| Full lesson | Create for a teacher a set of content for giving a lesson, beginning with the lesson plan. Each new block of materials must begin with an H1 heading (other subheaders must be H2, H3, etc). When you describe required pictures, write those descriptions in curly brackets, for example: {A picture of a triangle} |
| Which subject | Mathematics |
| What topic | Solving quadratic equations |
| What length (min) | 30 |
| What age group | Year or Grade 9 |
| Class size | 20 |
| What curriculum | |
| Include full script | |
| Check previous homework | |
| Ask some students to presents their homework | |
| Add a physical break | |
| Add group activities | |
| Include homework | |
| Show correct answers | |
| Prepare slide templates | |
| Number of slides | 5 |
| Create fill-in cards for students | |
| Create creative backup tasks for unexpected moments |
Mathematics
Solving Quadratic Equations
Grade 9
30 minutes
20
| Step Number | Step Title | Length (Minutes) | Details |
|---|---|---|---|
| 1 | Introduction to Quadratic Equations | 5 | Introduce the topic and explain the standard form of quadratic equations (ax^2 + bx + c = 0). Provide examples. |
| 2 | Methods of Solving | 10 | Explain the three main methods of solving quadratic equations: factoring, completing the square, and the quadratic formula. Show examples for each. |
| 3 | Student Activity | 5 | Distribute printable cards for students to fill out during the practice problems. Each card will include space for working out problems and recording answers. |
| 4 | Guided Practice | 5 | Students use their cards to work through example problems in pairs, applying the methods discussed. Circulate to provide support where needed. |
| 5 | Collect Student Work | 3 | Collect the printable cards to check for understanding and identify common areas of confusion without asking students to present their work. |
| 6 | Assign Homework | 2 | Assign homework that reinforces the lesson content, ensuring completion before the next class. Provide clear instructions on what to complete. |
"Good morning, everyone! Today, we are going to explore a really exciting topic in mathematics—quadratic equations. Can anyone tell me what they know about these types of equations?"
[Pause for a few students to respond.]
"Great responses! So, a quadratic equation is a second-degree polynomial equation in the standard form of ax² + bx + c = 0, where a, b, and c are constants, and a is not equal to zero. For example, the equation 2x² + 3x - 5 = 0 is a quadratic equation because it fits this form."
[Write the standard form on the whiteboard.]
"Let’s make sure we understand this concept—can anyone explain what each of the terms represents? Specifically, what are a, b, and c?"
[Encourage discussion and clarify if necessary.]
"Perfect! Now, I want you to think about situations where these equations might come up in real life. You might see them in physics, finance, or even in sports. Keep those ideas in mind as we move forward!"
“Now that we understand what quadratic equations are, let’s talk about how to solve them. There are three main methods: factoring, completing the square, and using the quadratic formula. Let's break each one down.”
[Move to the whiteboard and write the methods.]
“First, let’s look at factoring. This involves expressing the quadratic equation in its factored form. For example, the equation x² - 5x + 6 = 0 can be factored into (x - 2)(x - 3) = 0. Can anyone tell me how we would solve this once it’s factored?”
[Allow for student responses; guide them to the correct process.]
“Excellent! Now, the second method is completing the square. This involves rewriting the equation in the form of (x - p)² = q. For instance, if we have x² + 4x - 5 = 0, we can transform it. If you were to complete the square, what steps would you take?”
[Discuss and clarify the method.]
“Lastly, we have the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). This formula is useful when factoring is complicated. For example, for the equation 2x² + 3x - 5 = 0, we can plug the values into the formula to find the roots. Who can help me by substituting the values of a, b, and c into the quadratic formula?”
[Encourage students to participate and solve with guidance.]
“Wonderful! Now you have learned all the methods. Let’s put them into practice!”
“Alright, now it’s your turn! I will be handing out printable cards for you to fill out during our practice session. Each card has space for problems, as well as a spot for your work and answers.”
[Distribute cards to the students.]
“Work through the examples I just explained on your cards. Use the method that you think works best for you. You have 5 minutes—let’s get started!”
“Time’s up! Now, I want you to turn to your partner and discuss the problems you've worked on. Share your thought processes and solutions. This is a team effort, so help each other out.”
[Circulate around the room to provide support.]
“If you have questions or need clarification on anything, raise your hand, and I’ll come to help.”
[Observe student interactions, offering encouragement and guidance as needed.]
“Great job working together! Now, please hand in your printable cards. I’m going to review them to see how well everyone understood today’s lesson. Don’t worry; this isn’t a graded assignment, but it will help me understand where you might be having difficulties.”
[Collect the cards, giving students a moment to organize their work.]
“Thank you! I really appreciate your efforts today.”
“Before we wrap up, I want to give you some homework to reinforce what we learned. Please complete the problems on the handout I’m about to distribute. Make sure you apply the methods we discussed—factoring, completing the square, and the quadratic formula.”
[Distribute the homework handout.]
“Please make sure to complete it before our next class. If you have any questions or need help, feel free to reach out. Keep practicing those skills, and I’ll see you next time!”
Define a quadratic equation and provide an example in standard form.
In the equation (3x^2 + 6x + 2 = 0), identify the values of (a), (b), and (c).
Explain the process of factoring a quadratic equation. Factor the equation (x^2 - 8x + 15 = 0) and solve for (x).
Describe the method of completing the square. Solve the quadratic equation (x^2 + 10x + 9 = 0) by completing the square.
Use the quadratic formula to find the roots of the equation (4x^2 + 12x + 9 = 0). Show all your work.
Compare the three methods of solving quadratic equations: factoring, completing the square, and the quadratic formula. In what scenarios might one method be preferred over the others?
Create a real-life scenario where a quadratic equation could be applied. Write the equation that represents the scenario and explain how you could solve it.
Solve the quadratic equation (2x^2 - 4x - 6 = 0) using any method of your choice. Provide a detailed explanation of your steps.
Discuss how the discriminant ((b^2 - 4ac)) helps in determining the nature of the roots of a quadratic equation. Calculate the discriminant of (x^2 + 4x + 4 = 0) and interpret the results.
Create a quadratic equation based on a given set of roots: (x = 1) and (x = -5). Write the equation in standard form and verify your solution by expanding.
| Question | Answer |
|---|---|
| What is the standard form of a quadratic equation? | |
| Can you identify the values of a, b, and c in the equation 2x² + 3x - 5 = 0? | |
| What does it mean for a to not be equal to zero in a quadratic equation? | |
| How can you factor the equation x² - 5x + 6 = 0? | |
| What are the steps involved in completing the square for the equation x² + 4x - 5 = 0? | |
| When would you use the quadratic formula instead of factoring? | |
| Can you state the quadratic formula? | |
| How do you substitute values into the quadratic formula? | |
| What types of real-life situations might involve quadratic equations? | |
| How do the three methods of solving quadratic equations compare? |