The original drawing uses 1 cm = 4 ft and measures 5 cm by 6 cm. Reproduce it using 1 cm = 8 ft. What should the new drawing dimensions be?
Show reasoning / computation: __________________________________________
CCSS 7.G.A.1 · reproduce drawings at a different scale
Reproduce Scale Drawings at a New Scale Worksheets
Students first recover the actual dimensions represented by the original drawing, then rebuild the drawing under a new scale. This prevents the common error of multiplying by the new scale without preserving the real object.
Preview · US Letter
Reproduce Scale Drawings
Diagrams are part of the problem data, not decorative assets. Student pages keep solution-specific marks hidden; reveal answers or use the separate PDF key to check work.
Problem 1
Problem 2
The original drawing uses 1 cm = 4 ft and measures 7 cm by 5 cm. Reproduce it using 1 cm = 8 ft. What should the new drawing dimensions be?
Show reasoning / computation: __________________________________________
Problem 3
The original drawing uses 1 cm = 2 ft and measures 7 cm by 5 cm. Reproduce it using 1 cm = 4 ft. What should the new drawing dimensions be?
Show reasoning / computation: __________________________________________
Problem 4
The original drawing uses 1 cm = 3 ft and measures 3 cm by 4 cm. Reproduce it using 1 cm = 6 ft. What should the new drawing dimensions be?
Show reasoning / computation: __________________________________________
Problem 5
The original drawing uses 1 cm = 4 ft and measures 3 cm by 4 cm. Reproduce it using 1 cm = 8 ft. What should the new drawing dimensions be?
Show reasoning / computation: __________________________________________
Problem 6
The original drawing uses 1 cm = 4 ft and measures 7 cm by 5 cm. Reproduce it using 1 cm = 2 ft. What should the new drawing dimensions be?
Show reasoning / computation: __________________________________________
Problem 7
The original drawing uses 1 cm = 3 ft and measures 8 cm by 5 cm. Reproduce it using 1 cm = 6 ft. What should the new drawing dimensions be?
Show reasoning / computation: __________________________________________
Problem 8
The original drawing uses 1 cm = 4 ft and measures 3 cm by 4 cm. Reproduce it using 1 cm = 2 ft. What should the new drawing dimensions be?
Show reasoning / computation: __________________________________________
Redrawing a figure at a new scale
A scale tells how much real length one unit of the drawing stands for. To redraw at a new scale, first find the real length from the old drawing, then divide by the new scale to get the new drawing length. The real object stays the same, so a larger real-units-per-centimeter scale gives a smaller drawing.
Worked examples
- A wall is 4 cm long at 1 cm : 2 m, so it is really 4 × 2 = 8 m long. At 1 cm : 4 m the drawing length is 8 ÷ 4 = 2 cm.
- A pond is 6 cm wide at 1 cm : 5 m, so it is 30 m wide. At 1 cm : 3 m it is drawn 30 ÷ 3 = 10 cm wide.
- Check by converting back: 2 cm at 1 cm : 4 m is 8 m, which matches the real length.
Common slips
- Multiplying the old length by the new scale without finding the real length first.
- Making the drawing bigger when the scale number increases. A larger number of meters per centimeter makes the drawing smaller.
- Mixing units, such as using centimeters for the drawing and meters for the real length without converting.
How to use this worksheet
Ask students to write the real length on its own line before computing the new drawing length. The answer key lists both, so students can see where a mistake started.
Common Core connection
- 7.G.A.1 · Solve problems involving scale drawings, including finding actual or drawing lengths.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Note 1
The real object stays the same when the drawing scale changes.
Note 2
A larger real-units-per-centimeter scale produces a smaller drawing of the same object.
Note 3
Example: a shape drawn at 1 cm to 2 m becomes half as wide on paper when redrawn at 1 cm to 4 m, because each centimeter now stands for twice the real distance.
Note 4
Check the new dimensions by converting them back to actual size.
Continue the 7.G progression
Move to another Grade 7 geometry skill
Quick answers
Does the generator only enlarge drawings?
No. Seeds can require either enlargement or reduction depending on the old and new scales.
Are students expected to redraw the shape?
The worksheet gives a source diagram and space/dimensions for a new reproduction; the answer key gives the correct new dimensions.
Which standard does this practice?
CCSS 7.G.A.1, which explicitly includes reproducing a scale drawing at a different scale.