Chapter 6 · Consolidation and enhancement
Lesson 6.1 · Multiplication and division (1)
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:
- 01Calculate multi-digit × and ÷ with the column method.
- 02Check starred items carefully.
- 03Solve sharing and comparison applications (cards, running).
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. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Fluency | × ÷ algorithms | G3 M1 / M3 |
Core Concepts
Consolidate multiplication and division algorithms from Chapters 2 and 4.
Column × and ÷
Vertical calculation with self-check on marked items.
Check Answers
Use inverse operations: quotient × divisor + remainder; estimate products.
Applications
$673$ cards ÷ $6$ with $13$ left; compare runners’ speeds from a table; spend exactly $54$ yuan on pens.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Column method | Vertical algorithm. |
| Check | Verify with the inverse operation. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- Column method: $89\times6=534$;\; $801\div9=89$;\; $8\times356=2848$;\; $293\times5=1465$;\; $769\div7=109\,\mathrm{r}\,6$;\; $464\div8=58$
- Step by step: $6\times187-216=906$;\; $585\div5+78=195$;\; $1010-288\div8=974$;\; $367+205\times8=2007$;\; $240+240\div6=280$;\; $408\times7+973=3829$
- Fill in the brackets
- (1) between $200$ and $240$; product $236$
- (2) $370\times3\times2=2220$
- (3) $990\div3\div3$
- (4) $14$ (other factor $20$; $20-6=14$)
- Cards: $673-13=660$;\; $660\div6=110$ cards each
- Running: Pang $135$ m/min; Dingding $96$ m/min; Ming $136$ m/min. Fastest: Xiao Ming; slowest: Xiao Dingding
- Hairy crabs: $96$ more crabs; pay $198\times30=5940$ yuan
- Enhancement — pens for $54$ yuan (10 ways): $(18,9,6)$-counts = $(3,0,0)$, $(0,6,0)$, $(0,0,9)$, $(2,2,0)$, $(2,0,3)$, $(1,4,0)$, $(1,0,6)$, $(0,4,3)$, $(0,2,6)$, $(1,2,3)$
- Fill boxes: (1) $785\times9=7065$;\; (2) $822\div3=274$