Simplifying Radicals Lesson Plan

Objective:

Students will be able to simplify radicals by factoring out perfect squares, add and subtract radicals with like terms, multiply radicals, and divide radicals correctly.

Assessment:

Students will be given a worksheet with a variety of radical expressions to simplify using the key points covered in the lesson. They must also complete problems involving adding, subtracting, multiplying, and dividing radicals to demonstrate their understanding.

Key Points:

• Simplify Radicals: One way to simplify a radical is to factor out the perfect squares.

  • Formula: If √a * √a = a, then √(a^2) = a

• Adding Radicals: When adding radicals, you can only combine radicals with the same number underneath it.

  • Formula: √a + √a = 2√a

• Multiplying Radicals: To multiply two radicals, multiply what is under the radicals and what is in front.

  • Formula: √a * √b = √(ab)

• Dividing Radicals: To divide radicals, you need to simplify the denominator, which means multiplying the top and bottom of the fraction by the radical in the denominator.

  • Formula: √a / √b = √(a*b) / b

Opening:

• Begin the lesson by asking students to consider why simplifying radicals is important in mathematics.

• Engage students with a real-life scenario where simplifying radicals would be useful, such as calculating the length of a diagonal in a rectangular field.

Introduction to New Material:

• Explain the concept of radicals and the importance of simplifying them for easier calculations.

• Demonstrate how to simplify radicals by factoring out perfect squares with examples.

• Anticipate the misconception that students can combine radicals with different numbers underneath.

Guided Practice:

• Provide guided practice problems for students to simplify radicals following the demonstrated method.

• Scaffold questions from simple to complex examples to ensure understanding.

• Monitor student performance by circulating the classroom and providing feedback.

Independent Practice:

• Assign a worksheet for independent practice, including a variety of problems involving simplifying, adding, subtracting, multiplying, and dividing radicals.

• Encourage students to show all steps of their work clearly and neatly.

Closing:

• To close the lesson, have students pair up and summarize the key steps in simplifying radicals to a partner.

• Ask a few pairs to share their summaries with the class.

Extension Activity:

• For early finishers, provide a challenge where they need to simplify radicals with variables or explore the concept of rationalizing denominators.

Homework:

• Homework assignment: Create a set of 10 problems involving simplifying radicals and operations with radicals for practice.

Standards Addressed:

• CCSS.MATH.CONTENT.HSN.RN.A.2a: Rewrite expressions involving radicals and rational exponents using the properties of exponents.

• CCSS.MATH.CONTENT.HSN.RN.A.2b: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.