Grade 7 · Geometry · MAT-07-GEO-001
Use Scale Factors and Scale Drawings
Represent and solve use scale factors and scale drawings problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve use scale factors and scale drawings problems using precise mathematical notation, models, and reasoning.
- Explain why a method for use scale factors and scale drawings works, interpret the result in context, and verify it independently.
Prerequisite check
Make sure the foundation is ready.
The new lesson depends on this prerequisite as active knowledge.
Learn
Build the idea from meaning, not memorization.
Mathematical meaning
Use Scale Factors and Scale Drawings connects measurement to structure. Formulas are justified by decomposition, rearrangement, similarity, coordinate reasoning, or invariance.
Represent the relationship
The Math Box uses scale drawing to expose the structure. Change one input, predict the result, then connect the visual change to an equation, table, graph, number line, or geometric model.
Calculate, interpret, and verify
Verify with an inverse operation, equivalent representation, estimate, or second method so both the calculation and reasoning are auditable.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Scale Drawing Lab
- Model one example of use scale factors and scale drawings in the Math Box.
- Change one input, predict the effect, and test the prediction.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
A drawing length is 3 cm and is enlarged by scale factor 2. Find the new length.
3 × 2 = 6 cmEvery corresponding length uses the same scale factor.
A drawing length is 4 cm and is enlarged by scale factor 3. Find the new length.
4 × 3 = 12 cmEvery corresponding length uses the same scale factor.
A drawing length is 5 cm and is enlarged by scale factor 4. Find the new length.
5 × 4 = 20 cmEvery corresponding length uses the same scale factor.
A drawing length is 6 cm and is enlarged by scale factor 5. Find the new length.
6 × 5 = 30 cmEvery corresponding length uses the same scale factor.
A drawing length is 7 cm and is enlarged by scale factor 6. Find the new length.
7 × 6 = 42 cmEvery corresponding length uses the same scale factor.
A drawing length is 8 cm and is enlarged by scale factor 2. Find the new length.
8 × 2 = 16 cmEvery corresponding length uses the same scale factor.
A drawing length is 9 cm and is enlarged by scale factor 3. Find the new length.
9 × 3 = 27 cmEvery corresponding length uses the same scale factor.
A drawing length is 10 cm and is enlarged by scale factor 4. Find the new length.
10 × 4 = 40 cmEvery corresponding length uses the same scale factor.
A drawing length is 11 cm and is enlarged by scale factor 5. Find the new length.
11 × 5 = 55 cmEvery corresponding length uses the same scale factor.
A drawing length is 12 cm and is enlarged by scale factor 6. Find the new length.
12 × 6 = 72 cmEvery corresponding length uses the same scale factor.
A drawing length is 13 cm and is enlarged by scale factor 2. Find the new length.
13 × 2 = 26 cmEvery corresponding length uses the same scale factor.
A drawing length is 14 cm and is enlarged by scale factor 3. Find the new length.
14 × 3 = 42 cmEvery corresponding length uses the same scale factor.
A drawing length is 15 cm and is enlarged by scale factor 4. Find the new length.
15 × 4 = 60 cmEvery corresponding length uses the same scale factor.
A drawing length is 16 cm and is enlarged by scale factor 5. Find the new length.
16 × 5 = 80 cmEvery corresponding length uses the same scale factor.
A drawing length is 17 cm and is enlarged by scale factor 6. Find the new length.
17 × 6 = 102 cmEvery corresponding length uses the same scale factor.
A drawing length is 18 cm and is enlarged by scale factor 2. Find the new length.
18 × 2 = 36 cmEvery corresponding length uses the same scale factor.
A drawing length is 19 cm and is enlarged by scale factor 3. Find the new length.
19 × 3 = 57 cmEvery corresponding length uses the same scale factor.
A drawing length is 20 cm and is enlarged by scale factor 4. Find the new length.
20 × 4 = 80 cmEvery corresponding length uses the same scale factor.
A drawing length is 21 cm and is enlarged by scale factor 5. Find the new length.
21 × 5 = 105 cmEvery corresponding length uses the same scale factor.
A drawing length is 22 cm and is enlarged by scale factor 6. Find the new length.
