| 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 | Quadratics |
| What length (min) | 30 |
| What age group | Year or Grade 10 |
| 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
Quadratics
Year 10
30 minutes
20
This lesson corresponds with the UK national curriculum for Mathematics, focusing on understanding and applying knowledge of quadratic equations, their graphs, and properties.
| Step Number | Step Title | Length | Details |
|---|---|---|---|
| 1 | Introduction to Quadratics | 5 min | Briefly introduce the concept of quadratics. Discuss standard form and basic properties. |
| 2 | Key Features Overview | 5 min | Explain key features of quadratic graphs: vertex, axis of symmetry, x-intercepts. |
| 3 | Printable Card Activity | 10 min | Distribute printable cards. Students fill them in with examples of quadratics and graph features. |
| 4 | Maths Practice | 5 min | Guide students in solving a few example problems on the board, inviting participation. |
| 5 | Checking Understanding | 3 min | Collect or randomly check the filled cards, providing feedback on common errors. |
| 6 | Summary and Homework Assignment | 2 min | Summarise key points of the lesson. Assign homework related to quadratics for further practice. |
Assign students to complete a worksheet on quadratic equations and to practice graphing any five quadratics of their choice. Homework will be collected the following lesson without oral presentations.
"Good morning, everyone! Today, we are going to dive into the fascinating world of quadratics. Can anyone tell me what they think a quadratic equation is? Yes, that's right! A quadratic equation is a polynomial equation of the second degree, usually written in the form ( ax^2 + bx + c = 0 ).
Now, we'll explore its standard form, recognizing that 'a', 'b', and 'c' are constants and 'a' cannot be zero. Throughout this lesson, we’ll talk about its features and how to graph it. Let’s work together and see what we can discover about these equations!"
"Next, we'll discuss the key features of a quadratic graph. Who can remind me what a graph looks like? Exactly! It's a U-shaped curve, known as a parabola.
Now, let’s focus on three important features: the vertex, the axis of symmetry, and the x-intercepts.
Does everyone understand these features? Let’s keep these in mind as we move to our next activity!"
"Now it's time for a fun activity with the printable cards I have prepared for you. Please take one card and a pen or pencil.
On these cards, you will need to write down different examples of quadratic equations and identify their key features: the vertex, axis of symmetry, and x-intercepts. You have ten minutes to complete this.
Feel free to work with a partner—discuss your findings and help each other! I will walk around to assist you as needed. Ready? Let’s start!"
"Alright! Now that you've completed your cards, let's do some practice problems together. I will solve a quadratic equation on the board, and I’d like you all to participate.
Can anyone start off by telling me the standard form of a quadratic? Great! Now, let's say we have ( x^2 - 4x - 5 = 0 ).
How would we find the x-intercepts? That's right, by factoring or using the quadratic formula! Let's work through the first few steps together. Who wants to give it a try? Yes, excellent! Keep your thoughts coming, and let’s solve this one together!"
"Time is flying! Now, let’s gather the filled cards you worked on earlier. I will randomly check these and provide feedback.
As I do, I’d like you to think about any common errors you made, or something you found challenging during the cards. If I see a common misconception among the class, I will address it and clarify it for everyone."
"Great work today, everyone! To summarize, we learned what a quadratic equation is, how to identify key features of its graph—the vertex, axis of symmetry, and x-intercepts—and applied this knowledge through various activities.
For homework, I want you to complete the worksheet on quadratic equations, and also practice graphing any five quadratics of your choice. Remember, we will collect these next lesson, so be ready!
Wonderful participation today; I look forward to seeing your homework next time!"
| Question | Answer |
|--------------------------------------------------------------------------------------------------------------|--------|
| What is the standard form of a quadratic equation? | |
| Can you identify the three key features of a quadratic graph? | |
| What shape does a quadratic graph form? | |
| What is the vertex of a quadratic graph? | |
| How does the axis of symmetry relate to the vertex in a parabola? | |
| What are x-intercepts and why are they important in quadratic equations? | |
| If the quadratic opens upwards, what does that indicate about the vertex? | |
| How would you find the x-intercepts of a quadratic equation? | |
| Can you give an example of a quadratic equation? | |
| What challenges did you face while completing the printable card activity? | |
| How do you feel about graphing quadratic equations after today’s lesson? | |
| What common errors might occur when identifying the vertex or axis of symmetry? | |
| Why is it important to understand the features of a quadratic equation? | |
| What will you need to prepare for the homework assignment related to quadratic equations? | |