Disney Linear Functions: Graphing the Magic
Materials Needed
- Graph paper or a digital graphing tool
- Pencil and colored pencils
- Calculator, optional
- Disney-themed practice cards or the examples below
- Exit ticket
Learning Target
I can graph linear functions given in function notation and identify and interpret key features.
Success Criteria
By the end of the lesson, I can:
- Identify the slope and y-intercept of a linear function.
- Use the y-intercept and slope to graph a line.
- Identify x- and y-intercepts when appropriate.
- Interpret what key features mean in a Disney-themed situation.
Introduction: Bell Work and Hook — 2 Minutes
Bell Work: Revisit Prior Knowledge
Complete the following without using a graphing tool:
- In the equation y = 3x + 2, what number represents the slope?
- What number represents the y-intercept?
- What is the first point you could plot to graph this equation?
Quick review: In slope-intercept form, y = mx + b, m is the slope and b is the y-intercept.
Hook: Imagine that a Disney park creates a special attraction where the total number of Magic Points depends on how many rides you enjoy. How could a graph show how your points increase?
Body: Gradual Release of Responsibility — 11 Minutes
I Do: Teacher Modeling — 3 Minutes
Consider the Disney-themed function:
p(x) = 4x + 10
This function represents the number of Magic Points, p(x), earned after visiting x attractions.
- Identify the slope: The slope is 4. This means the visitor earns 4 Magic Points for each attraction.
- Identify the y-intercept: The y-intercept is 10. This means the visitor starts with 10 Magic Points before visiting any attractions.
- Plot the y-intercept: Plot the point (0, 10).
- Use the slope: A slope of 4 means “up 4, right 1.” From (0, 10), plot (1, 14), then (2, 18).
- Draw the line: Connect the points with a straight line and add arrows if the graph represents all real-number inputs.
Key features:
- Slope: 4; the Magic Points increase by 4 per attraction.
- y-intercept: (0, 10); the visitor begins with 10 points.
- x-intercept: Set p(x) equal to 0: 0 = 4x + 10, so x = −2.5. In this situation, that value is not realistic because a visitor cannot visit −2.5 attractions.
- Domain: x ≥ 0, because the number of attractions cannot be negative.
- Range: p(x) ≥ 10, because the visitor starts with 10 points.
We Do: Guided Practice — 4 Minutes
Work together to analyze this function:
r(t) = 2t + 6
This function represents the number of Disney character stickers collected after visiting t character stations.
- What is the slope?
- What is the y-intercept?
- What point should be plotted first?
- Use the slope to find two additional points.
- What does the slope mean in this situation?
- What does the y-intercept mean?
Expected responses:
- Slope: 2
- y-intercept: 6
- First point: (0, 6)
- Additional points: (1, 8) and (2, 10)
- Interpretation of slope: 2 stickers are collected at each character station.
- Interpretation of y-intercept: The visitor starts with 6 stickers.
Think-Pair-Share option: Explain to a learning partner, family member, or imaginary Disney tour guide how you knew where to begin the graph.
You Do: Independent Disney Challenge — 4 Minutes
Choose one of the following challenges.
Challenge A: Disney Snack Stand
The total cost of buying Disney-themed cupcakes is modeled by:
C(x) = 5x + 8
where x is the number of cupcakes and C(x) is the total cost in dollars.
Challenge B: Pixar Movie Marathon
The number of minutes watched during a movie marathon is modeled by:
M(n) = 105n + 15
where n is the number of movies watched and M(n) is the total number of minutes.
For your chosen challenge:
- Identify the slope and y-intercept.
- State the coordinate of the y-intercept.
- Create a table with at least three input-output pairs.
- Graph the function.
- Write one sentence interpreting the slope.
- Write one sentence interpreting the y-intercept.
- State a reasonable domain and range for the situation.
Conclusion: Recap and Exit Ticket — 2 Minutes
Recap
Complete this sentence aloud or in writing:
“To graph a linear function in the form y = mx + b, I first __________. Then I use __________ to find more points.”
Exit Ticket
Given the function F(x) = 3x + 9:
- Identify the slope and y-intercept.
- Give two points that can be used to graph the function.
- Interpret the y-intercept in this Disney-themed situation: F(x) represents the number of Fantasy Points earned after completing x magical quests.
Expected answer: The slope is 3, the y-intercept is 9, possible points are (0, 9) and (1, 12), and the visitor starts with 9 Fantasy Points.
Assessment
Formative Assessment
- Bell work responses
- Questions during the teacher model
- Think-Pair-Share explanation
- Guided practice responses
- Teacher or parent observation of graphing steps
Summative Assessment
Use the independent Disney Challenge and exit ticket to determine whether the learner can:
- Correctly identify slope and y-intercept.
- Graph a line using an accurate starting point and slope.
- Interpret key features using the context.
- Choose a reasonable domain and range.
Differentiation and Extension
Support
- Provide the sentence frame: “The slope is ____, so the graph goes up/down ____ units for every 1 unit to the right.”
- Use a color to highlight m and another color to highlight b in y = mx + b.
- Allow the learner to use a slope triangle or a digital graphing tool.
- Begin with positive whole-number slopes and nonnegative inputs.
Extension
- Write a Disney-themed linear function with a negative slope and explain what the decrease represents.
- Find the x-intercept and explain whether it makes sense in the chosen context.
- Create a table, equation, and written description for the same function, then show that all three representations match.
Real-World Connection
Linear functions can model costs, time, points, distance, rewards, and other situations that change at a constant rate. Identifying slope and intercepts helps us understand both how quickly something changes and where it begins.