Chapter 7 · Consolidation and enhancement
Lesson 7.6 · Mathematics plaza — matching
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 142–144).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Count boy–girl host pairs. (Question 1)
- 02Count games if every two play once. (Question 2)
- 03Order river-crossing steps. (Question 3)
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.OA.D.8 | Multi-step reasoning. |
| MP.7 | Look for structure. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Combinations | Pairs | G3 plaza |
| Order | Sequence | G3 plaza |
Core Concepts
Count pairings, games, and river-crossing step orders.
Pair Selections
Choose 1 boy from B and 1 girl from G → $B \times G$ ways.
Tournament Games
Every two of 5 play once → $5\times4\div2 = 10$ games.
Arrange the Order
River crossing: dog, rabbit, grass — sequence steps so nothing is eaten.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Combination | A selection without regard to order. |
| Permutation | An ordered sequence of steps. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- $3\times2=6$ selections.
- $3\times3\times2=18$ outfits.
- $4\times5=20$ two-digit numbers.
- $C(5,2)=10$ games.
- (1) 3 routes; (2) route ② (1000 m).
- MCQ: C (7 lengths); C (7 masses).
- Order: A → D → B → C.
- Tickets 72; fares 36.
- 16 ways (compositions of 5).
- 72 ways on $4\times4$ grid.