Cover lesson · RE · Year 9 · Advanced
DCF: Data and computational thinking → Problem-solving and modelling
Name: Class: Date:
Print: this sheet, one per pupil, and the stimulus sheet “How the date of Easter is set”, one between two. No computers are needed. Pupils need a pen and a calculator. Every answer can be checked: the table at the end of the stimulus sheet gives the correct date of Easter for every year from 2020 to 2040.
Run: 5 min pupils read the stimulus in pairs · 7 min Step 2, div and mod with a calculator · 12 min Step 3, read the worked example for 2027 and trace 2030 · 8 min Step 4, trace 2031 alone · 6 min Step 5, what each part of the algorithm does · 7 min Step 6, complete the flowchart · 7 min Step 7, Ash Wednesday and Pentecost · 5 min Step 8, explain why Easter moves, alone. Total 57 minutes.
Collect: this sheet. It is digital competence practice in problem-solving and modelling: following a precise algorithm step by step, recording every value in a trace table, breaking the algorithm into parts and turning the church’s Easter rule into a flowchart. It also gives you numeracy evidence of calculation to assess: the div and mod answers in Step 2, the 2030 and 2031 trace tables in Steps 3 and 4 (look for the whole-number division and the remainder worked out and written down at every line, not just final values), and the day counts across months for Ash Wednesday and Pentecost in Step 7. In RE, Step 8 shows whether pupils can explain why Easter is on a Sunday and why it follows the spring full moon. If a pupil’s date does not match the stimulus table, ask them to find their mistake rather than copy the date.
Christmas is always on 25 December, but Easter Sunday can fall on any date from 22 March to 25 April. Churches set the date with a rule linked to the moon. Mathematicians have turned that rule into an algorithm: a precise list of steps that any person, or any computer, can follow and always get the same answer. You will learn 2 kinds of division that computers use, follow the algorithm by hand for 2 years, work out what each part of it does, draw the church’s rule as a flowchart and then use the date of Easter to find 2 other Christian festivals.
Read the whole stimulus sheet with a partner. Make sure you can say what Christians remember on Easter Sunday, why Easter is linked to Passover and the full moon, and what the rule in the box says.
The algorithm uses 2 kinds of whole-number division:
| Question | Calculator shows | div | Multiply back and subtract | mod |
|---|---|---|---|---|
| 100 and 7 | ||||
| 2025 and 19 | ||||
| 500 and 30 | ||||
| 45 and 7 | ||||
| 150 and 31 |
Y is the year. Work down the list in order. Each line uses answers from the lines above it.
| Letter | Rule | Letter | Rule |
|---|---|---|---|
| a | Y mod 19 | h | (19a + b − d − g + 15) mod 30 |
| b | Y div 100 | i | c div 4 |
| c | Y mod 100 | k | c mod 4 |
| d | b div 4 | l | (32 + 2e + 2i − h − k) mod 7 |
| e | b mod 4 | m | (a + 11h + 22l) div 451 |
| f | (b + 8) div 25 | n | h + l − 7m + 114 |
| g | (b − f + 1) div 3 | month | n div 31 (3 = March, 4 = April) |
| day | (n mod 31) + 1 |
“19a” means 19 × a, “2e” means 2 × e, and so on. Work out the brackets first.
Worked example: Y = 2027. This is called a trace table: it records the value of every letter as the algorithm runs.
| Letter | Working | Value |
|---|---|---|
| a | 2027 ÷ 19 = 106.68..., so div is 106. 106 × 19 = 2014. 2027 − 2014 = 13 | 13 |
| b | 2027 ÷ 100 = 20.27, so div is 20 | 20 |
| c | 2027 − 20 × 100 = 2027 − 2000 = 27 | 27 |
| d | 20 ÷ 4 = 5 | 5 |
| e | 20 − 5 × 4 = 0 | 0 |
| f | (20 + 8) ÷ 25 = 28 ÷ 25 = 1.12, so div is 1 | 1 |
| g | (20 − 1 + 1) ÷ 3 = 20 ÷ 3 = 6.66..., so div is 6 | 6 |
| h | 19 × 13 = 247. 247 + 20 − 5 − 6 + 15 = 271. 271 ÷ 30 = 9.03..., so div is 9. 9 × 30 = 270. 271 − 270 = 1 | 1 |
| i | 27 ÷ 4 = 6.75, so div is 6 | 6 |
| k | 6 × 4 = 24. 27 − 24 = 3 | 3 |
| l | 32 + 0 + 12 − 1 − 3 = 40. 40 ÷ 7 = 5.71..., so div is 5. 5 × 7 = 35. 40 − 35 = 5 | 5 |
| m | 13 + 11 + 110 = 134. 134 ÷ 451 = 0.29..., so div is 0 | 0 |
| n | 1 + 5 − 0 + 114 = 120 | 120 |
| month | 120 ÷ 31 = 3.87..., so div is 3: March | 3 |
| day | 3 × 31 = 93. 120 − 93 = 27. 27 + 1 = 28 | 28 |
Easter Sunday 2027 is 28 March. The stimulus table agrees.
