Question 1: Map distance (2 points)
\(4.25\times 12=51\).
Answer: 51 miles.
Scoring: 1 point for multiplying by 12; 1 point for 51 with the unit.
Question 2: Finding a scale (2 points)
Divide: \(10: 2.5=4\). Check: \(2.5\times 4=10\).
Answer: \(1\text{ in}=4\text{ ft}\).
Scoring: 1 point for the division; 1 point for the correct scale.
Question 3: Bedroom blueprint (2 points)
Length: \(2.4\times 5=12\text{ ft}\). Width: \(2\times 5=10\text{ ft}\).
Answer: \(12\text{ ft}\) by \(10\text{ ft}\).
Scoring: 1 point for each correct dimension.
Question 4: Garden area (2 points)
Actual dimensions: \(3\times 4=12\text{ ft}\) and \(2\times 4=8\text{ ft}\). Area: \(12\times 8=96\text{ ft}^{2}\).
Answer: \(96\text{ ft}^{2}\).
Scoring: 1 point for the actual dimensions; 1 point for the area with square units.
Question 5: Redraw the pool (2 points)
Actual: \(5\times 5=25\text{ ft}\) and \(2\times 5=10\text{ ft}\). New drawing: \(25: 2.5=10\text{ in}\) and \(10: 2.5=4\text{ in}\).
Answer: \(10\text{ in}\) by \(4\text{ in}\).
Scoring: 1 point for the actual dimensions; 1 point for the new drawing dimensions.
Question 6: Model truck (2 points)
Actual length in inches: \(18\times 12=216\text{ in}\). The scale in inches is \(6:216=1:36\). Since \(36\text{ in}=3\text{ ft}\), the scale is \(1\text{ in}=3\text{ ft}\).
Shortcut: \(18: 6=3\).
Answer: \(1\text{ in}=3\text{ ft}\).
Scoring: 1 point for a correct method; 1 point for the correct scale.
Question 7: Fractional map scale (3 points)
(a) \(\frac{1}{2}\text{ in}=5\text{ mi}\), so \(1\text{ in}=10\text{ mi}\).
(b) \(3\times 10=30\text{ mi}\).
(c) \(85: 10=8.5\text{ in}\).
Scoring: 1 point per part.
Question 8: Area mistake (3 points)
(a) \(12\times 5^{2}=12\times 25=300\text{ ft}^{2}\).
(b) Marcus multiplied the area by the scale, 5. Area has two dimensions, so both lengths grow by 5.
(c) \(25\).
Scoring: 1 point per part.
Question 9: Fitting on a card (2 points)
\(20: 8=2.5\text{ in}\) and \(14: 8=1.75\text{ in}\).
Since \(2.5\le 3\) and \(1.75\le 2\), the drawing fits.
Answer: \(2.5\text{ in}\) by \(1.75\text{ in}\); yes.
Scoring: 1 point for the dimensions; 1 point for a correct comparison with the card.
20 points
See every chapter on the Grade 7 math page.