3B · Chapter 13 · Lesson 1
Area
Understand area as the amount of planar region covered without gaps or overlaps.
Today's mathematical question
A rectangular garden covers 4 rows of 5 equal unit squares. Find its area.
Learning target
Understand area as the amount of planar region covered without gaps or overlaps.
Before starting: Arrays and multiplication from Chapters 8 and 3A. 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
Find 6 groups of 10. Can you use 5 groups plus one more?
Reveal explanation
Answer: 60
6 groups of 10 make 6 × 10 = 60. Or find 5 × 10 and add 10.
6 rows of 10 dots = 60 dots. - P2
Compute 6 × 4. Explain a strategy using a known fact.
Reveal explanation
Answer: 24
6 groups of 4 make 6 × 4 = 24. Or find 5 × 4 and add 4.
6 rows of 4 dots = 24 dots. - P3
There are 6 equal trays with 4 counters on each tray. How many counters are there?
Reveal explanation
Answer: 24
6 groups of 4 make 6 × 4 = 24. Or find 5 × 4 and add 4.
6 rows of 4 dots = 24 dots.
Learn and understand
Area tells how much flat region is covered. To measure an area with squares, cover it without leaving gaps and without overlapping pieces. Count the total equal squares covering the region. A long, thin shape may have the same area as a short, wide one. Cover a rectangle with unit squares and count complete squares, not just rows. Two rows of five unit squares cover an area of ten square units.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Cover a rectangle with unit squares and count them one by one, then organize them into equal rows.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- area
- amount of flat space covered
- unit square
- square with side length one unit
- cover
- fill without overlap or gaps
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
A rectangular garden covers 4 rows of 5 equal unit squares. Find its area.
- Identify the whole, the units, and what the question asks.
- There are 4 rows of 5 equal square units: 5 × 4 = 20 square units.
- Check that the answer uses the right units and makes sense.
Answer: 20 square units
Check your understanding 1
A rectangular garden covers 4 rows of 4 equal unit squares. Find its area.
Reveal answer and explanation
16 square units — There are 4 rows of 4 equal square units: 4 × 4 = 16 square units.
Worked example 2
Explore, calculate, verify
A rectangular garden covers 3 rows of 8 equal unit squares. Find its area.
- Identify the whole, the units, and what the question asks.
- There are 3 rows of 8 equal square units: 8 × 3 = 24 square units.
- Check that the answer uses the right units and makes sense.
Answer: 24 square units
Check your understanding 2
A rectangular garden covers 2 rows of 9 equal unit squares. Find its area.
Reveal answer and explanation
18 square units — There are 2 rows of 9 equal square units: 9 × 2 = 18 square units.
Worked example 3
Explore, calculate, verify
A rectangular garden covers 5 rows of 4 equal unit squares. Find its area.
- Identify the whole, the units, and what the question asks.
- There are 5 rows of 4 equal square units: 4 × 5 = 20 square units.
- Check that the answer uses the right units and makes sense.
Answer: 20 square units
Check your understanding 3
A rectangular garden covers 2 rows of 6 equal unit squares. Find its area.
Reveal answer and explanation
12 square units — There are 2 rows of 6 equal square units: 6 × 2 = 12 square units.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
A rectangular garden covers 5 rows of 7 equal unit squares. Find its area.
Reveal explanation
Answer: 35 square units
There are 5 rows of 7 equal square units: 7 × 5 = 35 square units.
Square-unit grid; count only visible squares without gaps or overlap. - G2
A rectangular garden covers 2 rows of 8 equal unit squares. Find 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. - G3
A rectangular garden covers 2 rows of 4 equal unit squares. Find its area.
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. - G4
A rectangular garden covers 6 rows of 6 equal unit squares. Find its area.
Reveal explanation
Answer: 36 square units
There are 6 rows of 6 equal square units: 6 × 6 = 36 square units.
Square-unit grid; count only visible squares without gaps or overlap. - G5
A rectangular garden covers 5 rows of 6 equal unit squares. Find its area.
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.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
A rectangular garden covers 5 rows of 3 equal unit squares. Find 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 rectangular garden covers 4 rows of 3 equal unit squares. Find 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. - I3
A rectangular garden covers 6 rows of 5 equal unit squares. Find its area.
Reveal explanation
Answer: 30 square units
There are 6 rows of 5 equal square units: 5 × 6 = 30 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I4
A rectangular garden covers 3 rows of 6 equal unit squares. Find its area.
Reveal explanation
Answer: 18 square units
There are 3 rows of 6 equal square units: 6 × 3 = 18 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I5
A rectangular garden covers 3 rows of 9 equal unit squares. Find 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. - I6
A rectangular garden covers 4 rows of 6 equal unit squares. Find its area.
Reveal explanation
Answer: 24 square units
There are 4 rows of 6 equal square units: 6 × 4 = 24 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I7
A rectangular garden covers 3 rows of 7 equal unit squares. Find its area.
Reveal explanation
Answer: 21 square units
There are 3 rows of 7 equal square units: 7 × 3 = 21 square units.
Square-unit grid; count only visible squares without gaps or overlap. - I8
A rectangular garden covers 3 rows of 3 equal unit squares. Find 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.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
A 7-by-5 rectangle and a 1-by-35 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 35 square units must have perimeter 35 units. Explain why this is not generally true using a 7-by-5 example.
Reveal explanation
Answer: Perimeter 24 units
The area is 7 × 5 = 35 square units, but its perimeter is 2 × (7+5) = 24 units. Area and perimeter measure different things.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
A rectangular garden covers 6 rows of 8 equal unit squares. Find 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. - E2
A rectangular garden covers 6 rows of 9 equal unit squares. Find 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. - E3
A rectangular garden covers 6 rows of 7 equal unit squares. Find its area.
Reveal explanation
Answer: 42 square units
There are 6 rows of 7 equal square units: 7 × 6 = 42 square units.
Square-unit grid; count only visible squares without gaps or overlap.