KSP Математика 6 grade: Наибольший общий делитель

This Grade 6 Mathematics lesson plan on “Greatest Common Divisor (GCD)” helps teachers teach students to find the largest common divisor of two or more numbers using prime factorization and other methods.

Lesson objective: to teach students to find the GCD of numbers and apply it for simplifying calculations and solving practical problems.

Expected outcomes:

students understand the concept of GCD;
can find GCD using prime factorization;
apply Euclid’s algorithm for GCD;
use GCD for simplifying fractions and problem-solving.

Lesson structure:

Organization
Greeting.
Prior knowledge
Review prime factorization, divisor, common divisor concepts.
New topic
GCD as the largest divisor common to two or more numbers
Methods to find GCD:
Prime factorization
Euclid’s algorithm
Examples:
GCD(24, 36) = 12
GCD(48, 180) using Euclid’s algorithm
Practice
Find GCD of 36 and 60 using prime factorization
Find GCD of 84 and 126 using Euclid’s algorithm
Solve problems where GCD is needed to simplify fractions or divide items equally
Consolidation
Pair work: discuss solutions and check each other’s steps.
Reflection
Discuss applications of GCD in daily life, mathematics, and practical tasks.
Conclusion
Summary and brief feedback.

Teaching methods: explanation, practical work, pair work, discussion.

What is GCD?
Greatest common divisor is the largest number that divides two or more numbers without remainder.

What methods exist to find GCD?
Prime factorization and Euclid’s algorithm.

How is GCD applied in practice?
Simplifying fractions, dividing items equally, solving problems.

Can GCD be found for more than two numbers?
Yes, by finding GCD sequentially for pairs of numbers.

How to reinforce learning?
Through practical exercises and pair checking.