Chapter 4 · Dividing by a one-digit number
Lesson 4.2 · Dividing a two-digit number by a one-digit number (1)
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 65–67).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Compute two-digit ÷ one-digit mentally where facts allow.
- 02Name dividend, divisor, quotient, remainder and use the relationship.
- 03Solve equal-group word problems (apples, paper flowers).
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.OA.A.2 | Interpret whole-number quotients. |
| 3.OA.A.3 | Multiply/divide within 100 to solve word problems. |
| 3.OA.B.5 | Apply properties of operations. |
| 3.OA.B.6 | Understand division as unknown-factor. |
| 3.OA.C.7 | Fluently multiply and divide within 100. |
| 3.OA.D.8 | Two-step word problems. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Unknown factor | Division meaning | G3 M1 |
| Remainder | Interpret leftover | G3 M1 Topic B |
Core Concepts
Introduce two-digit ÷ one-digit with division vocabulary and remainders.
Parts of Division
$$\text{dividend} = \text{divisor} \times \text{quotient} + \text{remainder}$$
Remainder must be less than the divisor.
Mental Division
Use known facts and “how many groups of …” language.
Remainder Language
Fill: when dividend is 23 and divisor is __, quotient and remainder are given.
Applications
Baskets of apples; children cutting flowers — average / equal share.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Dividend | The number being divided. |
| Divisor | The number you divide by. |
| Quotient | The result of division. |
| Remainder | What is left after equal groups are made. |
| Relationship | dividend = divisor × quotient + remainder |
Key Answers
Quick reference for this lesson’s exercise answers.
1. Mental division
- $9\div2=4\ldots1$,\; $25\div4=6\ldots1$,\; $27\div5=5\ldots2$,\; $38\div6=6\ldots2$
- $19\div3=6\ldots1$,\; $36\div5=7\ldots1$,\; $39\div4=9\ldots3$,\; $47\div5=9\ldots2$
2. Greatest number in the brackets
- $6\times(5)<32$,\; $(6)\times9<60$,\; $(6)\times8<53$
- $8\times(6)<50$,\; $7\times(8)<62$,\; $(8)\times9<78$
3. Sharing sweets
$73\div5=14\ldots3$
4. Let’s try
- $64\div4=16$,\; $92\div4=23$,\; $84\div7=12$,\; $81\div7=11\ldots4$,\; $86\div6=14\ldots2$
5. Fill in the brackets
- $48\div4$ is read as forty-eight divided by four
- $27$ is $(3)$ times $9$;\; $72$ is $(8)$ times $9$
- There are $(8)$ eights in $64$;\; $64$ is $(8)$ times $8$
- Quotient $(5)$, remainder $(3)$
- Divisor $(6)$
- Dividend $(48)$
- $(8)$ less than $22$
6. Write the number sentences and calculate
- $75\div5=15$
- $75\times5=375$
7. Application problems
- $25\times4=100>96$ — yes, can finish on time
- $88\div4=22$ stamps
- $64\div4=16$ apples per basket
- Average of three: $17$;\; with Fangfang: $18$
8–9. Enhancement
- $4-4+4-4=0$;\; $(4-4)+(4\div4)=1$;\; $(4\div4)+(4\div4)=2$;\; $(4+4+4)\div4=3$;\; $((4\times4)+4)\div4=5$;\; $(4\div4)+(4+4)=9$
- $(1+2)\div3=1$;\; $1\times2+3-4=1$;\; $1+2-3-4+5=1$;\; $1+2+3-4+5-6=1$