on a grid
Write the answer with its unit, such as 8 square centimeters
Pick a sensible unit: square inches for a book cover, square feet for a floor
Compare the areas of two shapes by counting their squares

Example

A shape on grid paper has a row of 5 squares, with a row of 3 squares on top of it. Each square is 1 square centimeter. What is the area of the shape?

Count the bottom row: 5 squares.
Count the top row: 3 squares.
$5 + 3 = 8$ , so the area of the shape is 8 square centimeters.

Where children usually get stuck

Your child covers a shape with tiles that leave gaps, or lets two tiles overlap, and counts them anyway.
The shape looks covered, so the count seems done. Each gap leaves space that no tile counts, and each overlap counts the same space twice.
What helps. Cover a placemat with sticky notes or crackers together. Look for gaps and overlaps before you count.
Your child counts 8 squares on a grid and writes the area as 8 centimeters.
Rulers and lengths come first in school, so a unit of length sounds right. Area counts squares, so the unit has to say square.
What helps. Ask your child to point to one of the things being counted. It is a square, so the answer is 8 square centimeters.
Your child says a long, thin strip of 8 squares has more area than a square made of 9 squares, because the strip is longer.
Length is easier to see than area, so the child compares the longest sides. Area is the number of squares, and 9 squares is more than 8.
What helps. Build both shapes out of crackers or coins and count them. Then ask which one covers more of the table.

Try four practice questions

Real 3rd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Which sentence describes what area measures?
A
How much surface a shape covers.
B
The longest side of a shape.
C
The number of sides a shape has.
D
How tall a shape is.
Show the answer and how to solve it
The correct sentence is 'How much surface a shape covers.' Area measures the surface inside a shape — how much room the shape takes up flat on a page or table.
1. 1Think about what area means. Area is the amount of surface a shape covers — the space inside the shape's outline.
2. 2The sentence 'How much surface a shape covers' talks about the surface inside the shape — that matches area.
3. 3The sentence about 'the number of sides' just counts a feature of the shape. Counting sides does not measure how much surface the shape covers.
4. 4The sentence about 'the longest side' describes only one measurement of the shape. Area is about the whole surface inside, not just one side.
5. 5The sentence about 'how tall a shape is' describes only one direction. Area is about the whole surface inside the shape, not just its height.
6. 6The correct answer is the sentence that says area is how much surface a shape covers.
Common mistake. A common mistake is thinking area is just one side or one measurement of a shape. Area is not the longest side or how tall a shape is — area is the whole surface inside the shape.
The idea underneath. Area is about the INSIDE of a shape — the surface it covers. Perimeter is about the OUTSIDE — the distance around it. Whenever a question asks about the surface a shape takes up, that is area.
2On level
The shape below is covered with unit squares. What is the area of the shape?
square units
Show the answer and how to solve it
Answer. 10
The area is $10$ square units, because the rectangle is covered by $2$ rows of $5$ unit squares, and $2 \times 5 = 10$ .
1. 1Look at the rectangle. It is covered with unit squares arranged in rows.
2. 2Count the rows and the number of unit squares in each row. There are $2$ rows, and each row has $5$ unit squares.
3. 3Multiply the number of rows by the number of unit squares in each row:
4. 4The area is $10$ square units.
Common mistake. A common mistake is counting the edges along the outside of the shape (which would give the perimeter) instead of the tiles themselves, or adding the dimensions ( $2 + 5 = 7$ ) instead of multiplying.
The idea underneath. Area is the count of unit squares that exactly cover a shape. For a rectangle, you can multiply rows by columns instead of counting one tile at a time.
3On level
Which sentence describes what area measures?
A
How much surface a shape covers.
B
The distance around a shape.
C
The longest side of a shape.
D
The number of sides a shape has.
Show the answer and how to solve it
The correct sentence is 'How much surface a shape covers.' Area measures the surface inside a shape — how much room the shape takes up flat on a page or table.
1. 1Think about what area means. Area is the amount of surface a shape covers — the space inside the shape's outline.
2. 2The sentence 'How much surface a shape covers' talks about the surface inside the shape — that matches area.
3. 3The sentence 'The distance around a shape' describes the path along the outside of the shape. That is perimeter, not area.
4. 4The sentence about 'the longest side' describes only one side, not the whole surface inside the shape.
5. 5The sentence about 'the number of sides' just counts a feature of the shape. Counting sides does not measure how much surface the shape covers.
6. 6The correct answer is the sentence that says area is how much surface a shape covers.
Common mistake. A common mistake is confusing area with perimeter. Perimeter is the distance around the outside of a shape, but area is the surface inside the shape. If you can shade the inside, you are showing area; if you trace the outline, you are showing perimeter.
The idea underneath. Area is about the INSIDE of a shape — the surface it covers. Perimeter is about the OUTSIDE — the distance around it. Whenever a question asks about the surface a shape takes up, that is area.
4Stretch
Select all statements that give a reasonable area for the surface described.
A
A photo in a family album has an area of 28 square inches.
B
A placemat for one dinner plate has an area of 7 square feet.
C
A rug beside a bed has an area of 48 square inches.
D
A bath mat has an area of 6 square feet.
Show the answer and how to solve it
The reasonable statements describe the photo in a family album (28 square inches) and the bath mat (6 square feet).
1. 1Picture each surface. Check whether the number and square unit together describe a size that fits.
2. 2The photo in a family album: An area of 28 square inches could be 4 inches by 7 inches. 4 × 7 = 28 square inches. That is a reasonable size for the photo in a family album. This statement is reasonable.
3. 3The bath mat: An area of 6 square feet could be 2 feet by 3 feet. 2 × 3 = 6 square feet. That is a reasonable size for the bath mat. This statement is reasonable.
4. 4The placemat for one dinner plate: An area of 7 square feet could be 1 foot by 7 feet. 1 × 7 = 7 square feet. That is too big for the placemat for one dinner plate. This statement is not reasonable.
5. 5The rug beside a bed: An area of 48 square inches could be 6 inches by 8 inches. 6 × 8 = 48 square inches. That is too small for the rug beside a bed. This statement is not reasonable.
6. 6Select the photo in a family album (28 square inches) and the bath mat (6 square feet).
Common mistake. Checking only the unit can lead to a mistake. Two areas can use the same unit and still describe very different sizes.
The idea underneath. An area includes a number and a square unit. Think about the size they describe together, then check whether it fits the surface.