| 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 | Function |
| What length (min) | 30 |
| What age group | Year or Grade 8 |
| 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 |
Functions
Year 8 / Grade 8
Mathematics
20 students
This lesson corresponds with the mathematics national curriculum for Year 8, focusing on the properties and applications of functions.
| Step Number | Step Title | Length | Details |
|---|---|---|---|
| 1 | Homework Review | 5 mins | Check homework from last lesson using homework check sheets; provide feedback without student presentations. |
| 2 | Introduction to Functions | 5 mins | Introduce the concept of functions, explain function notation, and provide examples. |
| 3 | Printable Card Activity | 10 mins | Distribute printable cards to students. Instruct them to fill in definitions and examples of functions. |
| 4 | Group Discussion | 5 mins | Facilitate a discussion in pairs or small groups about the differences between functions and non-functions. |
| 5 | Collecting/Random Checking | 3 mins | Collect or randomly check the filled-in cards to assess understanding of the concept. |
| 6 | Assigning Homework | 2 mins | Briefly explain the homework assignment related to functions (without providing the specifics). |
This lesson plan provides a structured approach for teaching functions in a Year 8 mathematics class, encouraging both individual and collaborative learning while ensuring alignment with the national curriculum.
"Good morning, class! Before we dive into today's lesson, let's take a moment to review the homework from our last class. Please take out your homework check sheets. I will give you a few moments to look through your work, and I will walk around the classroom to check your understanding. Remember, this isn’t a presentation; I’m here to provide feedback. If you had difficulties with any questions, make a note of them for our discussion later."
"Now that we've reviewed your homework, let’s move on to today’s topic: Functions. Can anyone tell me what a function is? [Pause for responses] Great! A function is a special relationship between two sets of numbers where each input has exactly one output. You will often see functions written in a notation like ( f(x) ). For example, if we have ( f(x) = 2x + 3 ), that means that for any number you put in for ( x ), there is a unique output. Let's look at a few more examples on the board."
"Now, I have a fun activity for you! I’m going to hand out printable cards. On these cards, I want you to fill in the definition of a function and write down at least two examples of functions. You can use your textbooks or notes for references. Take your time, and I will give you about ten minutes for this activity. Please remember to write clearly and legibly."
[Distribute printable cards, walk around to assist students if needed]
"Alright, class! Please pair up with a partner or form small groups. I want you to discuss the differences between functions and non-functions. Think about what makes a relation a function and the characteristics that distinguish it from a non-function. For example, consider the vertical line test you may have learned before. I’ll give you five minutes for this discussion. If you finish early, feel free to brainstorm examples."
[Monitor groups, prompting discussion if necessary]
"Thank you for your thoughtful discussions! Now, I'd like to collect your cards or randomly check them to ensure everyone's on the right track with the definitions and examples of functions that you’ve written. I will go around and check a few cards, and I'll ask some of you to share your examples with the class as well."
[Collect cards or check randomly, invite a few students to share]
"To wrap up, I’d like to assign some homework that relates directly to today's lesson on functions. You’ll be working on some exercises that will require you to evaluate functions at given points and identify functions and non-functions from sets of ordered pairs. I will provide the specific sheets as you leave today. Remember to ask if you have questions about anything before I dismiss you!"
[Ensure students know what to prepare for the next class]
Define a function in your own words. What is the main characteristic that distinguishes a function from a non-function?
Given the following relations, identify which are functions and which are not. Explain your reasoning for each one:
Describe the vertical line test and explain how it can be used to determine if a graph represents a function.
Evaluate the following functions at the given points:
Create a function that includes at least three different ordered pairs. Provide the ordered pairs and then explain if your relation is a function. If it is not a function, describe what makes it so.
Write down the definition of a non-function. Give an example of a relation that is a non-function and describe why it doesn't meet the criteria of a function.
Compare and contrast the characteristics of functions and non-functions by creating a Venn diagram. Include at least three unique characteristics for each category.
Reflect on today’s lesson. What are two new things you learned about functions that you didn’t know before? How do you think understanding functions will help you in mathematics?
| Question | Answer |
|---|---|
| What is a function? | |
| How can we represent a function in notation? | |
| What does the notation ( f(x) = 2x + 3 ) represent? | |
| Describe the vertical line test and its significance in identifying functions. | |
| List two examples of functions. | |
| What characteristics distinguish a function from a non-function? | |
| Why is it important to understand functions in mathematics? | |
| What did you learn from the group discussion about functions? | |
| How do you evaluate a function at a certain point? | |
| Can a relation have more than one output for a given input? Explain. |