Limits Of Functions Lesson Plan for 11th Grade Example Students

Topic: Limits of Functions

Objectives & Outcomes

• Understand the concept of limits and how to calculate them.

Materials

• Calculator
• Pen and paper for writing calculations

Warm-up

• Ask students if they have heard of the concept of limits.
• Ask students to give an example of a limit that they have encountered in a math class.
• Write the following equations on the board and ask students to solve them:

`lim_(x->0) (3x-2)/(x-1)`

`lim_(x->2) (x^2+7x+9)/(x-2)`

Direct Instruction

• Introduce the concept of limits and their role in evaluating functions.
• Explain that limits are used to determine what values a function approaches as a variable approaches a specific value.
• Explain that the term "factorization" will be used to determine the limits of functions.
• Define the three types of factorization: factorization by factorizing the numerator and denominator, factorization by combining like terms, and factorization by combining unlike terms.
• Show examples of each type of factorization on the board.
• Explain the difference between limits by factorization and limits by substitution.

Guided Practice

• Provide students with a handout containing several examples of functions with defined limits.
• Have students work in pairs to solve the problems using the method of factorization.
• Have students present their solutions to the class and discuss any issues or challenges they had with the problem-solving process.
• As a class, discuss what characteristics the functions had that made them amenable to factorization.

Independent Practice

• Provide students with a worksheet containing multiple problems that require them to find the limits of functions by factorization.
• Have students work through the problems on their own or in pairs, and check their answers against the solution key.

Closure

• Review the concept of finding the limit of a function by factorization and how to apply it to real-world problems.
• Ask students to share any challenges they experienced when working on the independent practice problems and how they resolved them.

Assessment

• Observe students during the guided practice and independent practice to assess their understanding of the concept of limits by factorization and their ability to apply it to real-world problems.
• Collect and review their written answers to the independent practice problems to assess their ability to apply the concept of limits by factorization and their ability to write explanations, definitions, and algebraic calculations for real-world problems.