Testinar Grade 7 math

Proportional Reasoning with Scale Models

Students will build Grade 7 mastery of proportional reasoning with scale models using models, equations, and test-style reasoning.

CH01-07 Ratios and Proportional Relationships
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A scale model of a building uses a scale of \(1\) inch \(: 12\) feet. If the actual building is \(84\) feet tall, how tall is the model (in inches)?

    1. \(6\) inches
    2. \(12\) inches
    3. \(8\) inches
    4. \(7\) inches

  2. A map uses a scale of \(1\) centimeter \(: 50\) kilometers. If two cities are \(3.5\) cm apart on the map, what is the actual distance between them?

    1. \(53.5\) km
    2. \(140\) km
    3. \(175\) km
    4. \(200\) km

  3. A toy car is \(\frac{1}{10}\) the size of a real car. If the toy is \(8\) inches long, how long is the real car?

    1. \(0.8\) feet
    2. \(4\) feet
    3. \(6.67\) feet
    4. \(80\) inches

  4. A blueprint has a scale of \(1\) inch \(: 8\) feet. A room on the blueprint is \(3\) inches by \(2.5\) inches. What are the actual dimensions?

    1. \(9\) feet \(\times\) \(8\) feet
    2. \(3\) feet \(\times\) \(2.5\) feet
    3. \(11\) feet \(\times\) \(10.5\) feet
    4. \(24\) feet \(\times\) \(20\) feet

  5. A model airplane has a scale of \(1 : 72\). If a real airplane is \(72\) meters long, how long is the model?

    1. \(1\) cm
    2. \(72\) cm
    3. \(1\) meter
    4. \(100\) cm

  6. A floor plan uses a scale of \(\frac{1}{4}\) inch to \(1\) foot. If a hallway on the plan is \(1.5\) inches long, what is the actual length?

    1. \(8\) feet
    2. \(4\) feet
    3. \(2\) feet
    4. \(6\) feet

  7. According to the scale, what are the actual dimensions of this rectangular room?

    Proportional Reasoning with Scale Models visual for G7-C01-T07-Q007
    1. \(10\) m \(\times\) \(20\) m
    2. \(4\) m \(\times\) \(3\) m
    3. \(12\) m \(\times\) \(15\) m
    4. \(20\) m \(\times\) \(15\) m

  8. A garden is \(15\) feet long and \(10\) feet wide. A scale drawing uses \(1\) inch \(= 5\) feet. What are the dimensions on the drawing?

    1. \(1.5\) inches \(\times\) \(1\) inch
    2. \(5\) inches \(\times\) \(4\) inches
    3. \(3\) inches \(\times\) \(2\) inches
    4. \(15\) inches \(\times\) \(10\) inches
Teacher and parent reference

Answer key and explanations

  1. D. \(7\) inches

    Divide the actual height by the scale factor: \(84 \div 12 = 7\) inches.

  2. C. \(175\) km

    Multiply the map distance by the scale factor: \(3.5 \times 50 = 175\) km.

  3. D. \(80\) inches

    If the toy is \(\frac{1}{10}\) the size, the real car is \(10\) times larger: \(8 \times 10 = 80\) inches.

  4. D. \(24\) feet \(\times\) \(20\) feet

    Multiply each dimension by the scale factor: \(3 \times 8 = 24\) feet and \(2.5 \times 8 = 20\) feet.

  5. C. \(1\) meter

    Divide the real length by the scale factor: \(72 \div 72 = 1\) meter.

  6. D. \(6\) feet

    The scale \(\frac{1}{4}\) inch \(: 1\) foot means \(1\) inch \(: 4\) feet. So \(1.5 \times 4 = 6\) feet.

  7. D. \(20\) m \(\times\) \(15\) m

    Using the scale \(1\) cm \(= 5\) m: width is \(4 \times 5 = 20\) m; height is \(3 \times 5 = 15\) m.

  8. C. \(3\) inches \(\times\) \(2\) inches

    Divide actual dimensions by scale: \(15 \div 5 = 3\) inches; \(10 \div 5 = 2\) inches.

Free Testinar sample Reviewed November 6, 2026 testinar.com
Page UP