Lesson 3.3 · Common year and leap year
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 49–51).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Define common year vs leap year (days / February).
- 02Apply the leap-year rules (÷4 and ÷400 for centuries).
- 03Explain day and quarters using Earth / calendar language.
- 04Convert among simple time units.
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.MD.A.1 | Time; intervals. |
| 3.OA.A.4 | *(related)* Unknowns in ×÷ (multiples of 4 / 400). |
| 4.OA.B.4 | *(preview)* Multiples and factors. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Leap year | Calendar rules | Time / number sense |
| Quarters | Structure of a year | Calendar |
Core Concepts
Distinguish common years and leap years; connect Earth motion to day and year.
Common Year & Leap Year
| Type | Days in year | February |
|---|---|---|
| Common year | $365$ | $28$ days |
| Leap year | $366$ | $29$ days |
Leap-Year Rule
- If the year is a multiple of $4$, it is usually a leap year.
- If it is a whole-hundreds year, it must be a multiple of $400$ to be a leap year.
Day, Year, Quarters
- One rotation of Earth ≈ 24 hours = 1 day.
- A year has 4 quarters; each quarter has 3 months.
Time Conversions
Practice links such as minutes ↔ hours (e.g. $12$ minutes as a fraction of an hour) mixed with fluency items.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Common year | Year with 365 days. |
| Leap year | Year with 366 days; February has 29. |
| Multiple of 4 / 400 | Leap-year tests. |
| Quarter | Three-month part of a year. |
Key Answers
Quick reference for this lesson’s exercise answers.
1. 8; 51; 3200; 89; 17; 120; 6; 27; 450; 647; 263; 28.
2. Leap: 2000, 2004, 2008, 2012, 2016, 2020, 2024.
3. 7 big / 4 small; next leaps 2020 & 2024; 26 mo = 2 y 2 mo; Jul & Aug; 365 common · Feb extra → 366 leap; 24 h = day; 4 quarters × 3 mo; e.g. 2023 not leap, 2028 leap.
4. MC: C · C · A · C (2800).
5. T/F: ✓ (Q1 common = 90) · ✓ (second half = 184).
6. 720 s; 3 days; 90 min; 1 h 20 min; 60 mo; 2 weeks; 288 h; 168 h.
7. 10th watering: 1 Mar 2012, 7 a.m.
8. Next 1 Jan: +1 weekday (common) or +2 (leap).