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Fraction Classroom · 2.3.0 · Student pages

Cover an area without gaps or overlaps

Build a rectangle with equal square units, then connect a complete covering to rows and multiplication.

Anonymous group code: __________   Date: __________

Three rows of five equal unit squares cover the rectangle completely. Each small square represents one square unit.5 units across; 3 units tall
Three rows of five equal unit squares cover the rectangle completely. Each small square represents one square unit.

Build the idea

model. A rectangle has 3 rows with 5 unit squares in each row. How much area does it cover?

  1. 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.
  2. 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.
  3. Trace one row of five squares, then count the three rows. Mark each counted row so no square is counted twice.
  4. Record 3 × 5 = 15 square units. Turn the page: five rows of three give the same covering and the same area.

Worked example: 15 square units. The three complete rows contain 5 + 5 + 5 squares, so 3 × 5 = 15.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. A rectangle has 4 rows of 3 unit squares. Find its area in square units.

p2. A rectangle has 2 rows of 7 unit squares. Find its area in square units.

p3. A tiled rectangle has area 20 square units and 4 squares in every row. How many rows are there?

e1. Independently draw 6 rows of 3 unit squares. State the area in square units and explain each factor.

Transfer the idea

transfer. Two drawings each contain 12 equal unit squares, but the squares are arranged differently. Must their areas be equal?