Binder Page

Composite Figures and Scale Drawings

Students decompose composite figures and apply scale factors to lengths, perimeters, and areas.

Find It. Learn It. Master It.

My Progress
Beginner 15–20 minutes Volume & Area
Volume & Area Page 4 of 8
Inside Cover

At a Glance

Composite Figures and Scale Drawings
Binder SectionVolume & Area
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
Essential Question

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

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.

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

Watch, pause, and explain

Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.

Not Started
Open video
Now Playing

Composite Figures lesson and examples

Next Step

Ready to practice?

Use Practice It to apply what you just watched.

Go to Practice It →
Build Your Skills

Practice until you can explain it

Move from a quick warm-up to guided practice, independent work, and deeper challenges.

0% 0 of 4 stages complete
Warm-Up Guided Independent Challenge
1
Quick Start

Warm-Up

Warm-up 1

Directions: Solve the problem. Show your thinking, then enter only your final answer.

A 12×9 rectangle has a 4×3 corner removed. Find area.

Picture the area and perimeterUse the picture to organize what you know before you solve.
5 units3 units

Choose how you want to work or answer.

2
We Do

Guided Practice

3
You Do

Independent Practice

Independent 1

Directions: Solve independently. Show your work, check it, then enter only your final answer.

A 12×9 rectangle has a 4×3 corner removed. Find area.

Picture the area and perimeterUse the picture to organize what you know before you solve.
5 units3 units

Choose how you want to work or answer.

Independent 2

Directions: Solve independently. Show your work, check it, then enter only your final answer.

Create and solve a second example with different values.

Picture your planUse the picture to organize what you know before you solve.
What do Iknow?Which rulefits?What must Ifind?

Choose how you want to work or answer.

4
Stretch Your Thinking

Challenge & Real-World Practice

🧩 Challenge

Design a composite figure with total area 150 square units. Provide two valid solution methods and compare their efficiency.

IXL

Khan Academy

DeltaMath

BUILD YOUR PERSONAL MATH LIBRARY

Save today’s lesson and grow your MathBinder

Collect lesson resources, revisit recent pages, build review packets, and watch your binder grow over time.

Open My Binder →
My Binder 0 Lessons in My Binder
Start your collection
Today’s Lesson

Printable Resources

0 resources collected
Lesson Resource

Printable Lesson Notes

Guided notes that follow this lesson and are ready to print and place in your binder.

  • Vocabulary
  • Worked examples
  • Guided notes
Coming Soon
Skill Practice

Practice Pages

Guided and independent practice pages for mastering today’s lesson.

  • Guided practice
  • Independent practice
  • Challenge question
Coming Soon
Extension

Challenge Problems

Stretch your thinking with higher-level questions, puzzles, and enrichment activities.

  • Extension problems
  • Math puzzles
  • Enrichment
Coming Soon
Adult Support

Teacher & Parent Resources

Answer keys, teaching tips, intervention ideas, extensions, and discussion prompts.

  • Answer key
  • Teaching tips
  • Discussion prompts
Coming Soon
Your Collection

Recently Added

Your saved lessons will appear here.Build a binder you can use all year.
Binder Preview

My MathBinder

MathBinder Find It. Learn It. Master It. 0 lessons
Number SystemRatiosAlgebraGeometry
Open Full Binder →
Study Tools

Build a Review Packet

My Collected Lessons

Create a printable list of the lessons saved in this browser.

Favorite This Lesson

Save this page for quick access from your MathBinder dashboard.

Milestones

Your Binder Achievements

1First Lesson
5Five Lessons
10Growing Binder
25Binder Builder
Finish Strong

Learned. Watched. Practiced. Saved.

Now capture the most important idea in My Math Journal.

Go to My Math Journal →
Parent Tip

Spend five minutes reviewing one saved lesson together each week. Ask your child to explain one example aloud.

MY PRIVATE MATH SPACE

My Math Journal

Capture your thinking, questions, and reflections. Everything is saved automatically on this device.

Saved on this device Ready
Confidence Check

How confident do you feel?

Quick Reflection

Complete the thought

My Math Notes

What do you want to remember?

0 words
Learning Record

My Journal History

Revisit reflections saved from other MathBinder lessons on this device.

0 entries
Your journal history will grow as you reflect. Complete this lesson’s journal to begin your learning record.
Next Step

Ready to check your understanding?

Move into Mastery Check when your reflection feels complete.

Go to Mastery Check →

Your Math Journal is automatically saved on this device.
Clearing your browser data will erase your saved journal entries.

Show What You Know

Can you do this on your own?

Complete each question without hints. Your result is saved privately on this device.

5–8 Minutes
0 of 5 answered 0%
Success Criteria

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?

5
Question 5

What should a student do after finding an error?

Confidence Check

How confident do you feel?

Lesson Complete

Great job on Composite Figures and Scale Drawings!

You reviewed the lesson, practiced the skill, and completed the mastery check.

Next Lesson: Nets and Surface Area → Back to Binder Topics

Powered by