Presentation: Following an Algorithm to Find the Date of Easter

Slide 1 of 7 · Settling starter · RE · Year 9

5 minutes

Following an algorithm to find the date of Easter

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, and 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.

While the register is called: write your name, class and date on your worksheet, then read the whole stimulus sheet, How the date of Easter is set, with a partner (Step 1).

Starter question: What do Christians remember on Easter Sunday, and why is Easter always on a Sunday?

DCF: Data and computational thinking → Problem-solving and modelling No computers needed · pen and calculator

Supply teacher script (no subject knowledge needed)

Hand out: one worksheet per pupil and one stimulus sheet (How the date of Easter is set) between two. Every pupil needs a pen and a calculator. Every answer in this lesson 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.

Say aloud: “Write your name, class and date at the top of your worksheet. While I take the register, read the whole stimulus sheet with your 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.”

Starter answer: Easter Sunday remembers the resurrection, Jesus rising from the dead. All four Gospels say the women found the tomb empty on the first day of the week, the Sunday, so Easter is always on a Sunday. The rule in the box: Easter Sunday is the first Sunday after the church’s full moon that falls on or after 21 March.

Slide 2 of 7 · Today’s brief and key words · RE · Year 9

3 minutes

Your brief: follow the algorithm by hand, then explain it

You will learn 2 kinds of division that computers use, follow the Easter algorithm by hand for 2030 and 2031, work out what each part of it does, draw the church’s rule as a flowchart, then use the date of Easter to find Ash Wednesday and Pentecost.

div

“How many whole times does it go in?” 17 div 5 = 3. Never round up.

mod

“What is the remainder?” 17 mod 5 = 2, because 3 × 5 = 15 and 17 − 15 = 2.

Trace table

A table that records the value of every letter as the algorithm runs, line by line.

Decompose

Break a long algorithm into parts and work out the job of each part.

LNF: Numeracy → Understanding the number system helps us to represent and compare relationships between numbers and quantities → Calculation Show the working on every line, not just the answer

Slide 3 of 7 · Steps 2 and 3: div and mod, then trace 2030 · RE · Year 9

14 minutes

Step 2 & Step 3: practise div and mod, then follow the algorithm for 2030

Step 2 (4 min): calculator method. Divide, take the whole-number part (div), multiply back and subtract (mod). The remainder must be smaller than the number you divided by.

Question	Calculator shows	div	Multiply back and subtract	mod
2027 and 19	106.68...	106	106 × 19 = 2014; 2027 − 2014 = 13	13
100 and 7	14.28...	14	14 × 7 = 98; 100 − 98 = 2	2

Step 3 (10 min): read the worked example for Y = 2027 (Easter Sunday 28 March), then trace Y = 2030. Work down the list in order; each line uses answers from the lines above. Tip: b, d, e, f and g depend only on the century, so they are the same as 2027: 20, 5, 0, 1, 6.

Steps 2 and 3 on your worksheet · 14 minutes Never round up: 500 div 30 is 16, not 17

Supply teacher script (no subject knowledge needed)

Say aloud: “4 minutes for Step 2. The method and one answer row are on the board: divide, take the whole-number part, multiply back, subtract. Then read the 2027 worked example in Step 3 carefully and fill in the 2030 trace table with working on every line. Check your date against the stimulus table.”

Quick check, Step 2: 2025 and 19: 106.57..., div 106, 106 × 19 = 2014, 2025 − 2014 = 11, mod 11. 500 and 30: 16.66..., div 16, 480, mod 20. 45 and 7: 6.42..., div 6, 42, mod 3. 150 and 31: 4.83..., div 4, 124, mod 26. The most common mistake is rounding up instead of taking the whole-number part.

Quick check, 2030 trace: a = 16, b = 20, c = 30, d e f g = 5, 0, 1, 6, h = 28 (19 × 16 = 304; 304 + 20 − 5 − 6 + 15 = 328; 328 mod 30 = 28), i = 7, k = 2, l = 2 (32 + 0 + 14 − 28 − 2 = 16; 16 mod 7 = 2), m = 0 (368 div 451), n = 144, month = 4 (April), day = 144 − 124 = 20, 20 + 1 = 21. Easter Sunday 2030 is 21 April, and the stimulus table agrees.

Slide 4 of 7 · Steps 4 and 5: trace 2031 alone, then decompose · RE · Year 9

14 minutes

Step 4 & Step 5: trace 2031 on your own, then say what each part does

Step 4 (8 min): 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 and find the line where it went wrong.

Step 5 (6 min): decompose the algorithm. Answer (a) to (c), then match each part to its job in (d).

Part of the algorithm	Job (A to E)
a	B: finds the year’s place in the 19-year moon cycle

Steps 4 and 5 on your worksheet · 14 minutes, Step 4 in silence h counts days after 21 March; Easter is l + 1 days after the full moon

Supply teacher script (no subject knowledge needed)

Say aloud: “Step 4 is 2031 on your own, in silence, 8 minutes. Same method, full working on every line, then check the stimulus table. Then 6 minutes for Step 5: the first row of the matching table is on the board.”

Quick check, 2031 trace: a = 17, b = 20, c = 31, d e f g = 5, 0, 1, 6, h = 17 (323 + 20 − 5 − 6 + 15 = 347; 347 mod 30 = 17), i = 7, k = 3, l = 5 (32 + 0 + 14 − 17 − 3 = 26; 26 mod 7 = 5), m = 0 (17 + 187 + 110 = 314, div 451 = 0), n = 136, month = 4 (April), day = 136 − 124 = 12, 12 + 1 = 13. Easter Sunday 2031 is 13 April, matching the table.

