Lesson 4.3 · Unit fractions (2)
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 83–85).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Relate unit fractions to yuan, hour, kilogram. (Question 1)
- 02Compare unit fraction size when denominators change. (Question 2)
- 03Solve enhancement problems with diagrams. (Question 3–5)
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.NF.A.1 | Unit fractions. |
| 3.NF.A.3 | Compare fractions (same numerator). |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Measures | 1/10 yuan, 1/60 hour | G3 M5 |
| Compare | More parts → smaller | G3 M5 |
Core Concepts
Connect unit fractions to money, time, mass; more parts → smaller each part.
Fractions in Measures
1 jiao = $\frac{1}{10}$ yuan; 1 minute = $\frac{1}{60}$ hour; 1 g = $\frac{1}{1000}$ kg.
Size Sense
For the same whole, more equal parts → each part is smaller.
Compare Unit Fractions
$\frac{1}{8} < \frac{1}{4}$ because eighths are smaller pieces.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Unit fraction | Numerator 1. |
| Compare | Same whole; larger denominator → smaller unit fraction. |
Key Answers
Quick reference for this lesson’s exercise answers.
1. Fill in
- $1$ jiao $=\frac{1}{10}$ yuan;\; $1$ fen $=\frac{1}{100}$ yuan;\; $1\,\mathrm{g}=\frac{1}{1000}\,\mathrm{kg}$;\; $1$ min $=\frac{1}{60}$ hour;\; $1$ s $=\frac{1}{60}$ min.
- More equal parts → each part smaller; fewer equal parts → each part bigger.
- $\frac{1}{2}>\frac{1}{4}>\frac{1}{8}$.
- $\frac{1}{3}\,\mathrm{m}>\frac{1}{4}\,\mathrm{m}$;\; $\frac{1}{8}\,\mathrm{m}<\frac{1}{3}\,\mathrm{m}$;\; $\frac{1}{17}<1$.
2. Multiple choice
(1) $\frac{1}{7}$ day;\; (2) C $\frac{1}{100}$, $\frac{1}{100}\,\mathrm{m}$;\; (3) B $\frac{1}{4}$;\; (4) B $4$ folds.
3. Circled parts
$\frac{1}{6}$ (one sixth);\; $\frac{1}{2}$ (one half);\; $\frac{1}{4}$ (one fourth);\; $\frac{1}{9}$ (one ninth).
4. Circle items
$\frac{1}{3}$ of $15$ → $5$ hearts;\; $\frac{1}{4}$ of $12$ → $3$ suns.
5–6. Enhancement
- (1) B $\frac{1}{6}$;\; (2) $5$ Chinese roses (A), $20$ azaleas (D).
- $10\,\mathrm{m}$ rope → each piece $\frac{1}{10}$ of $10\,\mathrm{m}$, that is $1\,\mathrm{m}$.