Chapter 1 · Revising and improving
Lesson 1.5 · Area of combined figures
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 13–15).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Decompose combined figures into rectangles. (Question 1)
- 02Find the area of each part and add. (Question 2)
- 03Compare different split methods for the same shape. (Question 3)
- 04Solve floor-plan and tiling problems. (Question 4–5)
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.MD.C.7 | Area by multiplication; composite figures. |
| 3.OA.D.8 | Multi-step area problems. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Q1–2 | Split & add | G3 M4 composite |
| Q3 | Same total, different split | G3 M4 reasoning |
| Applications | Plans / tiles | G3 M4 application |
Core Concepts
Split a combined figure into rectangles, find each area, then add.
Decompose
Draw one or two lines to split an L-shape or polygon into rectangles (no gaps/overlaps).
Add Areas
Area of whole figure = sum of rectangle areas: $A = A_1 + A_2 + \cdots$
Label each rectangle’s length and width before multiplying.
Different Splits
Two correct splits should give the same total area — good check for errors.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Combined figure | A shape made of two or more parts. |
| Decompose | Split into simpler shapes. |
| Composite area | Sum of part areas. |
Key Answers
Quick reference for this lesson’s exercise answers.
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