Quick check, Step 5: (a) 2046 (2027 + 19); the algorithm divides by 19 because of the Metonic cycle: every 19 years the phases of the moon fall on almost the same dates again. (b) 2027: h = 1, so 22 March; 2031: h = 17, so 21 + 17 = 38, 38 − 31 = 7 April. (c) full moon 22 March, l = 5, Easter 6 days later = 28 March, correct; the full moon was on a Monday. (d) a = B; b, d, e, f, g = E; h = C; c, i, k, l = D; n, month, day = A.

Slide 5 of 7 · Steps 6 and 7: flowchart, Ash Wednesday and Pentecost · RE · Year 9

14 minutes

Step 6 & Step 7: the church’s rule as a flowchart, then count the days

Step 6 (7 min): the rule is simple: Easter Sunday is the first Sunday after the church’s full moon that falls on or after 21 March. Write one word-bank phrase in each of boxes 1 to 4, label the Yes and No arrows, then test it on 2038 and answer (c).

Step 7 (7 min): Ash Wednesday is 46 days before Easter Sunday; Pentecost is 49 days after. March and May have 31 days, April 30, February 28 in 2030 and 2031.

Model, 2027 (Easter Sunday 28 March): Ash Wednesday: back 28 days reaches 28 February; 46 − 28 = 18 still to go; 28 − 18 = 10, so 10 February 2027. Pentecost: forward 3 days reaches 31 March; 49 − 3 = 46; all 30 days of April leave 16, so 16 May 2027.

Steps 6 and 7 on your worksheet · 14 minutes Count to the end of each month and write down the days still to go

Supply teacher script (no subject knowledge needed)

Say aloud: “7 minutes for the flowchart in Step 6, then 7 minutes for Step 7. The 2027 worked example for Step 7 is on the board: count to the end of the month, write down how many days are still to go, and use the right number of days in each month.”

Quick check, Step 6: box 1 Find the church’s full moon on or after 21 March; box 2 (diamond) Is the church’s full moon on a Sunday?; Yes branch, box 3 Easter Sunday is 7 days after the full moon; No branch leads to the printed box; box 4 Output: the date of Easter Sunday. Not needed: “Count back 46 days”. (b) 2038: full moon Sunday 18 April, so Yes, Easter is 18 + 7 = 25 April 2038; the table agrees. (c) The full moon is always on or after 21 March and Easter must be after it, so the earliest Easter is 22 March, never 21 March.

Quick check, Step 7: 2030 (21 April): Ash Wednesday back 21 days to 31 March, 25 still to go, 31 − 25 = 6 March 2030; Pentecost forward 9 to 30 April, 40 to go, all 31 of May leaves 9: 9 June 2030. 2031 (13 April): back 13 to 31 March, 33 to go, all 31 of March reaches 28 February, 2 left: 26 February 2031; forward 17 to 30 April, 32 to go, 31 of May leaves 1: 1 June 2031. (b) 49 = 7 × 7, exactly 7 whole weeks, so Pentecost always lands on the same day of the week as Easter, a Sunday.

Slide 6 of 7 · Step 8 and self check · RE · Year 9

5 minutes

Step 8: why does Easter move? Then check your work

On your own, write 4 or 5 sentences explaining to a Year 7 pupil why Easter Sunday is on a different date each year. Use the 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. Then tick the success criteria you have met and correct 1 thing.

I can work out div and mod with a calculator and show my working.
I can follow an algorithm step by step and record every value in a trace table.
I can check my result against a trusted source and find my own mistakes.
I can decompose an algorithm by explaining what each part of it does.
I can show a rule as a flowchart with a decision and 2 branches, and test it.
I can count days across months accurately to find Ash Wednesday and Pentecost.
I can explain why the date of Easter moves, using the words resurrection, Passover and full moon correctly.

Step 8 on your worksheet · 5 minutes, on your own Finished early? Trace 2038, or find Shrove Tuesday 2028

Supply teacher script (no subject knowledge needed)

Say aloud: “Step 8 is on your own. 4 or 5 sentences for a Year 7 pupil using all 5 words on the board. When you finish, tick the success criteria you have met and go back to correct 1 thing, for example a remainder that is bigger than the number you divided by.”

Walk the room: a secure answer says Jesus rose from the dead on a Sunday (resurrection), so Easter is always a Sunday; Jesus died at Passover, which begins at the spring full moon, so Easter follows the full moon on or after 21 March; Sundays and full moons fall on different dates each year, so Easter moves between 22 March and 25 April; Orthodox churches still use the older Julian calendar, so their Easter is 2 May in 2027.

Extension answers: 2038 gives 25 April (a = 5, h = 29, l = 5, m = 434 div 451 = 0, only 17 below 451, n = 148). 2028: Ash Wednesday is 1 March 2028, so Shrove Tuesday is 29 February, the leap day. Same-day Easters: 2025, 2028, 2031, 2034, 2037 and 2038; in 2027 the two Easters are 5 weeks apart (35 days).

Slide 7 of 7 · Plenary review · RE · Year 9

2 minutes

Quick-check answers before handing in

Check your main answers before your worksheets are collected.

Question	Correct answer
What is 500 div 30 and 500 mod 30?	div 16 (not 17), mod 20, because 16 × 30 = 480 and 500 − 480 = 20.
What dates did the algorithm give for Easter Sunday 2030 and 2031?	21 April 2030 and 13 April 2031, both matching the stimulus table.
Why can Easter Sunday never be on 21 March?	The church’s full moon is on or after 21 March and Easter must be after the full moon, so the earliest is 22 March.

Check your name and class are on your worksheet Leave stimulus sheets and calculators neat on the desk