Chapter 4 · Dividing by a one-digit number
Lesson 4.10 · Dividing a three-digit number by a one-digit number (4)
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 87–89).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Solve “exactly n times as many” problems with division.
- 02Find a number from quotient and remainder.
- 03Use dividend = divisor × quotient + remainder in harder forms.
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)* Multi-step; interpret remainders. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Comparison | Times as many | G3 M1 / M3 |
| Remainder | Recover dividend | G3 M1 |
Core Concepts
Harder three-digit ÷ problems: comparisons and recovering unknowns.
“Times as Many” with ÷
152 literature books is exactly 8 times comic books → comics $= 152 \div 8$.
Find the Unknown
÷5 gives quotient 123 remainder 2 → number $= 5 \times 123 + 2$.
Full Relationship
Quotient = remainder = 3; divisor = 3 × remainder → find dividend.
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 calculation
- $64\div4=16$,\; $36\div3=12$,\; $86\div2=43$,\; $95\div5=19$
- $50\div6=8\ldots2$,\; $640\div8=80$,\; $110\div5=22$,\; $240\times0=0$
2. Dance / choir / brass band
- $144$ in the choir
- $16$ in the brass band
- $9$ times
3. Library books
- $304$ storybooks
- $19$ comic books
- $16$ times
4. Column method
- $563\div4=140\ldots3$,\; $540\div3=180$,\; $250\div6=41\ldots4$
5. Multiple choice
- A
- D
- C
6. True or false
- $\times$
- $\surd$
- $\times$
7–8. Further practice
- $617$
- $30$
9–10. Enhancement
- $70$ metres each minute
- $2$ yuan each