Your turn: Y = 2030. Show your working on every line. Tip: b, d, e, f and g depend only on the century (the first 2 digits of the year), so for every year from 2000 to 2099 they are the same as in 2027.
| Letter | Rule | Working | Value |
|---|---|---|---|
| a | Y mod 19 | ||
| b | Y div 100 | ||
| c | Y mod 100 | ||
| d, e, f, g | Same as 2027 | ||
| h | (19a + b − d − g + 15) mod 30 | ||
| i | c div 4 | ||
| k | c mod 4 | ||
| l | (32 + 2e + 2i − h − k) mod 7 | ||
| m | (a + 11h + 22l) div 451 | ||
| n | h + l − 7m + 114 | ||
| month | n div 31 | ||
| day | (n mod 31) + 1 |
Easter Sunday 2030 is: Does it match the stimulus table?
Follow the algorithm for Y = 2031 without help. Show your working on every line, then check your date against the stimulus table. If it does not match, go back through your table and find the line where it went wrong.
| Letter | Rule | Working | Value |
|---|---|---|---|
| a | Y mod 19 | ||
| b | Y div 100 | ||
| c | Y mod 100 | ||
| d, e, f, g | Same as 2027 | ||
| h | (19a + b − d − g + 15) mod 30 | ||
| i | c div 4 | ||
| k | c mod 4 | ||
| l | (32 + 2e + 2i − h − k) mod 7 | ||
| m | (a + 11h + 22l) div 451 | ||
| n | h + l − 7m + 114 | ||
| month | n div 31 | ||
| day | (n mod 31) + 1 |
Easter Sunday 2031 is: Does it match the stimulus table?
Programmers understand a long algorithm by decomposing it: breaking it into parts and working out the job of each part.
(a) a = Y mod 19, so a can only be a whole number from 0 to 18. For 2027, a = 13. Which is the next year after 2027 that will also have a = 13? Use the stimulus sheet to explain why the algorithm divides by 19.
(b) h is the number of days from 21 March to the church’s full moon. (In a few years, such as 2030, the church’s tables put the full moon 1 day earlier than this, but the algorithm is built so that Easter still comes out right.) Use your values of h to find the date of the church’s full moon in 2027 and in 2031. Show your working.
(c) l tells you how far the full moon is from the next Sunday: Easter Sunday is l + 1 days after the church’s full moon. Check this for 2027. On which day of the week was the church’s full moon in 2027?
(d) Match each part of the algorithm to its job. Write the letter of the job in the right-hand column.
| Part of the algorithm | Job (A to E) |
|---|---|
| a | |
| b, d, e, f and g | |
| h | |
| c, i, k and l | |
| n, month and day |
The algorithm is hard to read. The rule it carries out is simple: Easter Sunday is the first Sunday after the church’s full moon that falls on or after 21 March.
(a) Complete the flowchart. Write one phrase from the word bank in each of boxes 1 to 4. Write Yes and No on the 2 arrows that leave the diamond. One phrase is not needed.
Word bank: Is the church’s full moon on a Sunday? · Output: the date of Easter Sunday · Count back 46 days · Find the church’s full moon on or after 21 March · Easter Sunday is 7 days after the full moon
(b) Test your flowchart. In 2038 the church’s full moon is on Sunday 18 April. Follow your flowchart. What date is Easter Sunday 2038? Does the stimulus table agree?
(c) Use the rule to explain why Easter Sunday can never be on 21 March.
Lent begins on Ash Wednesday, 46 days before Easter Sunday. Pentecost is 49 days after Easter Sunday. Count across the ends of months. March and May have 31 days, April has 30 days, and February has 28 days in 2027, 2030 and 2031 (none of them is a leap year).
Worked example: 2027 (Easter Sunday 28 March).
Ash Wednesday: going back 28 days from 28 March reaches 28 February. 46 − 28 = 18 days still to go back. 28 − 18 = 10, so Ash Wednesday is 10 February 2027.
Pentecost: going forward 3 days from 28 March reaches 31 March. 49 − 3 = 46 days still to go. All 30 days of April take it to 30 April, leaving 46 − 30 = 16. So Pentecost is 16 May 2027.
(a) Find Ash Wednesday and Pentecost for 2030 and 2031 in the same way. Show your working.
| Year | Easter Sunday (from Steps 3 and 4) | Ash Wednesday: working and date | Pentecost: working and date |
|---|---|---|---|
| 2030 | |||
| 2031 |
(b) Pentecost is always on a Sunday. Use the number 49 to explain why.
Write 4 or 5 sentences explaining to a Year 7 pupil why Easter Sunday is on a different date each year. Use these words: resurrection, Sunday, Passover, full moon, 21 March. In your last sentence, explain why Orthodox Christians celebrate Easter on 2 May in 2027, when Western churches celebrate it on 28 March.