Chapter 6 · Consolidation and enhancement
Lesson 6.5 · Problem solving (3)
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:
- 01Simplify multi-factor expressions (order of operations / properties).
- 02Solve rectangle area and delivery-mass problems.
- 03Apply unit price leftovers and rate scaling (lucky stars).
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.OA.A.3 | Multiply/divide to solve word problems. |
| 3.OA.D.8 | Two-step word problems. |
| 3.OA.C.7 | Fluently multiply and divide within 100. |
| 3.NBT.A.2 | Add/subtract within 1000. |
| 3.NBT.A.3 | Multiply one-digit × multiples of 10. |
| 3.MD.C.5–7 | Area concepts and rectangle area. |
| 3.MD.A.2 | *(related)* Measure/solve with units. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Multi-step | Mixed strands | Ch. 2–5 review |
Core Concepts
Mixed problem solving — smart calculation, area, mass, money, rates.
Calculate Smartly
Step-by-step with regrouping when helpful ($37\times5\times2$, etc.).
Area & Mass Stories
Rectangle length $=4\times$ width → area; green vegetables vs potatoes delivery.
Rates & Money
Paddle $66$ yuan + balls $6$ yuan from $100$; $20$ stars in $5$ min by some children → scale to $7$ children / $10$ min.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Calculate smartly | Use properties to simplify. |
| Rate | Amount per unit time. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- Step by step: $370$;\; $9000$;\; $44$;\; $104$;\; $936$;\; $37$;\; $300$;\; $648$
- Pandas: $560$ kg
- Chalk: $12000$ sticks
- Ribbon: $225$ cm at first
- Rectangle area: $256$ cm²
- Vegetables: green vegetables $315$ kg
- Desk & chair: $335$ yuan
- Fruit: $48$ yuan
- Table tennis: $5$ balls
- Hotel rooms: $18$ fewer rooms
- Car return: $72$ km/h
- Enhancement: (12) $70$ stars;\; (13) $3$ min;\; (14) $18$ pencils;\; (15) $9$ cats