A focused Grade 6 learning session for Ratios with Scale Drawings using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving ratios with scale drawings.
Ratios with Scale Drawings means choosing a model, naming what each number means, and explaining the strategy.
Question: Below is a scale drawing of a room with a scale bar shown. What is the actual length of the room (the longer side)?
Why it works: The drawing shows \(4\) cm. Using the scale \(1\) cm = \(2\) ft: \(4 \times 2 = 8\) feet.
Answer: \(8\) feet
Question: A double number line shows the relationship between drawing measurements and actual distances. According to the double number line, \(3\) inches on the drawing represents how many feet?
Answer: \(18\) feet
Question: A map shows a road with a scale bar. The scale bar indicates that the distance on the map from one point to another is equivalent to \(15\) kilometers in reality. The scale bar shows that \(2\) cm on the map represents \(15\) km in real life. What is the scale per centimeter?
Answer: \(7.5\) km per cm
Question: A scale drawing uses a scale of \(1\) inch \(= 4\) feet. If a room is drawn as \(3.5\) inches wide, what is the actual width?
Why it works: Multiply the drawing width by the scale: \(3.5\times4=14\) feet.
Answer: \(14\) feet
Ratios with Scale Drawings becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A scale drawing uses a scale of \(1\) inch \(= 4\) feet. If a room is drawn as \(3.5\) inches wide, what is the actual width?
Answer C: \(14\) feet
Multiply the drawing width by the scale: \(3.5\times4=14\) feet.
A map uses a scale of \(1\) cm \(= 5\) km. What actual distance does \(2\) cm on the map represent?
Answer A: \(10\) km
Use the scale: \(2 \text{ cm} \times 5 \text{ km/cm} = 10\) km.
A scale drawing of a garden uses the scale \(1\) inch \(= 6\) feet. How long is the actual garden if the drawing shows \(2.5\) inches?
Answer C: \(15\) feet
Multiply: \(2.5 \times 6 = 15\) feet.
Below is a scale drawing of a room with a scale bar shown. What is the actual length of the room (the longer side)?
Answer C: \(8\) feet
The drawing shows \(4\) cm. Using the scale \(1\) cm = \(2\) ft: \(4 \times 2 = 8\) feet.
A scale drawing has a scale of \(1\) inch \(= 12\) feet. If the actual length of a building is \(60\) feet, what is its length in the drawing?
Answer B: \(5\) inches
Divide the actual length by the scale factor: \(60 \div 12 = 5\) inches.
A map uses a scale of \(1\) inch \(= 25\) miles. Two cities are \(5\) inches apart on the map. How far apart are they in reality?
Answer D: \(125\) miles
Multiply: \(5 \text{ inches} \times 25 \text{ miles/inch} = 125\) miles.
A scale of \(1\) cm \(= 3\) m is used to draw a plan. If the actual width of a room is \(9\) m, what is the width in the drawing?
Answer B: \(3\) cm
Divide: \(9 \text{ m} \div 3 \text{ m/cm} = 3\) cm.
Below is a floor plan of a small house with a scale of \(1\) inch \(= 8\) feet. What is the actual length of the bedroom (shown as \(3\) inches in the drawing)?
Answer C: \(24\) feet
Use the scale: \(3 \text{ inches} \times 8 \text{ feet/inch} = 24\) feet.
A scale drawing uses a scale of \(1\) inch \(= 5\) feet. A rectangular room is drawn with dimensions \(4\) inches by \(3\) inches. What is the perimeter of the actual room?
Answer C: \(70\) feet
Actual dimensions: \(4 \times 5 = 20\) feet and \(3 \times 5 = 15\) feet. Perimeter: \(2(20 + 15) = 70\) feet.
A map has a scale of \(1\) cm \(= 10\) km. A rectangular region on the map measures \(4\) cm by \(6\) cm. What is the area of the actual region?
Answer C: \(2400\) km\(^2\)
Actual dimensions: \(4 \times 10 = 40\) km and \(6 \times 10 = 60\) km. Area: \(40 \times 60 = 2400\) km\(^2\).
A scale drawing is made with a scale of \(1\) inch \(= 3\) feet. What is the scale factor?
Answer C: \(36\)
Convert to the same units: \(1\) inch \(= 3\) feet \(= 36\) inches. Scale factor is \(36:1\).
