Proportional Reasoning with Scale Drawings — Drills
Proportional Reasoning with Scale Drawings has 7 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 11 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
- Scale factor — The number every length is multiplied by.
- Similar figures — Same shape, different size: equal angles, proportional sides.
- Corresponding sides — Sides in matching positions in two similar figures.
- Perimeter — Distance all the way around the outside.
- Area — Space inside, measured in square units.
- Volume — Space inside, in cubic units.
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Factor — A number that divides evenly into another.
- Scale — What one grid step is worth — and where the axis starts.
- Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
Scalefactor
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A figure is enlarged by scale factor 2.5. A side of 8 cm becomes how long?
Worked answer
20
8 × 2.5 = 20 cm
Problem 2
A figure is enlarged by scale factor 3. A side of 7 cm becomes how long?
Worked answer
21
7 × 3 = 21 cm
Readscale
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A drawing uses scale 1 : 25. A line measures 9 cm. How long is the real object in cm?
Worked answer
225
9 × 25 = 225 cm
That is 2.25 m.
Problem 2
A drawing uses scale 1 : 40. A line measures 7 cm. How long is the real object in cm?
Worked answer
280
7 × 40 = 280 cm
That is 2.8 m.
Similar
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A triangle has sides 9, 12, 15. A similar triangle has its shortest side equal to 22.5. Find its perimeter.
Worked answer
90
k = 22.59 = 2.5
Original perimeter: 36
36 × 2.5 = 90
Problem 2
A triangle has sides 3, 4, 5. A similar triangle has its shortest side equal to 6. Find its perimeter.
Worked answer
24
k = 63 = 2
Original perimeter: 12
12 × 2 = 24
Areascale
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A shape of area 20 is scaled by factor 2. Find the new area.
Worked answer
80
k2 = 22 = 4
20 × 4 = 80
Problem 2
A shape of area 12 is scaled by factor 3. Find the new area.
Worked answer
108
k2 = 32 = 9
12 × 9 = 108
Indirect
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A 5 ft person casts a 6 ft shadow. At the same moment a tree casts a 54 ft shadow. How tall is the tree?
Worked answer
45
56 = t54
6t = 270
t = 45 ft
Problem 2
A 6 ft person casts a 5 ft shadow. At the same moment a tree casts a 30 ft shadow. How tall is the tree?
Worked answer
36
65 = t30
5t = 180
t = 36 ft
Map
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
On a map, 1 cm represents 2.5 km. How many km does 12 cm represent?
Worked answer
30
12 × 2.5 = 30 km
Problem 2
On a map, 1 cm represents 3 km. How many km does 10 cm represent?
Worked answer
30
10 × 3 = 30 km
Volscale
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cylinder's lengths are all multiplied by 5. Its volume is multiplied by what?
Worked answer
125
k3 = 53 = 125
A 1-cube holds 1; a 5-cube holds 125.
Problem 2
A prism's lengths are all multiplied by 6. Its volume is multiplied by what?
Worked answer
216
k3 = 63 = 216
A 1-cube holds 1; a 6-cube holds 216.