Chapter 7 · Consolidation and enhancement
Lesson 7.4 · Perimeters and areas
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 136–138).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Find area when perimeter and one side are known. (Question 1)
- 02Compare rectangle vs square from the same wire. (Question 2)
- 03Compute area increase when length and width grow. (Question 3)
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.MD.D.8 | Perimeter. |
| 3.MD.C.7 | Area. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| P→A | Find missing side | G3 M7 |
| Same wire | Square vs rect | G3 M7 |
Core Concepts
Given perimeter find area; same wire → different shapes; enlarge sides.
From P to A
$P=66$, one side 22 → other side $=66\div2-22$, then area.
Same Wire
Same perimeter string: rectangle $9\times3$ vs square — compare areas.
Enlarge Sides
Increase length and width by 5 dm — draw before/after to find extra area.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Perimeter | Around. |
| Area | Inside. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- A = 242 cm².
- A = 729 m².
- Xiao Ming: P 14 m, A 12 m²; parents 16 m, 16 m²; lounge 18 m, 20 m²; study 12 m, 9 m²; hallway P 18 m, A 10 m².
- (1) square 36 cm²; (2) wire 28 cm.
- Equal areas ⇏ equal perimeters; equal square areas ⇒ equal perimeters.
- Blank 108 cm²; P 60 cm.
- Area increase 85 dm².
- Inscribed rectangle 180 cm².