Worked example · RE · Year 9
DCF: Data and computational thinking → Problem-solving and modelling
A secure Year 9 response, annotated to show which success criterion each part meets. It is also your answer key. The key results: Easter Sunday 2030 is 21 April and Easter Sunday 2031 is 13 April, both matching the stimulus table. Ash Wednesday is 6 March 2030 and 26 February 2031; Pentecost is 9 June 2030 and 1 June 2031. The most common mistake is rounding up instead of taking the whole-number part (for example writing 328 div 30 = 11 instead of 10). Calculator decimals are shown to 2 decimal places; pupils may write more or fewer.
| Question | Calculator shows | div | Multiply back and subtract | mod |
|---|---|---|---|---|
| 100 and 7 | 14.28... | 14 | 14 × 7 = 98; 100 − 98 = 2 | 2 |
| 2025 and 19 | 106.57... | 106 | 106 × 19 = 2014; 2025 − 2014 = 11 | 11 |
| 500 and 30 | 16.66... | 16 | 16 × 30 = 480; 500 − 480 = 20 | 20 |
| 45 and 7 | 6.42... | 6 | 6 × 7 = 42; 45 − 42 = 3 | 3 |
| 150 and 31 | 4.83... | 4 | 4 × 31 = 124; 150 − 124 = 26 | 26 |
The pupil takes the whole-number part without rounding up (500 div 30 is 16, not 17), multiplies back and subtracts to find each remainder, and every remainder is smaller than the number divided by. Evidences criterion 1.
| Letter | Working | Value |
|---|---|---|
| a | 2030 ÷ 19 = 106.84..., so div is 106. 106 × 19 = 2014. 2030 − 2014 = 16 | 16 |
| b | 2030 ÷ 100 = 20.3, so div is 20 | 20 |
| c | 2030 − 2000 = 30 | 30 |
| d, e, f, g | Same as 2027 | 5, 0, 1, 6 |
| h | 19 × 16 = 304. 304 + 20 − 5 − 6 + 15 = 328. 328 ÷ 30 = 10.93..., so div is 10. 10 × 30 = 300. 328 − 300 = 28 | 28 |
| i | 30 ÷ 4 = 7.5, so div is 7 | 7 |
| k | 7 × 4 = 28. 30 − 28 = 2 | 2 |
| l | 32 + 0 + 14 − 28 − 2 = 16. 16 ÷ 7 = 2.28..., so div is 2. 2 × 7 = 14. 16 − 14 = 2 | 2 |
| m | 16 + 308 + 44 = 368. 368 ÷ 451 = 0.81..., so div is 0 | 0 |
| n | 28 + 2 − 0 + 114 = 144 | 144 |
| month | 144 ÷ 31 = 4.64..., so div is 4: April | 4 |
| day | 4 × 31 = 124. 144 − 124 = 20. 20 + 1 = 21 | 21 |
Easter Sunday 2030 is 21 April. Yes, it matches the stimulus table.
Every line follows the rule in order, uses values from the lines above, and shows the division, the whole-number part and the remainder. The brackets are worked out first (32 + 2 × 0 + 2 × 7 − 28 − 2). The final date is checked against a trusted source. Evidences criteria 1, 2 and 3.
| Letter | Working | Value |
|---|---|---|
| a | 2031 ÷ 19 = 106.89..., so div is 106. 106 × 19 = 2014. 2031 − 2014 = 17 | 17 |
| b | 2031 ÷ 100 = 20.31, so div is 20 | 20 |
| c | 2031 − 2000 = 31 | 31 |
| d, e, f, g | Same as 2027 | 5, 0, 1, 6 |
| h | 19 × 17 = 323. 323 + 20 − 5 − 6 + 15 = 347. 347 ÷ 30 = 11.56..., so div is 11. 11 × 30 = 330. 347 − 330 = 17 | 17 |
| i | 31 ÷ 4 = 7.75, so div is 7 | 7 |
| k | 7 × 4 = 28. 31 − 28 = 3 | 3 |
| l | 32 + 0 + 14 − 17 − 3 = 26. 26 ÷ 7 = 3.71..., so div is 3. 3 × 7 = 21. 26 − 21 = 5 | 5 |
| m | 17 + 187 + 110 = 314. 314 ÷ 451 = 0.69..., so div is 0 | 0 |
| n | 17 + 5 − 0 + 114 = 136 | 136 |
| month | 136 ÷ 31 = 4.38..., so div is 4: April | 4 |
| day | 4 × 31 = 124. 136 − 124 = 12. 12 + 1 = 13 | 13 |
Easter Sunday 2031 is 13 April. Yes, it matches the stimulus table.
