Great Inheritance Mathematics Term A · Independent learning

Fractions and Area

Learning target: Calculate rectangle area when sides have fractional lengths and interpret square units.

Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.

Opening task

Explore · fractional rectangle area

A rectangle has length 1/4 m and width 1/3 m. Find its area.

Show answer and worked explanation

Answer: 1/12 m²

How it works: Area = length × width = 1/4 m × 1/3 m = 1/12 m². Units multiply to square meters.

Lesson-specific prerequisite checkpoint

Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.

Find the area of a 5 m by 3 m rectangle.

Show answer and worked explanation

Answer: 15 m²

How it works: Square meters describe two-dimensional coverage.

Understand the idea

Calculate rectangle area when sides have fractional lengths and interpret square units.

Rectangle area counts square units. With fractional side lengths, refine a unit-square grid so every tile has a fractional width and height. The area is length×width and has squared units, even when the side lengths are fractions.

Vocabulary focus: unit conversion, perpendicular height, square units. Make a small labeled model, work through the arithmetic, and explain the result in words.

Watch for: Using a linear unit for area or multiplying only numerators.

Model to study: Fractional-area tile lattice.

Worked examples

Worked examples 1 · fractional rectangle area

A rectangle has length 1/3 m and width 3/4 m. Find its area.

Solution: 1/4 m²

Why: Area = length × width = 1/3 m × 3/4 m = 1/4 m². Units multiply to square meters.

Worked examples 2 · fractional rectangle area

A rectangle has length 1/2 m and width 5/3 m. Find its area.

Solution: 5/6 m²

Why: Area = length × width = 1/2 m × 5/3 m = 5/6 m². Units multiply to square meters.

Worked examples 3 · fractional rectangle area

A rectangle has length 1/2 m and width 4/3 m. Find its area.

Solution: 2/3 m²

Why: Area = length × width = 1/2 m × 4/3 m = 2/3 m². Units multiply to square meters.

Check understanding

Check understanding 1 · fractional rectangle area

A rectangle has length 1/3 m and width 5/3 m. Find its area.

Show answer and worked explanation

Answer: 5/9 m²

How it works: Area = length × width = 1/3 m × 5/3 m = 5/9 m². Units multiply to square meters.

Check understanding 2 · fractional rectangle area

A rectangle has length 3/2 m and width 1/4 m. Find its area.

Show answer and worked explanation

Answer: 3/8 m²

How it works: Area = length × width = 3/2 m × 1/4 m = 3/8 m². Units multiply to square meters.

Guided practice

Guided practice 1 · fractional rectangle area

A rectangle has length 2 m and width 5/2 m. Find its area.

Show answer and worked explanation

Answer: 5 m²

How it works: Area = length × width = 2 m × 5/2 m = 5 m². Units multiply to square meters.

Guided practice 2 · fractional rectangle area

A rectangle has length 1/3 m and width 1/2 m. Find its area.

Show answer and worked explanation

Answer: 1/6 m²

How it works: Area = length × width = 1/3 m × 1/2 m = 1/6 m². Units multiply to square meters.

Guided practice 3 · fractional rectangle area

A rectangle has length 1/4 m and width 3/2 m. Find its area.

Show answer and worked explanation

Answer: 3/8 m²

How it works: Area = length × width = 1/4 m × 3/2 m = 3/8 m². Units multiply to square meters.

Independent practice

Independent practice 1 · fractional rectangle area

A rectangle has length 1 m and width 3/4 m. Find its area.

Show answer and worked explanation

Answer: 3/4 m²

How it works: Area = length × width = 1 m × 3/4 m = 3/4 m². Units multiply to square meters.

Independent practice 2 · fractional rectangle area

A rectangle has length 3/2 m and width 3/4 m. Find its area.

Show answer and worked explanation

Answer: 9/8 m²

How it works: Area = length × width = 3/2 m × 3/4 m = 9/8 m². Units multiply to square meters.

Independent practice 3 · fractional rectangle area

A rectangle has length 2 m and width 4/3 m. Find its area.

Show answer and worked explanation

Answer: 8/3 m²

How it works: Area = length × width = 2 m × 4/3 m = 8/3 m². Units multiply to square meters.

Independent practice 4 · fractional rectangle area

A rectangle has length 3/4 m and width 2/3 m. Find its area.

Show answer and worked explanation

Answer: 1/2 m²

How it works: Area = length × width = 3/4 m × 2/3 m = 1/2 m². Units multiply to square meters.

Independent practice 5 · fractional rectangle area

A rectangle has length 1/2 m and width 1 m. Find its area.

Show answer and worked explanation

Answer: 1/2 m²

How it works: Area = length × width = 1/2 m × 1 m = 1/2 m². Units multiply to square meters.

Challenge and error analysis

Challenge and error analysis 1 · worked-error diagnosis

Error-analysis notebook: Learner notebook (LESSON): “2 m × 2 m = 4 m; I left the area in a linear unit.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: A rectangle has length 2 m and width 2 m. Find its area.

Show answer and worked explanation

Answer: 4 m²

How it works: Wrong step/assumption: Learner notebook (LESSON): “2 m × 2 m = 4 m; I left the area in a linear unit.” Diagnosis: Convert linear measures consistently, use a perpendicular height for triangles, avoid counting overlapping regions, and report area in squared units. Correct computation: Area = length × width = 2 m × 2 m = 4 m². Units multiply to square meters.

Challenge and error analysis 2 · reasoning transfer

Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). A rectangle has length 3/2 m and width 1 m. Find its area.

Show answer and worked explanation

Answer: 3/2 m²

How it works: Area = length × width = 3/2 m × 1 m = 3/2 m². Units multiply to square meters. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.

Targeted mastery: model, calculate, explain

These additional original examples address specific 5A mastery requirements. Compare the visual and the reasoning before trying the independent questions.

Targeted 1 · targeted mastery: grid

Draw equal fractional tiles for a rectangle 3/4 m by 2/3 m and calculate area.

Solution: 1/2 m²

Why: A one-meter-square grid has 4 columns × 3 rows =12 equal cells; 3 columns × 2 rows overlap in 6 cells, giving 6/12=1/2 m².

Targeted 2 · targeted mastery: grid

For a rectangle 5/6 m × 3/4 m, count overlapping tiles and simplify its area.

Solution: 5/8 m²

Why: Grid has 6×4=24 cells; 5×3=15 occupied cells; 15/24=5/8 m².

Targeted 3 · targeted mastery: grid

Find the area of 2/3 m by 3/5 m using an equal-part grid.

Show answer and worked explanation

Answer: 2/5 m²

How it works: Use a 3-column by 5-row equal-part grid, 15 cells total. The 2×3 overlap covers 6 cells, giving 6/15 = 2/5 m².

Targeted 4 · targeted mastery: grid

Show 1/2 m by 3/4 m as overlapping partitions and give the area.

Show answer and worked explanation

Answer: 3/8 m²

How it works: Draw 2 equal columns and 4 equal rows, 8 cells total. The 1×3 overlap covers 3 cells; area = 3/8 m².

Exit check

Exit check 1 · fractional rectangle area

A rectangle has length 1 m and width 1/2 m. Find its area.

Show answer and worked explanation

Answer: 1/2 m²

How it works: Area = length × width = 1 m × 1/2 m = 1/2 m². Units multiply to square meters.

Exit check 2 · fractional rectangle area

A rectangle has length 1 m and width 1/4 m. Find its area.

Show answer and worked explanation

Answer: 1/4 m²

How it works: Area = length × width = 1 m × 1/4 m = 1/4 m². Units multiply to square meters.

Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.