Chapter 2 · Multiplying by a one-digit number
Lesson 2.2 · Multiplying whole tens and whole hundreds (2)
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 18–19).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Extend multiplication patterns for tens and hundreds. (Question 1)
- 02Multiply tens×tens and count zeros correctly. (Question 1–2)
- 03Combine related products using the distributive idea. (Question 2)
- 04Solve multi-step money and length problems. (Applications)
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.NBT.A.3 | Multiply one-digit numbers by multiples of 10. |
| 3.OA.B.5 | Apply properties of operations. |
| 3.OA.D.8 | Two-step word problems. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Patterns | Tens/hundreds fluency | G3 M3 |
| Distributive | Combine like products | G3 M1 / M3 |
| Applications | Money / length | G3 M3 |
Core Concepts
Extend whole-tens/hundreds multiplication — including tens × tens and combining related products.
Extend the Pattern
$$3 \times 9 = 27 \Rightarrow 3 \times 90 = 270 \Rightarrow 3 \times 900 = 2700$$
$$4 \times 8 = 32 \Rightarrow 40 \times 8 = 320 \Rightarrow 4 \times 80 = 320 \Rightarrow 40 \times 80 = 3200$$
Tens × Tens / Hundreds
Multiply non-zero digits, then count all the zeros from both factors.
Example: $70 \times 60$ → $7 \times 6 = 42$, then two zeros → $4200$.
Combine Related Products
$$4 \times 500 + 6 \times 500 = (4+6) \times 500 = 10 \times 500 = 5000$$
Distributive thinking: same second factor → add the first factors.
Applications
- “Times as expensive” (laptop = 5 × washing machine).
- Rope cut into equal pieces + leftover: $50 \times 4 + 20$.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Multiple of 10 / 100 | Whole tens / whole hundreds. |
| Distributive property | $a\times c + b\times c = (a+b)\times c$. |
| Times as many | One quantity is a multiple of another. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- Calculate with reasoning
- $3×9=27$, $3×90=270$, $3×900=2700$, $30×90=2700$
- $4×8=32$, $40×8=320$, $4×80=320$, $40×80=3200$
- $7×6=42$, $700×6=4200$, $70×60=4200$, $60×700=42000$
- Fill in the brackets
- (1) $5$; $35$; $3500$
- (2) $9×20=180$; $10×500=5000$
- (3) $4$ zeros ($500×60=30000$)
- Compare: (1) $=$ (2) $=$ (3) $>$ (4) $=$ (5) $>$ (6) $=$
- Match: $5×80→400$; $500×8→4000$; $50×800→40000$; $5×8→40$; $500×800→400000$
- Multiple choice: (1) C ($360$) (5) B ($630$)
- Applications: (1) $4500$ yuan; $3600$ yuan more (2) $220$ cm
- Continue the sequence (all $=16000$): $80$, $20$, $4000$, $16$, $160$, $400$, $32$