Completed without help, with the same full working on every line, so any slip could be found and fixed. Note that 11h is 11 × 17 = 187 and 22l is 22 × 5 = 110. Evidences criteria 1, 2 and 3.
(a) 2046 (2027 + 19 = 2046; 2046 − 107 × 19 = 2046 − 2033 = 13). The algorithm divides by 19 because of the Metonic cycle: every 19 years the phases of the moon fall on almost exactly the same dates again, so the remainder a tells the algorithm where the year sits in the 19-year cycle of the church’s full moon tables. (Easter 2046 is not on the same date as 2027, 25 March instead of 28 March, because the full moon falls on a different day of the week.)
(b) 2027: h = 1, so 21 March + 1 day = 22 March. 2031: h = 17, so 21 + 17 = 38 “March”, and 38 − 31 = 7, so 7 April.
(c) 2027: full moon 22 March, l = 5, so Easter is 5 + 1 = 6 days later: 22 + 6 = 28 March. Correct. Easter Sunday is 6 days after the full moon, so the full moon was on a Monday.
(d)
| Part of the algorithm | Job |
|---|---|
| a | B: the place in the 19-year moon cycle |
| b, d, e, f and g | E: corrections for the century |
| h | C: the church’s full moon, in days after 21 March |
| c, i, k and l | D: the day of the week, to jump to the next Sunday |
| n, month and day | A: turns a count of days into a month and a day |
The pupil links a part of the algorithm to the real-world idea it models (the 19-year cycle on the stimulus sheet), uses h and l to find the full moon and check the jump to Sunday, and matches every part to its job. This is decomposition. Evidences criterion 4.
Phrase not needed: “Count back 46 days” (that finds Ash Wednesday, not Easter).
(b) The full moon is on Sunday 18 April, so the answer to the diamond is Yes. Easter is 7 days later: 18 + 7 = 25 April 2038. The stimulus table agrees.
(c) The church’s full moon is always on or after 21 March, and Easter must be after the full moon, never on the same day. So the earliest the full moon can be is 21 March and the earliest Easter can be is the day after, 22 March (when 21 March is a Saturday full moon). Easter can never be on 21 March itself.
The flowchart has one start and one end, a single decision with Yes and No branches, and both branches join before the output. The pupil tests it on a real case where the full moon is on a Sunday (the trickiest path) and uses it to reason about the earliest possible date. Evidences criteria 3 and 5.
| Year | Easter Sunday | Ash Wednesday (46 days before) | Pentecost (49 days after) |
|---|---|---|---|
| 2030 | 21 April | Back 21 days from 21 April reaches 31 March. 46 − 21 = 25 still to go. 31 − 25 = 6. 6 March 2030 | Forward 9 days from 21 April reaches 30 April. 49 − 9 = 40 still to go. All 31 days of May reach 31 May, leaving 40 − 31 = 9. 9 June 2030 |
| 2031 | 13 April | Back 13 days from 13 April reaches 31 March. 46 − 13 = 33 still to go. All 31 days of March reach 28 February, leaving 33 − 31 = 2. 28 − 2 = 26. 26 February 2031 | Forward 17 days from 13 April reaches 30 April. 49 − 17 = 32 still to go. All 31 days of May reach 31 May, leaving 1. 1 June 2031 |
(b) 49 = 7 × 7, so Pentecost is exactly 7 whole weeks after Easter Sunday. Moving forward a whole number of weeks always lands on the same day of the week, so Pentecost is always a Sunday.
The pupil counts to the end of each month, keeps track of the days still to go, and uses the right number of days in each month (February 2031 has 28). 6 March 2030 and 26 February 2031 are both Wednesdays, which is a useful check. Evidences criterion 6.
Christians believe that Jesus rose from the dead on a Sunday, so Easter, the festival of the resurrection, is always on a Sunday. The Gospels say Jesus died at the time of the Jewish festival of Passover, and the Last Supper is described as a Passover meal. Passover follows the moon and begins at the spring full moon, so Christians also linked Easter to the full moon in spring. The rule is that Easter Sunday is the first Sunday after the church’s full moon on or after 21 March, and because full moons and Sundays fall on different dates each year, Easter moves between 22 March and 25 April. In 2027 Orthodox Christians celebrate Easter on 2 May because most Orthodox churches still work out Easter with the older Julian calendar, not the Gregorian calendar used in Wales, so their date is 5 weeks later.
All 5 key words are used accurately, the religious reason (the resurrection on a Sunday) comes before the astronomical one, the Passover link explains why the moon matters, and the last sentence explains the Orthodox date using the two calendars. Evidences criterion 7.