3B · Chapter 13 · Lesson 3
Area of Rectangles
Derive and apply area as number of rows times number of columns.
Today's mathematical question
A rectangle is 7 unit squares across and 4 unit squares down. What is its area?
Learning target
Derive and apply area as number of rows times number of columns.
Before starting: Prior lesson: Units of Area. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
A tiled mat is 8 square units across and 4 square units down. How many unit squares cover it?
Reveal explanation
Answer: 32 square units
There are 4 rows of 8 equal square units: 8 × 4 = 32 square units.
Square-unit grid; count only visible squares without gaps or overlap. - P2
A tiled mat is 6 square units across and 5 square units down. How many unit squares cover it?
Reveal explanation
Answer: 30 square units
There are 5 rows of 6 equal square units: 6 × 5 = 30 square units.
Square-unit grid; count only visible squares without gaps or overlap. - P3
A tiled mat is 4 square units across and 2 square units down. How many unit squares cover it?
Reveal explanation
Answer: 8 square units
There are 2 rows of 4 equal square units: 4 × 2 = 8 square units.
Square-unit grid; count only visible squares without gaps or overlap.
Learn and understand
A rectangle covered with unit squares has equal numbers of squares in each row. If the width is 7 and the height is 4, there are four rows of seven squares: 28 square units. The rule area = length × width comes from counting the grid, not from memorizing a formula. A 4-by-6 grid has four rows of six square units, so it contains 24 squares. The number of squares equals the product because each row is equal.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Draw a grid with the given number of rows and columns and find the product. Check whether rotating the rectangle changes the number of squares.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- rectangle
- four-right-angle quadrilateral
- area
- number of unit squares
- dimension
- measurement of a side
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
A rectangle is 7 unit squares across and 4 unit squares down. What is its area?
- Identify the whole, the units, and what the question asks.
- There are 4 rows of 7 equal square units: 7 × 4 = 28 square units.
- Check that the answer uses the right units and makes sense.
Answer: 28 square units
Check your understanding 1
A rectangle is 6 unit squares across and 2 unit squares down. What is its area?
Reveal answer and explanation
12 square units — There are 2 rows of 6 equal square units: 6 × 2 = 12 square units.
Worked example 2
Explore, calculate, verify
A rectangle is 6 unit squares across and 6 unit squares down. What is its area?
- Identify the whole, the units, and what the question asks.
- There are 6 rows of 6 equal square units: 6 × 6 = 36 square units.
- Check that the answer uses the right units and makes sense.
Answer: 36 square units
Check your understanding 2
A rectangle is 6 unit squares across and 5 unit squares down. What is its area?
Reveal answer and explanation
30 square units — There are 5 rows of 6 equal square units: 6 × 5 = 30 square units.
Worked example 3
Explore, calculate, verify
A rectangle is 4 unit squares across and 4 unit squares down. What is its area?
- Identify the whole, the units, and what the question asks.
- There are 4 rows of 4 equal square units: 4 × 4 = 16 square units.
- Check that the answer uses the right units and makes sense.
Answer: 16 square units
Check your understanding 3
A rectangle is 6 unit squares across and 3 unit squares down. What is its area?
Reveal answer and explanation
18 square units — There are 3 rows of 6 equal square units: 6 × 3 = 18 square units.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
A rectangle is 3 unit squares across and 2 unit squares down. What is its area?
Reveal explanation
Answer: 6 square units
There are 2 rows of 3 equal square units: 3 × 2 = 6 square units.
Square-unit grid; count only visible squares without gaps or overlap. - G2
A rectangle is 5 unit squares across and 3 unit squares down. What is its area?
Reveal explanation
Answer: 15 square units
There are 3 rows of 5 equal square units: 5 × 3 = 15 square units.
Square-unit grid; count only visible squares without gaps or overlap. - G3
A rectangle is 9 unit squares across and 3 unit squares down. What is its area?
Reveal explanation
Answer: 27 square units
There are 3 rows of 9 equal square units: 9 × 3 = 27 square units.
Square-unit grid; count only visible squares without gaps or overlap. - G4
A rectangle is 9 unit squares across and 2 unit squares down. What is its area?
Reveal explanation
Answer: 18 square units
There are 2 rows of 9 equal square units: 9 × 2 = 18 square units.
Square-unit grid; count only visible squares without gaps or overlap. - G5
A rectangle is 9 unit squares across and 6 unit squares down. What is its area?
Reveal explanation
Answer: 54 square units
There are 6 rows of 9 equal square units: 9 × 6 = 54 square units.
Square-unit grid; count only visible squares without gaps or overlap.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
A rectangle is 3 unit squares across and 5 unit squares down. What is its area?
Reveal explanation
Answer: 15 square units
There are 5 rows of 3 equal square units: 3 × 5 = 15 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I2
A rectangle is 3 unit squares across and 6 unit squares down. What is its area?
Reveal explanation
Answer: 18 square units
There are 6 rows of 3 equal square units: 3 × 6 = 18 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I3
A rectangle is 4 unit squares across and 3 unit squares down. What is its area?
Reveal explanation
Answer: 12 square units
There are 3 rows of 4 equal square units: 4 × 3 = 12 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I4
A rectangle is 8 unit squares across and 5 unit squares down. What is its area?
Reveal explanation
Answer: 40 square units
There are 5 rows of 8 equal square units: 8 × 5 = 40 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I5
A rectangle is 5 unit squares across and 2 unit squares down. What is its area?
Reveal explanation
Answer: 10 square units
There are 2 rows of 5 equal square units: 5 × 2 = 10 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I6
A rectangle is 8 unit squares across and 6 unit squares down. What is its area?
Reveal explanation
Answer: 48 square units
There are 6 rows of 8 equal square units: 8 × 6 = 48 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I7
A rectangle is 3 unit squares across and 4 unit squares down. What is its area?
Reveal explanation
Answer: 12 square units
There are 4 rows of 3 equal square units: 3 × 4 = 12 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I8
A rectangle is 7 unit squares across and 2 unit squares down. What is its area?
Reveal explanation
Answer: 14 square units
There are 2 rows of 7 equal square units: 7 × 2 = 14 square units.
Square-unit grid; count only visible squares without gaps or overlap.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
A 4-by-6 rectangle and a 1-by-24 rectangle have the same area. Must they have the same perimeter?
Reveal explanation
Answer: No
Both areas are equal, but different side dimensions usually give different boundary lengths.
- C2
A student says a rectangle with area 24 square units must have perimeter 24 units. Explain why this is not generally true using a 4-by-6 example.
Reveal explanation
Answer: Perimeter 20 units
The area is 4 × 6 = 24 square units, but its perimeter is 2 × (4+6) = 20 units. Area and perimeter measure different things.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
A rectangle is 8 unit squares across and 4 unit squares down. What is its area?
Reveal explanation
Answer: 32 square units
There are 4 rows of 8 equal square units: 8 × 4 = 32 square units.
Square-unit grid; count only visible squares without gaps or overlap. - E2
A rectangle is 3 unit squares across and 3 unit squares down. What is its area?
Reveal explanation
Answer: 9 square units
There are 3 rows of 3 equal square units: 3 × 3 = 9 square units.
Square-unit grid; count only visible squares without gaps or overlap. - E3
A rectangle is 8 unit squares across and 2 unit squares down. What is its area?
Reveal explanation
Answer: 16 square units
There are 2 rows of 8 equal square units: 8 × 2 = 16 square units.
Square-unit grid; count only visible squares without gaps or overlap.