Free 10th Grade Real Numbers Lesson Plan

Topic: Real numbers

Objectives & Outcomes

• By the end of this lesson, students will be able to prove the fundamental theorem of arithmetic and understand its implications on the nature of numbers.

Materials

• Whiteboard or blackboard
• Pencils and paper for students
• Calculator for teacher (optional)

Warm-up

• Ask students if they have ever heard of the fundamental theorem of arithmetic before.
• Ask them to explain what it is and what it is used for.
• Write down their answers on the board.

Direct Instruction

• Introduce the fundamental theorem of arithmetic, explaining that it is a theorem that says that any integer can be expressed as a unique product of prime numbers.
• Explain that a prime number is a number that is divisible only by itself and 1, and that a product is a multiplication of numbers.
• Provide examples of how to use the fundamental theorem of arithmetic to express an integer as a product of prime numbers. For example, say that we want to express the integer 24 as a product of prime numbers. We see that 24 can be divided by 1 and 24, so the theorem says that we can express 24 as a product of prime numbers by multiplying 1 by itself 24 times. This gives us 24 x 24 = 696, which is the unique product of prime numbers for 24.
• Explain that the fundamental theorem of arithmetic is useful because it allows us to decompose any integer into a unique product of prime numbers, which can be used to test for prime numbers and to factor an integer.

Guided Practice

• Provide students with a set of integers and have them use the fundamental theorem of arithmetic to express each integer as a product of prime numbers.
• Ask students to share their answers with the class and explain their reasoning.
• As a class, discuss the properties of the numbers that were expressed as products of prime numbers (for example, are they all prime numbers? are they all composite numbers? etc.)

Independent Practice

• Have students choose a number between 1 and 100 and use the fundamental theorem of arithmetic to find all prime numbers that divide into that number.
• Have students write a sentence to describe each prime number that they find, using the correct terminology (e.g. "prime number" rather than "prime factor").
• Have students share their sentences with the class and explain their reasoning.

Closure

• Review the main points of the lesson: the concept of a "prime number" and the fundamental theorem of arithmetic.
• Ask students to share one thing they learned about prime numbers during the lesson.

Assessment

• Observe students during the guided practice activity and the independent practice activity to assess their understanding of the definitions of a prime number and a composite number and the relationship between prime numbers and composite numbers.
• Collect and review the lists of prime numbers and composite numbers generated by students during the independent practice activity to assess their understanding of the concept of a prime number.
• Administer a short quiz at the end of the lesson to assess students' -understanding of the concepts of prime number and composite number and their ability to apply these concepts in identifying prime numbers and composite numbers.