Unit 5 · Teacher Resource

Unit 5 Projects — Teacher Answer Key

Worked solutions for both project versions using each calculator's default input values. Covers all four phases, quick-check answers, sample expert responses, and rubric scoring notes.

Version A — Dream Room Designer

Version A · 6.G.1

Dream Room Designer — Worked Solutions

Phase 1 · Parallelogram & Rectangle Area · 6.G.1

Main Floor: Rectangular / Parallelogram Shape

Base (b) = 12 ft Height (h) = 10 ft

Formula: Area = b × h
Area = 12 × 10 = 120 sq ft

120 sq ft

The height must be the perpendicular height (straight up from the base), not the slant side. For a rectangle the slant and perpendicular heights are equal, but students should record this distinction.

Phase 2 · Triangle Area · 6.G.1

Reading Nook: Triangular Corner

Base (b) = 6 ft Height (h) = 5 ft

Formula: Area = ½ × b × h
Area = ½ × 6 × 5
= 3 × 5
= 15 sq ft

15 sq ft

A triangle is exactly half a parallelogram. The ½ is critical — a common error is multiplying b × h without dividing by 2.

Phase 3 · Composite Area · 6.G.1

L-Shaped Bonus Room: Composite Figure

Rect A: base = 10 ft, height = 8 ft Rect B: base = 6 ft, height = 5 ft

Formula: Composite Area = Area A + Area B | Each part: b × h
Rectangle A: 10 × 8 = 80 sq ft
Rectangle B: 6 × 5 = 30 sq ft
Composite total: 80 + 30 = 110 sq ft

110 sq ft

Students must correctly decompose the L-shape into two non-overlapping rectangles. Either decomposition works as long as the dimensions are consistent with the shape.

Phase 4 · Area Application · 6.G.1

Flooring Cost Decision

Total area = 145 sq ft Price = $3.50/sq ft (Hardwood)

Formula: Cost = Total area × Price per sq ft
Cost = 145 × $3.50 = $507.50

$507.50

Note: the default area of 145 sq ft is a pre-filled "copy from above" value representing Phases 1–3 combined (120 + 15 + 10 = 145). If students use their own Phase 1–3 totals the answer will differ — that is expected and correct. Carpet at $2.25 gives $326.25; Vinyl at $1.80 gives $261.00.

Quick-Check Answer: A triangular nook with base = 6 ft and height = 4 ft.
Area = ½ × 6 × 4 = ½ × 24 = 12 sq ft
Hard-coded correct answer: 12 (see checkTriangle())

Sample Expert Response — Floor-Plan Summary (4 / Expert) My dream room's main floor is a parallelogram with base 12 ft and height 10 ft, giving an area of 120 sq ft (Area = b × h). The triangular reading nook adds 15 sq ft (½ × 6 × 5), and the L-shaped bonus room — split into a 10 × 8 rectangle (80 sq ft) and a 6 × 5 rectangle (30 sq ft) — contributes 110 sq ft, bringing the total room area to 145 sq ft. At $3.50 per sq ft, hardwood flooring costs $507.50; I chose hardwood over vinyl ($261.00) because the durability is worth the investment for a bedroom I'll use for years.

Sample 4 / 3 / 2 Rubric Scoring Note 4 — Expert: All four areas correct, formula and work shown for each, flooring cost correct, summary ties all numbers together and justifies the flooring choice.
3 — Proficient: All calculations correct; summary uses numbers but justification is brief.
2 — Developing: One minor arithmetic error (e.g., forgot ½ in triangle, or omitted one rectangle from composite); summary attempts to use numbers.

Version B — Community Mural & Garden Planner

Version B · 6.G.1

Community Mural & Garden Planner — Worked Solutions

Phase 1 · Trapezoid Area · 6.G.1

Garden Plot: Trapezoid Shape

Base 1 (b1) = 8 ft Base 2 (b2) = 12 ft Height (h) = 6 ft

Formula: Area = ½ × (b1 + b2) × h
Step 1 — add the bases: 8 + 12 = 20
Step 2 — multiply by height: 20 × 6 = 120
Step 3 — multiply by ½: 120 ÷ 2 = 60 sq ft

60 sq ft

The most common error is omitting the ½, giving 120 sq ft. Remind students the trapezoid formula is derived from two triangles (or one parallelogram cut in half).

Phase 2 · Triangle Area + Paint Coverage · 6.G.1

Mural Panel: Triangular Section & Paint Cans

Base (b) = 14 ft Height (h) = 10 ft Coverage per can = 50 sq ft

Formula: Area = ½ × b × h | Cans = ⌈ Area ÷ coverage ⌉ (round UP)
Triangle area = ½ × 14 × 10 = ½ × 140 = 70 sq ft
Cans needed = 70 ÷ 50 = 1.4 → ⌈1.4⌉ = 2 cans (ceiling round-up)

70 sq ft — 2 cans of paint

Key teaching point: 70 ÷ 50 = 1.4, so one can is not enough. Math.ceil(1.4) = 2. Students must buy 2 cans because a fractional can cannot be purchased at a store. This is a real-world application of ceiling rounding (6.G.1 application context).

Phase 3 · Parallelogram Area · 6.G.1

School Banner: Parallelogram Shape

Base (b) = 9 ft Height (h) = 4 ft

Formula: Area = b × h (perpendicular height — not slant side)
Area = 9 × 4 = 36 sq ft

36 sq ft

Emphasize using the perpendicular height. If a slanted parallelogram is drawn, the height shown is always the dashed vertical line, not the slanted leg.

Phase 4 · Budget Decision · 6.G.1 Application

Which Garden Plot Fits the Budget?

Plot 1: 60 sq ft @ $4.50/sq ft Plot 2: 45 sq ft @ $5.20/sq ft Budget: $600

Formula: Cost = Area × Price per sq ft
Plot 1: 60 × $4.50 = $270.00 ✓ within $600 budget
Plot 2: 45 × $5.20 = $234.00 ✓ within $600 budget
Both plots fit the budget. Plot 2 costs $36.00 less.

Plot 1: $270.00 | Plot 2: $234.00

With default values, both plots fit the $600 budget. Students should justify a choice based on size needs vs. cost — either choice can earn full credit with clear reasoning. The calculator's recommendation message will say "Both plots fit the budget."

Quick-Check Answer: A trapezoid with b1 = 4 ft, b2 = 6 ft, h = 3 ft.
Area = ½ × (4 + 6) × 3 = ½ × 10 × 3 = ½ × 30 = 15 sq ft
Hard-coded correct answer: 15 (see checkTrap())

Sample Expert Response — Planning Brief (4 / Expert) The trapezoid garden plot has an area of 60 sq ft — calculated as ½ × (8 + 12) × 6 — providing ample growing space for the school's herbs. The triangular mural panel is 70 sq ft (½ × 14 × 10), which requires 2 cans of paint because 70 ÷ 50 = 1.4 and we must round up to a whole can. The parallelogram banner covers 36 sq ft of fabric. I recommend Plot 2 for the garden because, at $234.00 vs. $270.00, it saves $36 while still meeting all planting goals — and both plots comfortably fit within our $600 project budget.

Sample 4 / 3 / 2 Rubric Scoring Note 4 — Expert: All four areas correct with formulas shown; paint cans rounded up with explanation; budget decision correct and brief justifies recommendation using all computed numbers.
3 — Proficient: Calculations correct; brief uses most numbers; rounding explained briefly.
2 — Developing: Trapezoid missing the ½, or paint cans not rounded up, or budget decision lacks justification.