Area: Covering Rectangles with Unit Squares
Lumi kneels on a sunlit wooden floor inside a treehouse, carefully placing small square tiles one by one to cover a rectangular rug, counting aloud as each tile clicks into place.
- Explain what area means using the idea of covering a flat surface with unit squares.
- Identify a unit square and describe why it is used to measure area.
- Calculate the area of a rectangle by counting unit squares in a grid.
- Calculate the area of a rectangle by multiplying its length by its width.
- Compare two rectangles and determine which has the greater area.
Key terms
- Area
- How much flat space a shape covers.
- Unit square
- A little square that is 1 unit on each side.
- Row
- One straight line of squares going across.
- Square units
- The words we use to count area.
Covering With Squares
Area is how many little squares fit inside a shape. We use unit squares, which are the same size all the time. We line them up with no gaps and no squares on top of each other. When the shape is full, we count the squares. That number is the area! It tells us how much flat space the shape takes up.
The Fast Way: Multiply
Counting every square takes a long time. Here is a faster trick! Count how many squares fit in one row going across. Then count how many rows go down. Now multiply those two numbers. Length times width gives you the area. It is the same answer as counting one by one, but much quicker. Try both ways and check that they match!
Worked examples
Find the area of a rectangle that is 4 long and 2 wide.
- Count the squares in one row going across: that is 4.
- Count how many rows there are going down: that is 2.
- Multiply: 4 times 2 equals 8.
Answer: 8 square units
Activity
Drag unit squares onto the rectangle to cover it completely, then count how many you used.
Practice
A rug is 3 units long and 3 units wide. What is its area?
Draw a rectangle with 5 squares in each of 2 rows. Count the area.
Common mistakes to avoid
- Area is the distance around the shape.That is perimeter. Area is the squares that fill the inside, not the edge.
- You add the two sides to get area.You multiply the sides, not add them. 4 and 3 make 12, not 7.
Check your understanding
A rectangle is 5 units long and 2 units wide. What is its area?
Which best describes what area measures?
Lumi covers a rectangle with unit squares and makes 3 rows with 6 squares in each row. What is the area?
Rectangle A has a length of 3 units and a width of 4 units. Rectangle B has a length of 2 units and a width of 7 units. Which rectangle has the greater area?
Recap
Area is how much flat space a shape covers. We count unit squares inside, with no gaps. The fast way is to multiply length times width, and we always say square units.
Reflect
Where in your room could you count squares to find area?