Objective
By the end of this lesson, you will be able to understand the basics of number theory, the number system, and properties of numbers in algebra 1.
Materials and Prep
- Paper and pencil
- Calculator (optional)
- No prior knowledge needed
Activities
- Activity 1: Prime or Composite?
Write down the numbers from 1 to 20 and identify which are prime numbers and which are composite numbers. Remember, a prime number has only two factors: 1 and itself. - Activity 2: Properties of Numbers
Pick any three numbers and explore the commutative, associative, and distributive properties of addition and multiplication with those numbers. Write down your findings. - Activity 3: GCD and LCM
Choose two numbers and find their Greatest Common Divisor (GCD) and Least Common Multiple (LCM). Use the Euclidean algorithm to find the GCD.
Talking Points
- "Number theory is the study of numbers and their properties. It helps us understand the relationships between numbers and how they behave."
- "The number system includes different types of numbers such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers."
- "Prime numbers are numbers that have exactly two factors: 1 and the number itself. For example, 2, 3, 5, 7 are prime numbers."
- "Composite numbers have more than two factors. For example, 4, 6, 8 are composite numbers as they have factors other than 1 and the number itself."
- "Properties of numbers like commutative, associative, and distributive properties help us understand how operations like addition and multiplication work with different numbers."
- "The Greatest Common Divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. The Least Common Multiple (LCM) is the smallest multiple that is common to two or more numbers."