Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define modular arithmetic.
• Perform addition, subtraction, and multiplication in modular arithmetic.
• Solve real-life problems using modular arithmetic.
• Apply modular arithmetic to situations like time management.

Lesson summary

Modular arithmetic, often called "clock arithmetic," is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus. Think about how we tell time: 3 hours after 11:00 AM is not 14:00 AM, but 2:00 PM. We use a 12-hour cycle. In Ghana, we see this concept in our market day cycles (e.g., a market that comes every 5 days), in scheduling tro-tro departures, and even in patterns in our Kente cloth designs. This lesson will help us understand the mathematics behind these cycles and use it to solve practical, everyday problems.

Lesson notes

A. What is Modular Arithmetic? The Clock Analogy

Imagine a standard wall clock with numbers 1 to 12. If it is 9:00 now, what time will it be in 5 hours? We calculate: 9 + 5 = 14. But there is no "14 o'clock" on our clock. After 12, we start over from 1. So, 14 o'clock is the same as 2 o'clock.

This "wrapping around" is the core idea of modular arithmetic. The cycle is 12. We say we are working in modulo 12.

Mathematically, when we divide 14 by 12, we get a quotient of 1 and a remainder of 2. The remainder is what matters in modular arithmetic. B. Congruence Modulo m

Evaluation guide

• Model and solve real -life problems involving modular arithmetic
• Experiential Learning, Problem -based Learning, Group Work/Collaborative Learning.
• In an interactive and differentiated learning environment, model simple situations involving
• reasoning