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Lunar New Year maths activities for IGCSE and GCSE

A ready-to-teach lesson for Lunar New Year, whenever it falls: the 12-year cycle of animals as remainders, lanterns and LCM, and repeating patterns. A 5-minute starter, a 35-minute main activity, an extension and full worked answers.

Level
IGCSE and GCSE (Higher and Extended)
Time
40 minutes, plus a 10-minute extension
Topics
Remainders and repeating patterns; HCF and LCM; Linear sequences and the nth term; Ratio
Equipment
No calculator needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minThe 12-year cycle
Main: task B11 minLanterns and lions
Main: task C12 minRemainders and ratio
Extension10 minFast finishers or homework

Starter (5 minutes)

No calculator.

  1. Find the remainder when 2030 is divided by 12.
  2. Find the LCM of 10 and 12.
  3. Find the HCF of 36 and 60.
  4. Find the nth term of 8, 20, 32, 44, …

Main activity (35 minutes)

Task A: The 12-year cycle (12 min)

Number the 12 animals of the cycle 1 to 12 in the traditional order (Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, Pig). In this activity, for the lunar year that begins in calendar year Y: work out Y − 4, divide by 12 and add 1 to the remainder to get the animal number.

  1. Find the animal number for the lunar year that begins in 2031.
  2. Which calendar years from 2001 to 2100 give animal number 1? How many are there?
  3. The years in part (b), continued for ever, form a sequence. Find its nth term, starting with 2008, and its 50th term.

Task B: Lanterns and lions (11 min)

LCM and HCF problems.

  1. Red lanterns hang every 4 m along a street and gold lanterns every 6 m, both starting at 0 m. How often are a red and a gold lantern at the same place? How many such places are there from 0 m to 100 m?
  2. A lion dance team has 48 dancers and 36 drummers. They split into identical groups with no one left over. What is the greatest number of groups?
  3. Lanterns of three colours hang every 4 m, 6 m and 9 m, all starting at 0 m. Where do all three next meet?

Task C: Remainders and ratio (12 min)

Work with remainders and ratio.

  1. Find the smallest positive number that leaves remainder 3 when divided by 12 and remainder 2 when divided by 5.
  2. 156 coins are shared between two children in the ratio 5 : 7. How many does each get?
  3. A string of beads repeats a pattern of 12 colours. Which colour (1 to 12) is the 500th bead?

Extension (10 minutes)

For fast finishers, or as homework.

  1. Find the smallest number greater than 1 that leaves remainder 1 when divided by 7, by 10 and by 12.
  2. A 10-year cycle and a 12-year cycle start together. After how many years do they next start together, and how many times has each cycle been completed?

For teachers

Teacher notes and full worked answers
  • Lunar New Year falls on a different date each year: use this pack in the weeks around it.
  • If students test the rule on their own birth year, remind them that the lunar year usually begins in January or February.
  • Task B (b): students who find a common factor but not the highest one (for example 6 groups) have the right idea; ask for the greatest.

Starter

  1. 2
    • 12 × 169 = 2028, so the remainder is 2.
  2. 60
    • Multiples of 12: 12, 24, 36, 48, 60. 60 is the first that is also a multiple of 10.
  3. 12
    • 36 = 22 × 32, 60 = 22 × 3 × 5, so HCF = 22 × 3 = 12.
  4. 12n − 4
    • Difference 12; 8 = 12 − 4.

Task A: The 12-year cycle

  1. 12
    • 2031 − 4 = 2027 = 12 × 168 + 11
    • 11 + 1 = 12
  2. 2008, 2020, …, 2092: 8 years
    • We need Y − 4 to be a multiple of 12: Y = 2008, 2020, 2032, 2044, 2056, 2068, 2080, 2092.
  3. 12n + 1996; 2596
    • Difference 12; 2008 = 12 + 1996.
    • 12 × 50 + 1996 = 2596

Task B: Lanterns and lions

  1. Every 12 m; 9 places
    • LCM(4, 6) = 12.
    • 0, 12, 24, 36, 48, 60, 72, 84, 96: 9 places.
  2. 12 groups (4 dancers and 3 drummers each)
    • HCF(48, 36) = 12
  3. At 36 m
    • LCM(4, 6, 9) = 36

Task C: Remainders and ratio

  1. 27
    • 3, 15, 27: 27 = 5 × 5 + 2.
  2. 65 and 91
    • 156 ÷ 12 = 13; 5 × 13 = 65 and 7 × 13 = 91.
  3. Colour 8
    • 500 = 12 × 41 + 8, so the 500th bead is the 8th colour.

Extension

  1. 421
    • LCM(7, 10, 12) = 420; 420 + 1 = 421
  2. 60 years; 6 and 5 times
    • LCM(10, 12) = 60
    • 60 ÷ 10 = 6 and 60 ÷ 12 = 5

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

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