A day-of-the-week or clock problem: find the day or time after a given number of days or hours.

1. 1 · Write what is given and what is to be found. Note the starting day or time and how many days or hours pass.
2. 2 · Choose the modulus from the situation. Days of the week: mod 7. Hours in a day: mod 24 (mod 12 for a 12-hour clock).
3. 3 · Write the formula or theorem. If a = nq + r, 0 ≤ r < n, then a ≡ r (mod n).
4. 4 · Divide by the modulus. Write the number in the form nq + r, e.g. 100 = 7 × 14 + 2, so 100 ≡ 2 (mod 7).
5. 5 · Count on. The q full cycles bring you back to the start; move r more steps forward.
6. 6 · Check and box the answer. Box the day or time. In clock problems, also say which day it is.

Scoring tip: Write the congruence line with '≡' and '(mod 7)'. It shows the method and earns the method mark.