Chapter 6 · Consolidation and enhancement
Lesson 6.9 · Mathematics plaza — tree planting problems
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:
- 01Relate number of cuts / poles to number of intervals.
- 02Find path length from trees on both sides.
- 03Solve circular planting (around a lake) problems.
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.OA.D.8 | Multi-step. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Interval problems | n objects → n−1 gaps | Classic Chinese primary type |
Core Concepts
Tree-planting / interval problems — objects vs gaps.
Intervals vs Objects
Sawing wood into $7$ parts needs $6$ cuts. $n$ trees in a line → usually $n-1$ gaps.
Both Sides of a Path
$40$ trees on both sides including ends, $8\ \text{m}$ apart → pavement length.
Around a Lake
Perimeter $2100\ \text{m}$, a tree every $10\ \text{m}$ → how many trees around the lake?
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Interval | Gap between two neighbouring objects. |
| Tree planting problem | Find length or count from equal spacing. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- Fill brackets: (1) $6$ times;\; (2) $10$ pieces;\; (3) $8$ flights
- Corridor trees: $7$ trees
- Flower pots both sides: $62$ pots
- Corridor length: $69$ m
- Pavement: $152$ m
- Poles to remove: $19$ poles
- Street lights: $20$ m apart
- Steps: $640$ steps
- Lake poplars: $210$ trees
- Timber: $30$ dm
- Enhancement — bridge: length $28$ m; time $70$ s
- Enhancement — riverside: willow $201$; peach $400$