Practice 1
A rectangle has 4 rows of 3 unit squares. Find its area in square units.
Answer and teaching response
12 · Four complete rows each contain three squares.
Cover an area without gaps or overlaps
Build a rectangle with equal square units, then connect a complete covering to rows and multiplication.
Get the student and teacher materialsPrepare the group
Learning goal: A learner can justify an area count by showing that every equal unit square is counted exactly once.
You will need: Squared paper, pencil and 15 equal paper squares. Label each square as one square unit; screen size is not a physical ruler.
Start with this question
A rectangle has 3 rows with 5 unit squares in each row. How much area does it cover?
15 square units. The three complete rows contain 5 + 5 + 5 squares, so 3 × 5 = 15.
- Agree on one unit square. Every tile must cover the same amount of space; mixing large and small tiles does not give one consistent unit.
- Cover the rectangle completely. Move overlapping tiles and fill gaps before counting. A count describes area only when the covering is complete and non-overlapping.
- Trace one row of five squares, then count the three rows. Mark each counted row so no square is counted twice.
- Record 3 × 5 = 15 square units. Turn the page: five rows of three give the same covering and the same area.
Run the 15-minute workshop
- 3 minutes. Ask learners to tile a 3-by-5 outline. Pause if tiles overlap and have them repair the covering.
- 4 minutes. Compare counting every tile with counting complete rows. Label one row and ask what the other factor counts.
- 5 minutes. Complete the first three practice items. Require a sketch or a row explanation alongside each number.
- 3 minutes. Use the independent check, then ask whether turning the paper changes the number of tiles.
A useful error to discuss
A learner might say: There are 5 squares along the top and 3 down the side, so the area is 8.
Those counts name the row length and the number of rows. Trace the squares inside the rectangle: adding the two side counts misses most of the covering.
Practise, then check independently
Use the first three tasks for guided practice. Try the final task without help. Record a drawing or equation as well as the answer.
Practice 2
A rectangle has 2 rows of 7 unit squares. Find its area in square units.
Answer and teaching response
14 · Count two equal groups of seven square units.
Practice 3
A tiled rectangle has area 20 square units and 4 squares in every row. How many rows are there?
Answer and teaching response
5 · Five groups of four cover all twenty squares.
Independent check
Independently draw 6 rows of 3 unit squares. State the area in square units and explain each factor.
Answer and teaching response
18 · Six names the rows; three names the unit squares in each row.
Transfer the idea
Two drawings each contain 12 equal unit squares, but the squares are arranged differently. Must their areas be equal?
Discuss a possible response
Yes, if the squares have the same unit size and do not overlap. Each arrangement covers 12 square units; its outline may differ.
Choose the next teaching step
Look for:
- Names square units rather than just units.
- Explains that the covering has no gaps or overlaps.
If the idea is not secure: Draw row boundaries and number one complete row before counting the remaining rows.
If the learner is ready: Build two different rectangles with 12 tiles and compare their areas before comparing their boundaries.
Materials for your group
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