MICRO LESSON 1
Geometry Before Euclid
Picture it:
People measured land long before formal proofs.
Simple:
Geometry began from practical needs such as measuring fields.
Example:
Egyptians used geometry after floods.
Quick Check:
Why did early societies need geometry?
MICRO LESSON 2
Euclid’s Contribution
Picture it:
Euclid organised geometry into a logical system.
Simple:
He began with definitions, axioms and postulates, then proved results.
Example:
His book Elements influenced mathematics for centuries.
Quick Check:
What was Euclid's famous work?
MICRO LESSON 3
Definitions
Picture it:
Words need clear meanings before reasoning.
Simple:
Definitions explain terms such as point and line.
Example:
A point has position but no size.
Quick Check:
What does a definition do?
MICRO LESSON 4
Axioms
Picture it:
Some truths are accepted for all mathematics.
Simple:
Axioms are self-evident statements.
Example:
Things equal to the same thing are equal to one another.
Quick Check:
Are axioms only for geometry?
MICRO LESSON 5
Postulates
Picture it:
Geometry has its own basic assumptions.
Simple:
Postulates are accepted statements specific to geometry.
Example:
A straight line can be drawn joining two points.
Quick Check:
Give one example of a postulate.
MICRO LESSON 6
Proof
Picture it:
A proof connects accepted facts to a conclusion.
Simple:
Every step must follow logically.
Example:
If equals are added to equals, sums are equal.
Quick Check:
Why are reasons needed?
MICRO LESSON 7
Equivalent Statements
Picture it:
Different statements may express the same idea.
Simple:
Logical forms can be equivalent.
Example:
A line segment has one and only one midpoint.
Quick Check:
What does equivalent mean?