Counting Round the Clock Tower: Modular Arithmetic on a Leicester Street Corner

Stand at the foot of Leicester's Clock Tower on a Saturday morning and you are standing inside a giant teaching aid. The tower has four faces, each divided into twelve hours. That is modular arithmetic in stone and glass. No worksheet required — just a landmark, a watch and a willingness to count round in circles.

A clock is a number line that loops

If it is 10 o'clock and you wait five hours, it is 3 o'clock, not 15 o'clock. You have done 15 mod 12 = 3. On a 24-hour timetable, 22:00 plus four hours is 02:00 the next day: 26 mod 24 = 2. The idea sounds abstract until you say it out loud next to a clock face. Then it is just the way time works.

Modular arithmetic is the maths of remainders and cycles. It explains why the minute hand returns to the same place every hour, why buses repeat on a timetable, and why calendars keep reusing the same seven weekdays. The Clock Tower is the perfect place to start because everyone already knows how to read it.

City-centre observation activity

Start at the Clock Tower and note the time on the face nearest you. Then try these mini-challenges.

• Add 137 minutes. Which number will the minute hand point to?
• Add 45 minutes, then another 45, then another. How many steps before the minute hand returns to where it started?
• Treat the four streets around the tower as quarter-turns. Call High Street 12, Church Gate 3, Gallowtree Gate 6 and Belvoir Street 9. Give each other directions using only clock numbers and turns.
• Walk to the Haymarket and back. Estimate how many minutes you were away, then work out the time on a 24-hour clock.

The geography does not have to be perfect. The point is the cycle: twelve positions, four quarters, and a reminder that numbers can wrap around.

Classroom problems: remainders, timetables and calendars

1. Late-night arithmetic. It is 23:47. What time will it be in 35 minutes?
2. Bus timetable. A bus leaves the Clock Tower stop every 12 minutes, starting at 07:05. List the departures between 08:00 and 09:00.
3. Calendar cycle. 8 November 2026 is a Sunday. What day of the week is 1 January 2027?
4. Minute-hand geometry. At 3:00, the minute hand moves 150 degrees. What time is it now?
5. Remainder practice. What is 100 mod 7? If today is Sunday, what day will it be in 100 days?
6. Timetable arithmetic. A train leaves Leicester at 17:52 and takes 1 hour 45 minutes. What time does it arrive?

Answers, for the curious: 00:22; 08:05, 08:17, 08:29, 08:41 and 08:53; Friday; 3:25; 2 and Tuesday; 19:37.

Why the Clock Tower works as a teaching tool

Modular arithmetic can feel like a secret code. Put it next to a familiar landmark and it becomes ordinary. Students can see the twelve-hour cycle, count the quarter-turns and connect the same idea to timetables, calendars and repeating patterns. The Clock Tower does not just tell the time; it shows how time is built.

Next time you pass through Leicester city centre, look up. The hands are moving, the numbers are cycling, and the maths is already there.