Addition and Subtraction Lecture Notes

Introduction to Mathematics

• Math has evolved significantly over the past few hundred years.
• Initial mathematical concepts were simple and rooted in communication and real-life contexts.
• The complexity of current mathematics can lead to frustration among learners.

Origins of Arithmetic

• Arithmetic is the first form of math developed by humans.
• Early humans created symbols to represent counting numbers.
• Math was developed out of necessity, particularly for trade and inventory management.
• Common counting systems include:
  • Base 10 (most widely used today)
  • Base 20
  • Base 60

Basic Operations: Addition and Subtraction

Addition

• Definition: Addition combines two numbers to create a sum.
• Example: Getting apples from vendors:
  • 2 apples from one vendor + 3 apples from another = 5 apples total.
• Mathematical Representation:
  • 2 + 3 = 5 (where '+' means 'and' and '=' means 'is')

Subtraction

• Definition: Subtraction finds the difference between two numbers.
• Example: Eating apples:
  • 5 apples - 1 apple = 4 apples left.
• Mathematical Representation:
  • 5 - 1 = 4 (where '-' indicates a decrease)

Visualizing Subtraction

• Using a number line to show the distance between numbers:
  • Example: 14 - 11 = 3 (distance between 11 and 14 is 3)

Properties of Numbers

Addition Properties

• Commutative Property: Order does not matter.
  • Example: 2 + 3 = 5 and 3 + 2 = 5
• Associative Property: The grouping of numbers does not matter.
  • Example: (2 + 3) + 4 = 2 + (3 + 4)

Subtraction Properties

• Not Commutative: Order matters.
  • Example: 3 - 2 ≠ 2 - 3
• Not Associative: Grouping matters.
  • Example: (5 - 3) - 2 ≠ 5 - (3 - 2)

Conclusion

• Understanding the basic operations and their properties is crucial for grasping more complex mathematical concepts.
• All mathematical symbols and operations have concrete meanings rooted in the physical world.
• Goal: Make mathematical concepts relatable and understandable.

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