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Composite Figures and Scale Drawings
Students decompose composite figures and apply scale factors to lengths, perimeters, and areas.
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Beginner
15–20 minutes
Volume & Area
Volume & Area
Page 4 of 8
Inside Cover
Composite Figures and Scale Drawings
At a Glance
Binder SectionVolume & Area
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How can a complex region be reorganized into simpler measurable parts?
Build Understanding
A composite figure combines familiar shapes. Draw helpful boundaries, find missing dimensions, calculate each component, and add or subtract without double-counting.
A scale factor k multiplies every length. Perimeter changes by k, but area changes by k squared. Use the scale statement consistently and include units.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Decompose into known shapes.
- Find missing dimensions first.
- Add or subtract areas.
- Lengths scale by k.
- Areas scale by k squared.
Click each word
Interactive Vocabulary
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Reveal one step at a time
Worked Examples
Example 1
L-shaped region
1
Enclose it in a 10×8 rectangle and subtract a 4×3 cutout.
2
A=80−12=68 square units.
Example 2
Rectangle plus semicircle
1
Add rectangle area and half a circle’s area.
Ask and explain
Common Questions
Does area use the same scale factor as length? No, it uses k squared.
Can I split a figure in different ways? Yes, if pieces cover it exactly once.
Should a removed region be added? No, subtract it.
Notice and correct
Common Misconceptions
Double-counting overlapping regions
Mark each nonoverlapping part.
Subtracting an unlabeled length incorrectly
Use aligned total lengths to infer it.
Learn Through Video
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Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
A 12×9 rectangle has a 4×3 corner removed. Find area.
2
We Do
Guided Practice
Two nonoverlapping rectangles 8x5 and 3x4: total A=52.
15x10 rectangle minus 5x4 cutout: A=130.
Scale factor 3, original area 12: new area=108.
Map scale 1 cm:5 km, distance 7 cm: 35 km.
Scale factor 1/2, original perimeter 30: new perimeter=15.
3
You Do
Independent Practice
A 12×9 rectangle has a 4×3 corner removed. Find area.
Create and solve a second example with different values.
4
Stretch Your Thinking
Challenge & Real-World Practice
Design a composite figure with total area 150 square units. Provide two valid solution methods and compare their efficiency.
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Before you begin, I can…
- I can identify the important information.
- I can use accurate notation, labels, and units.
- I can justify and verify my conclusion.
1
Question 1
What should happen before calculating?
2
Question 2
Which response gives the strongest evidence?
3
Question 3
What is an effective accuracy check?
4
Question 4
Why are units or labels important?
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Question 5
What should a student do after finding an error?
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