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Scale Drawings | Grade 7

Student Concept Worksheet Answers
1
a) 200 miles | b) 3.5 inches
a) 4 in x 50 mi/in = 200 mi. b) 175 mi / 50 mi/in = 3.5 in
2
a) 10 meters | b) 4 cm
a) 5 cm x 2 m/cm = 10 m. b) 8 m / 2 m/cm = 4 cm
3
a) 168 inches = 14 feet | b) 3 inches
a) 7 in x 24 = 168 in = 14 ft. b) 72 in / 24 = 3 in
4
a) 1 inch = 5 feet | b) 1 cm = 25 km
a) 15 ft / 3 in = 5 ft/in. b) 100 km / 4 cm = 25 km/cm
Practice Worksheet Answers

Part A: Finding Actual Dimensions

# Answer Explanation
1120 miles6 in x 20 mi/in = 120 mi
240 m x 30 m8 cm x 5 m/cm = 40 m; 6 cm x 5 m/cm = 30 m
314 feet3.5 in / 0.25 in/ft = 14 ft (or 3.5 x 4 = 14)
430 meters15 cm x 200 = 3000 cm = 30 m

Part B: Finding Scale Dimensions

# Answer Explanation
56 inches300 ft / 50 ft/in = 6 in
612 cm180 km / 15 km/cm = 12 cm
72.5 inches180 in / 72 = 2.5 in

Part C: Finding Scale Factor

# Answer Explanation
81 in = 25 ft100 ft / 4 in = 25 ft/in
91 cm = 15 km90 km / 6 cm = 15 km/cm
101 : 9640 ft = 480 in; 480 in / 5 in = 96
111 cm = 20 miles70 mi / 3.5 cm = 20 mi/cm

Part D: Word Problems

12
2 inches by 2.5 inches
12 ft / 6 ft per 0.5 in = 12 / 6 = 2 half-inches = 1 in... Wait, let me recalculate: 1/2 in = 3 ft, so 1 in = 6 ft. 12 ft / 6 ft/in = 2 in. 15 ft / 6 ft/in = 2.5 in.
13
220 miles
5.5 in x 40 mi/in = 220 mi
14
32 feet
8 in x 48 = 384 in = 32 ft
15
20 cm by 15 cm
200 m / 10 m/cm = 20 cm; 150 m / 10 m/cm = 15 cm

Challenge Question #16:

a) Size: 20 ft by 20 ft (4 in x 5 ft/in = 20 ft)

b) Actual Area: 400 square feet (20 x 20 = 400)

c) The actual area is 25 times the blueprint area. Blueprint area = 16 sq in. Scale factor for area = 5 x 5 = 25. So 16 x 25 = 400 sq ft. When scale factor is k, area scales by k squared!

FAST Practice Quiz Answers
1
C) 175 miles
7 in x 25 mi/in = 175 mi. Common error: Adding instead of multiplying (B).
2
C) 112 feet
First find actual dimensions: 6 x 4 = 24 ft and 8 x 4 = 32 ft. Perimeter = 2(24) + 2(32) = 48 + 64 = 112 ft. Common error: Finding area instead of perimeter (D).
3
B) 6 inches
60 ft / 5 ft per 0.5 in = 60 / 5 = 12 half-inches = 6 inches. Or: 0.5 in / 5 ft = x / 60 ft, so x = 6 in.
4
Select: 3 in = 24 ft, 40 ft = 5 in, 56 ft = 7 in
3 in x 8 = 24 ft (correct)
40 ft / 8 = 5 in (correct)
2.5 in x 8 = 20 ft, not 16 ft (incorrect)
56 ft / 8 = 7 in (correct)
4 in x 8 = 32 ft, not 36 ft (incorrect)
5
B) 180 inches
7.5 in x 24 = 180 inches. Note: A (15 feet = 180 inches) is technically equivalent but not in inches as asked.
6
C) 540 square meters
Actual dimensions: 5 x 6 = 30 m by 3 x 6 = 18 m. Area = 30 x 18 = 540 sq m. Common error: Finding perimeter (B) or not scaling properly (A).
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for more complex proportional reasoning problems and similar figures.
4-5/6 Approaching Mastery Review multiply vs divide decision. Practice with "should answer be bigger or smaller?" strategy.
2-3/6 Developing Reteach using concrete examples (maps, rulers). Focus on setting up proportions correctly.
0-1/6 Needs Intervention Small group instruction with hands-on activities. Build understanding of proportional relationships first.
FAST Success Kit | Grade 7 | FL B.E.S.T. Standards: MA.7.GR.1.1, MA.7.GR.1.2, MA.7.GR.1.3 | Answer Key - Teacher Use Only