Unlocking the Secrets of Quadratic Expressions

Unlocking the Secrets of Quadratic Expressions

Learning Objective

At the end of the lesson, you will be able to factorize quadratic expressions and solve problems related to them.

Introduce the learning objective of the lesson and explain why it is important to be able to factorize quadratic expressions.

What do you already know about quadratic expressions and how to factorize them?

What are Quadratic Expressions?

Quadratic expressions are expressions with one or more squared variables. For example, x^2 + 2x + 1 is a quadratic expression.

Explain what quadratic expressions are and give some examples.

What is Factorization?

Factorization is the process of finding the factors of an expression. For example, the factors of x^2 + 2x + 1 are (x + 1)^2.

Define what factorization is and explain how it is related to quadratic expressions.

Factoring Quadratic Expressions

To factorize a quadratic expression, we need to find two expressions that multiply together to give the original expression. For example, x^2 + 2x + 1 can be factored into (x + 1)^2.

Explain the process of factoring quadratic expressions and give some examples.

Practise Questions 1

Factorize the following quadratic expression: x^2 + 6x + 9

Give students time to try the question and then provide the answer and explanation.

Practise Questions 2

Factorize the following quadratic expression: x^2 - 4x - 5

Give students time to try the question and then provide the answer and explanation.

Problem Solving Questions 1

If a quadratic expression can be factored into (x + 3)(x - 2), what are its roots?

Explain what roots are and give students time to try the question. Then provide the answer and explanation.

Problem Solving Questions 2

A quadratic expression has roots of 2 and -5. What is its factored form?

Give students time to try the question and then provide the answer and explanation.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.