Grading Priority: Verify that students remember to divide by 2 when computing triangle area. The most frequent error is calculating base × height without halving.
6. Right Triangle Perimeter (3, 4, 5 m) 2 pts
Formula: \(P = a + b + c\)
Calculation: \(3 + 4 + 5 = 12\)
Answer: 12 m
Rubric: 1 pt for setup \(3+4+5\), 1 pt for 12 m with correct linear units.
7. Right Triangle Area (b = 6 in, h = 4 in) 2 pts
Formula: \(A = (b \times h) \div 2\)
Calculation: \((6 \times 4) \div 2 = 24 \div 2 = 12\)
Answer: 12 in²
Error alert: \(24\text{ in}^2\) indicates student forgot to divide by 2 (award 1 pt).
8. Isosceles Perimeter (7, 7, 6 cm) 2 pts
Formula: \(P = \text{side}_1 + \text{side}_2 + \text{base}\)
Calculation: \(7 + 7 + 6 = 20\)
Answer: 20 cm
Rubric: 1 pt for adding all 3 sides, 1 pt for 20 cm.
9. Triangle Area (b = 8 cm, h = 5 cm) 2 pts
Formula: \(A = (b \times h) \div 2\)
Calculation: \((8 \times 5) \div 2 = 40 \div 2 = 20\)
Answer: 20 cm²
Note: Student must use perpendicular height (\(5\)), not slant edges.
10. Triangle Double Check (Sides: 8 ft, 6 ft, 10 ft)
Base = 8 ft, Height = 6 ft, Hypotenuse = 10 ft (1 pt each part).
2 pts
Part A: Perimeter
\(P = 8 + 6 + 10 = 24\text{ ft}\)
Perimeter = 24 ft
Part B: Area
\(A = (8 \times 6) \div 2 = 48 \div 2 = 24\text{ ft}^2\)
Area = 24 ft²
Teachable moment: Numbers match (\(24\)), but units distinguish length (\(\text{ft}\)) from area (\(\text{ft}^2\))! Hypotenuse (10) is NOT used for area!
Boundary Blueprint • Teacher Scoring Key Page 2 of 3
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10 Points Total
Context Checklist: Did the student correctly identify Perimeter vs. Area from the context? Fence = Perimeter; Flooring/Covering = Area; Sail cloth = Area.
11. Fencing a Garden (Rectangle: 9 m long, 5 m wide) Perimeter Problem
2 pts
Work: Fencing goes around → \(P = 2l + 2w = 2(9) + 2(5) = 18 + 10 = 28\text{ m}\)
Answer: 28 m
If student computed \(9 \times 5 = 45\text{ m}^2\), they solved for area instead of perimeter (0/2 or 1/2 with reasoning).
12. Tiling a Bathroom Floor (Rectangle: 8 ft long, 6 ft wide) Area Problem
2 pts
Work: Tiles cover the surface inside → \(A = l \times w = 8 \times 6 = 48\text{ ft}^2\)
Answer: 48 ft² (or 48 tiles)
If student answered \(28\text{ ft}\), they calculated perimeter instead of area.
13. Making a Triangular Sail (Triangle: b = 10 in, h = 7 in) Triangle Area
2 pts
Work: \(A = (b \times h) \div 2 = (10 \times 7) \div 2 = 70 \div 2 = 35\text{ in}^2\)
Answer: 35 in²
Common error: \(70\text{ in}^2\) (forgot to divide by 2). Award 1 pt if formula setup is shown.
14. Detective Work: Missing Width (Area = 28 ft², length = 7 ft) Inverse Operation
2 pts
Work: \(\text{Area} = l \times w \rightarrow 28 = 7 \times w \rightarrow w = 28 \div 7 = 4\text{ ft}\)
Answer: 4 ft
Check: \(7\text{ ft} \times 4\text{ ft} = 28\text{ ft}^2\). Linear unit: \(\text{ft}\) (not \(\text{ft}^2\)).
15. Community Park Challenge (Multi-Step Application)
Playground (12 m × 8 m) and Sandbox (right triangle: b = 4 m, h = 3 m).
2 pts
Part A: Playground Perimeter (1 pt)
\(P = 2(12) + 2(8) = 24 + 16 = 40\text{ m}\)
Perimeter = 40 m
Part B: Sandbox Area (1 pt)
\(A = (4 \times 3) \div 2 = 12 \div 2 = 6\text{ m}^2\)
Area = 6 m²
Award 1 pt for 40 m, and 1 pt for 6 m². Total for Q15 = 2 pts. Grand Total = 30 / 30 Points
Boundary Blueprint • Teacher Scoring Key Page 3 of 3
