Chapter 6 · Consolidation and enhancement
Lesson 6.8 · Calculate the area of Xiao Pang's home
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Read a floor plan and identify rooms.
- 02Calculate areas of rooms and composite figures.
- 03Draw a rectangle with the same area as a given square; solve fence perimeter problems.
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.MD.C.5–7 | Area concepts and rectangle area. |
| 3.MD.A.2 | *(related)* Measure/solve with units. |
| 3.OA.D.8 | Multi-step problems. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Floor plan | Composite area | G3 M4 |
Core Concepts
Apply area to a real floor plan and related perimeter/area problems.
Read the Floor Plan
Balcony, office, kitchen, dining room, etc. — use given dimensions.
Room Areas
Find each room; combine for totals where asked.
Same-Area Rectangles
Draw a rectangle equal in area to a square; field length $20\ \text{m}$, width half length; $20\ \text{m}$ fencing for a vegetable plot.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Floor plan | Scale drawing of rooms. |
| Composite area | Sum or difference of rectangle areas. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- Floor plan areas: Xiao Pang $12$; parents $16$; lounge $36$; dining $9$; kitchen $6$; balconies $6$; bathroom $6$; hallway $7$; total $98$ m²
- Same area rectangle: e.g. $8\times2$ (area $16$ cm²)
- L-figure area: follow labelled dimensions (workbook $65$ cm²)
- Fill brackets: (1) cm²; cm;\; (2) $110$ cm² remaining;\; (3) width $1$ cm
- Applications: (1) room $12$ m²;\; (2) field $200$ m²;\; (3) max fence area $25$ m²
- Enhancement: (6) large rectangle $336$ cm²;\; (7) original land $17680$ m²