| 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 notation & graphing functions |
| What length (min) | 30 |
| What age group | Doesn't matter |
| 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 |
Function Notation & Graphing Functions
Middle School to High School (Grades 6-10)
Mathematics
20 students
30 minutes
This lesson corresponds to the Common Core State Standards for Mathematics, specifically:
| Step Number | Step Title | Length (minutes) | Details |
|---|---|---|---|
| 1 | Introduction to Functions | 5 | Briefly explain what a function is using real-life examples. Discuss function notation. |
| 2 | Graphing Functions | 10 | Demonstrate how to graph a linear equation. Show examples step-by-step using the board. |
| 3 | Student Activity: Printable Cards | 5 | Distribute printed cards for students to complete during the lesson. |
| 4 | Guided Practice | 5 | Walk around as students fill in their cards, providing support and answering questions. |
| 5 | Collecting & Checking Cards | 2 | Randomly check the completed cards for understanding of function notation and graphing. |
| 6 | Assigning Homework | 3 | Explain the homework assignment related to function notation and graphing tasks. |
| 7 | Conclusion | 1 | Recap key points from the lesson and clarify any misconceptions. |
"Good morning, everyone! Today, we are going to dive into the exciting world of functions and how we can represent them using function notation. Let's start by understanding what a function is. A function is like a machine that takes an input, does something to it, and gives us an output. For example, think about a vending machine: you select a button (input) and get a snack (output).
Can anyone give me another real-life example of a function? [Wait for responses]
Great examples! Now, let's discuss function notation. We often write functions as f(x), where 'f' represents the function and 'x' is the input. For instance, if we have f(x) = 2x + 3, we can replace 'x' with any number to find the output.
Does anyone have questions about functions or function notation? [Pause for any questions]
Alright, let's move on to graphing!"
"Now that we understand what a function is, let's learn how to graph linear functions. We'll start with a simple equation: y = 2x + 1.
First, we need to create a table of values. Let's choose some x-values: -2, -1, 0, 1, and 2. [Draw a table on the board and fill in values together].
For x = -2, what is y? [students respond] Right, it’s -3!
Now, let’s plot these points on the graph. [Begin plotting points on the whiteboard].
Why do you think we connect these points? [Wait for responses] Exactly! Connecting the dots shows us the line that represents our function.
As you can see, the line goes through the points (−2,−3), (−1,−1), (0,1), (1,3), and (2,5). This is how we can visually represent functions.
Now, let's practice this with another example on the board."
"Now it’s your turn! I’m going to hand out some printable cards. Each card has a different function on it, and I want you to fill in the table of values just like we did for y = 2x + 1.
Take a moment to work on this individually or with a partner. Remember, you want to choose several x-values and calculate the corresponding y-values. Once you fill in your table, you’ll be ready to graph it. Go ahead! [Distribute cards and give students a few minutes to complete the activity]."
"Alright, everyone! Now that you've filled in your tables, it’s time to graph your functions. I’ll walk around the room to assist you. If you have any questions or need help plotting your points, just raise your hand.
As you're working, remember to check that each point is plotted accurately and that your lines are straight. You can use your rulers for this! Don't hesitate to ask questions as you go along."
"Okay, time's up! Let's quickly check your work. I’ll call on a few of you to share your functions and their graphs.
[Choose a few students at random to present their work].
Fantastic job! I'm going to quickly check the rest of the cards. Remember, I’m looking at your function notation, the accuracy of your plotted points, and your overall graph.
Feel free to help each other while I do this!"
"Great work today, everyone. Now, for homework, I want each of you to complete a set of problems that reinforce what you've learned about function notation and graphing. The assignments will focus on creating function tables and plotting the corresponding graphs.
Make sure you submit your homework by our next class. I won’t be asking you to present it, but I will check your understanding when you turn it in. If anyone has questions about the homework, please ask!"
"As we wrap up today’s lesson, let’s recap what we've learned. We discussed the concept of functions, practiced function notation, and graphing linear functions.
Was there anything today that was particularly challenging or that you want to go over again? [Pause to allow for any additional questions or clarifications]
Thank you for your hard work today! I can't wait to see your homework and what you’ve done with your new knowledge. Have a great day!"
Define what a function is in your own words and provide two real-life examples of functions, similar to the vending machine example discussed in class.
Using function notation, write the function that represents the following situation: A person has $50 and spends $5 each day. How would you express their remaining money as a function of the number of days?
Given the function f(x) = 3x - 4, create a table of values for x = -2, -1, 0, 1, and 2. Calculate the corresponding y-values (f(x)).
Plot the points from your table on a graph. Connect the dots to create a line representing the function. Label your axes.
Describe what the slope and y-intercept of the function f(x) = 3x - 4 represent in practical terms.
For the function g(x) = -2x + 5, fill in the table of values for x = -1, 0, 1, 2, and 3. Calculate the corresponding y-values (g(x)).
Graph the function g(x) = -2x + 5 using the points you generated in the previous question.
Choose one function from the cards you received in class, and create a detailed function table. Make sure to include at least five x-values and their corresponding y-values.
Write a brief paragraph explaining the steps you took to create your function table and how you used it to plot the graph.
Reflect on today’s lesson: What aspect of function notation or graphing did you find most challenging? How can you improve your understanding of these concepts?
| Question | Answer |
|-------------------------------------------------------------------|--------|
| What is a function? | |
| Can you provide a real-life example of a function? | |
| What does the notation f(x) represent? | |
| Given the function f(x) = 2x + 3, what is f(-1)? | |
| How do we find outputs from a function? | |
| Why is it important to connect the points when graphing a function? | |
| What are the x-values we used to create the table for y = 2x + 1? | |
| How do you calculate the corresponding y-value for a given x? | |
| What tools can you use to ensure your lines are straight while graphing? | |
| How will your understanding of functions be evaluated in homework? | |
| What challenges did you face while learning about functions today? | |
| Can you explain the steps to graph a linear function? | |