Field Notesgrade 7 math
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Solution key: Same shape, new size

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Camp · Same shape, new size

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1 of 8 · scale-c01

A side of length 5 is scaled by 4. What is the new length?

  1. A scale factor of 4 means the new side is four times the original.
  2. The original side is 5, so multiply 5 × 4.
  1. 5 × 4 = 20. The new length is 20.
  2. Check: 20 ÷ 5 = 4, the stated factor.

Answer: 20

2 of 8 · scale-c02

A side of length 18 is scaled by 1/2. What is the new length?

  1. The factor 1/2 makes the new side half as long.
  2. Half of the original 18 is 18 ÷ 2.
  1. 18 ÷ 2 = 9. The new length is 9.
  2. Check: two lengths of 9 make 18; the copy is smaller.

Answer: 9

3 of 8 · scale-c03

Two similar rectangles. One is 3 by 5. The other has a side of 15 matching the 5. What side matches the 3?

  1. Matching sides are original 5 and new 15.
  2. Find the new-to-original factor: 15 ÷ 5 = 3.
  1. Multiply the original side 3 by that same factor: 3 × 3 = 9.
  2. Check: 15/5 = 9/3 = 3, so both matching ratios agree.

Answer: 9

4 of 8 · scale-c04

A map scale is 1 cm = 5 km. A road is 7 cm on the map. How many kilometers is the road?

  1. One map cm stands for 5 real km.
  2. Seven map cm means seven groups of 5 km.
  1. 7 × 5 = 35. The road is 35 km long.
  2. Check: 35 ÷ 5 = 7 map cm.

Answer: 35 km

5 of 8 · scale-c05

Two similar triangles. A pair of matching sides is 4 and 10. What is the scale factor from small to large?

  1. The question asks for the factor going from small to large.
  2. Divide the large matching side 10 by small side 4.
  1. 10 ÷ 4 = 2.5, the scale factor.
  2. Check: 4 × 2.5 = 10; a factor greater than 1 enlarges.

Answer: 2.5

6 of 8 · scale-c06

A 2-inch drawing represents 16 feet. How many feet does a 5-inch drawing represent?

  1. Two drawing inches stand for 16 real feet.
  2. Find feet per drawing inch: 16 ÷ 2 = 8.
  1. Five drawing inches represent 5 × 8 = 40 feet.
  2. Check: the original two inches give 2 × 8 = 16 feet.

Answer: 40 ft

7 of 8 · scale-c07

A model uses scale 1:20. The model is 3 cm long. How long is the real object, in cm?

  1. Scale 1:20 means one model cm represents twenty real cm.
  2. The model is 3 cm, so take three groups of 20.
  1. 3 × 20 = 60. The real length is 60 cm.
  2. Check: 60 ÷ 3 = 20, the real-to-model factor.

Answer: 60 cm

8 of 8 · scale-c08

A small similar figure has perimeter 12. Scale factor 3. What is the large perimeter?

  1. Perimeter is the sum of every side length.
  2. Tripling each side length triples their total, so the perimeter is three times as long.
  1. 12 × 3 = 36. The new perimeter is 36.
  2. Check: 36 ÷ 12 = 3, the length factor.

Answer: 36