22 × 6 = 132 cmEvery corresponding length uses the same scale factor.
Practice
Guided practice with hints
01A drawing length is 23 cm and is enlarged by scale factor 2. Find the new length.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 23 × 2 = 46 cm
02A drawing length is 24 cm and is enlarged by scale factor 3. Find the new length.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 24 × 3 = 72 cm
03A drawing length is 25 cm and is enlarged by scale factor 4. Find the new length.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 25 × 4 = 100 cm
04A drawing length is 26 cm and is enlarged by scale factor 5. Find the new length.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 26 × 5 = 130 cm
05A drawing length is 27 cm and is enlarged by scale factor 6. Find the new length.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 27 × 6 = 162 cm
06A drawing length is 28 cm and is enlarged by scale factor 2. Find the new length.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 28 × 2 = 56 cm
Practice
Independent practice
01A drawing length is 29 cm and is enlarged by scale factor 3. Find the new length.
Answer: 29 × 3 = 87 cm
02A drawing length is 30 cm and is enlarged by scale factor 4. Find the new length.
Answer: 30 × 4 = 120 cm
03A drawing length is 31 cm and is enlarged by scale factor 5. Find the new length.
Answer: 31 × 5 = 155 cm
04A drawing length is 32 cm and is enlarged by scale factor 6. Find the new length.
Answer: 32 × 6 = 192 cm
05A drawing length is 33 cm and is enlarged by scale factor 2. Find the new length.
Answer: 33 × 2 = 66 cm
06A drawing length is 34 cm and is enlarged by scale factor 3. Find the new length.
Answer: 34 × 3 = 102 cm
07A drawing length is 35 cm and is enlarged by scale factor 4. Find the new length.
Answer: 35 × 4 = 140 cm
08A drawing length is 36 cm and is enlarged by scale factor 5. Find the new length.
Answer: 36 × 5 = 180 cm
Common mistakes
Learn to catch the error, not just the answer.
Label the figure and match each measure to the formula.
Use square units for area and cubic units for volume.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Estimate material, floor space, packaging, distance, surface coverage, and capacity.
- Use diagrams and coordinates to justify measurements rather than relying on appearance.
Challenge problems
A drawing length is 37 cm and is enlarged by scale factor 6. Find the new length.
37 × 6 = 222 cm
A drawing length is 38 cm and is enlarged by scale factor 2. Find the new length.
38 × 2 = 76 cm
A drawing length is 39 cm and is enlarged by scale factor 3. Find the new length.
39 × 3 = 117 cm
A drawing length is 40 cm and is enlarged by scale factor 4. Find the new length.
40 × 4 = 160 cm
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve use scale factors and scale drawings problems accurately and justify each result with a valid check.
Practice
Mastery check
01A drawing length is 41 cm and is enlarged by scale factor 5. Find the new length.
Answer: 41 × 5 = 205 cm
02A drawing length is 42 cm and is enlarged by scale factor 6. Find the new length.
Answer: 42 × 6 = 252 cm
03A drawing length is 43 cm and is enlarged by scale factor 2. Find the new length.
Answer: 43 × 2 = 86 cm
04A drawing length is 44 cm and is enlarged by scale factor 3. Find the new length.
Answer: 44 × 3 = 132 cm
05A drawing length is 45 cm and is enlarged by scale factor 4. Find the new length.
Answer: 45 × 4 = 180 cm
06A drawing length is 46 cm and is enlarged by scale factor 5. Find the new length.
Answer: 46 × 5 = 230 cm
07A drawing length is 47 cm and is enlarged by scale factor 6. Find the new length.
Answer: 47 × 6 = 282 cm
08A drawing length is 48 cm and is enlarged by scale factor 2. Find the new length.
Answer: 48 × 2 = 96 cm
Terminology
Words to know
- dimension
- A measurable extent such as length, width, or height.
- area
- Two-dimensional measure in square units.
- surface area
- Total area of exterior faces or surfaces.
- volume
- Three-dimensional space measured in cubic units.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Middle-school instructional guidance, mathematical practices, modeling, and coherent progression.Common Core State Standards for Mathematics — Grade 7
Grade-level expectations for ratios, number systems, algebra, geometry, statistics, and probability.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.