Chapter 4 · Dividing by a one-digit number
Lesson 4.11 · Application of division
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 90–92).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Check whether a division is correct using multiplication.
- 02Solve shopping / sharing problems with remainders.
- 03Decide how to treat leftovers in context (can’t buy a fraction of a case).
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. |
| 4.OA.A.3 | *(preview)* Interpret remainders. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Applications | ÷ in context | G3 M1 |
Core Concepts
Apply division in real contexts and emphasise checking.
Checking Division
Verify $251 \div \ldots$ style items: quotient × divisor + remainder = dividend.
Money Sharing
100 yuan for pencil cases at a given price — how many can he buy? (remainder = leftover money)
Sense-Making
Quotient is whole packs/cases; remainder is unused money or leftover items.
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 |
| Interpret remainder | Explain leftover in the story’s units. |
Key Answers
Quick reference for this lesson’s exercise answers.
1. Mental division
- $17\div3=5\ldots2$,\; $33\div7=4\ldots5$,\; $43\div8=5\ldots3$,\; $29\div9=3\ldots2$
- $52\div6=8\ldots4$,\; $75\div10=7\ldots5$,\; $25\div4=6\ldots1$,\; $42\div5=8\ldots2$
2. Column method
- $502\div5=100\ldots2$,\; $486\div8=60\ldots6$,\; $520\div5=104$,\; $725\div6=120\ldots5$
3. Write the number sentences and calculate
- Quotient $123$, remainder $3$
- Sum $270$
- $102$ times
4. Fill in the brackets
- $(83)\times(3)+(2)=(251)$
- $(2)$ zeros ($8000\div5=1600$)
- Quotient $(1)$;\; divisor $(1)$;\; dividend $(0)$
- At most $(16)$ notebooks
- $(52)$ weeks $+\;(1)$ day
5. Application problems
- At least $24$ boxes
- Each class $6$ boats;\; sharing: $11$ boats
- $12$ pencil cases
- $18$ exercise books;\; need $5$ more pieces
6–7. Enhancement
- $250$ kg dried fish
- Yes — $6$ cuts × $5=30$ minutes