Question

card sort
match each scale drawing with one or more possible way(s) of describing its scale. one scale description will have no match.
2 units to 6 meters
3 units to 9 meters
3 units to 5 meters
2 units to 5 meters
1 unit to 2.5 meters
2 units to 10 meters
15 m
12 m
10 m

Explanation:

Step1: Simplify given scales

2 units to 6 meters simplifies to 1 unit to 3 meters ($\frac{2}{6}=\frac{1}{3}$); 3 units to 9 meters simplifies to 1 unit to 3 meters ($\frac{3}{9}=\frac{1}{3}$); 3 units to 5 meters is $\frac{3}{5}$; 2 units to 5 meters is $\frac{2}{5}$; 1 unit to 2.5 meters is $\frac{1}{2.5}=\frac{2}{5}$; 2 units to 10 meters simplifies to 1 unit to 5 meters ($\frac{2}{10}=\frac{1}{5}$).

Step2: Analyze first rectangle (15 m)

Let's assume the number of units for the 15 - m side is $x$. For a scale of 1 unit to 2.5 meters, if 1 unit represents 2.5 meters, then $x=\frac{15}{2.5}=6$ units. And 2 units to 5 meters also gives the same ratio. So the first rectangle (15 m) matches 2 units to 5 meters and 1 unit to 2.5 meters.

Step3: Analyze second rectangle (12 m)

Let the number of units for the 12 - m side be $y$. For a scale of 1 unit to 3 meters (from 3 units to 9 meters and 2 units to 6 meters), $y = \frac{12}{3}=4$ units. So the second rectangle (12 m) matches 3 units to 9 meters and 2 units to 6 meters.

Step4: Analyze third rectangle (10 m)

Let the number of units for the 10 - m side be $z$. For a scale of 1 unit to 5 meters (from 2 units to 10 meters), $z=\frac{10}{5}=2$ units. So the third rectangle (10 m) matches 2 units to 10 meters.

Step5: Identify unmatched scale

The scale 3 units to 5 meters has no match.

Answer:

• 15 - m rectangle: 2 units to 5 meters, 1 unit to 2.5 meters
• 12 - m rectangle: 3 units to 9 meters, 2 units to 6 meters
• 10 - m rectangle: 2 units to 10 meters
• Unmatched scale: 3 units to 5 meters