Lesson 5.8 · Areas of rectangles and squares (2)
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 127–129).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Calculate areas or missing side lengths.
- 02Reason about how changing length changes area.
- 03Find areas of frames and shaded regions with midpoints.
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.MD.C.5 | Recognize area as attribute. |
| 3.MD.C.6 | Measure area by counting unit squares. |
| 3.MD.C.7 | Relate area to multiplication/addition. |
| 3.OA.D.8 | Multi-step area problems. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Composite area | Add/subtract regions | G3 M4 |
Core Concepts
Deepen rectangle/square area — changes, frames, shaded parts.
Compute Areas
Given sides in cm, find areas; find a missing side when area is known.
Changing Length
Length $18\ \text{cm}$; length $+5\ \text{cm}$ increases area by $40\ \text{cm}^2$ → find original width (draw a diagram).
Composite / Shaded
Photo frame border; midpoints of square sides — area of shaded part.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Composite figure | Shape made of simpler shapes. |
| Shaded area | Region marked for finding area. |
Key Answers
Quick reference for this lesson’s exercise answers.
1. $12\,\mathrm{cm}^2$; $25\,\mathrm{cm}^2$; $7\,\mathrm{cm}$.
2. Units — $\mathrm{cm}^2$; $\mathrm{m}^2$; $\mathrm{dm}^2$; m; $\mathrm{m}^2$.
3–6. $9450\,\mathrm{cm}^2$; $144\,\mathrm{cm}^2$; glass $160\,\mathrm{cm}^2$, strips $64\,\mathrm{cm}$; $1200\,\mathrm{cm}^2$.
7. Sum of all rectangles $280\,\mathrm{cm}^2$.
8–9. Cross $72\,\mathrm{cm}^2$; shaded $64\,\mathrm{cm}^2$.