Chapter 6 · Let's practise geometry
Lesson 6.4 · Perimeters of rectangles and squares (2)
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 118–120).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Find perimeters of composite shapes. (Question 1)
- 02Compare remaining figures after cutting equal squares. (Question 2)
- 03Convert a square string into a rectangle. (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 |
|---|---|---|
| Composite | Outer path | G3 M7 |
| Cut | P vs A | G3 M7 |
Core Concepts
Find perimeters of combined shapes; cutting can change P and A differently.
Composite Perimeter
Add outer edges only — shared inner edges cancel.
Cut & Compare
Cutting the same square from two figures may keep perimeters equal while areas differ (or vice versa).
Same String
Square side 18 cm → P = 72 cm = rectangle with length 19 → width = $(72\div2)-19$.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Composite shape | Made of rectangles/squares. |
| Fixed perimeter | Same string/wire length. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- Perimeters: 92 m; 68 cm; 60 cm.
- Table: length 150 cm, area 13 500 cm²; width 23 dm, P 84 dm; P 50 m, A 144 m².
- MCQ: (1) B (figures ② and ③).
- Cut squares: B (areas equal).
- Five squares: P 96 cm; A 320 cm².
- Field: original P 110 m.
- String: width 17 cm.
- Eight squares: 2 rectangles; perimeters 108 cm and 72 cm.
- Composite: 220 cm; 300 cm.