KSP Математика 6 grade: Основное свойство пропорции
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Introduction
This Grade 6 Mathematics lesson plan on “The Fundamental Property of Proportions” helps teachers teach students the key rule of proportions and how to apply it in solving problems.
Main material
Lesson objective: to develop understanding of the fundamental property of proportions and apply it to find unknown terms.
Expected outcomes:
students know the fundamental property of proportions;
apply it to find unknown values;
correctly form proportions;
use it in practical problems.
Lesson structure:
Organization
Greeting.
Prior knowledge
Review proportions and ratios.
New topic
Proportion: a : b = c : d
Property: product of extremes equals product of means
Form: a × d = b × c
Examples:
2 : 3 = 4 : 6
x : 5 = 10 : 2 → x = 25
Practice
Find x: x : 6 = 12 : 3
Find x: 4 : x = 8 : 2
Practical problem: if 2 kg of apples cost 600, how much do 5 kg cost?
Consolidation
Pair work: discuss, check, and correct mistakes.
Reflection
Discuss applications (prices, distance, scale).
Conclusion
Summary, brief feedback, mention results (5–10%).
Teaching methods: explanation, practical work, pair work, discussion.
Frequently Asked Questions
What is the fundamental property of proportions?
The product of extremes equals the product of means.
How is it written?
a × d = b × c.
How to find the unknown?
Use the equality and solve the equation.
Where is it used?
In price, distance, and scale problems.
What are common mistakes?
Mixing up extremes and means.