Roblox Obby Functions: Graphing and Finding Key Features
Materials Needed
- Paper or graph paper
- Pencil and colored pencils
- Ruler
- Calculator, optional
- Printed or handwritten activity table
- Desmos or another graphing tool, optional
Lesson Snapshot
Time: 15 minutes
Theme: Roblox obby checkpoints and player rewards
Standard: MA.912.AR.2.4 — Given a table, equation, or written description of a linear function, graph that function and determine and interpret its key features.
Learning Target: I can identify and interpret the domain, range, intercepts, and end behavior of a function from an input-output table or graph.
Learning Objectives
By the end of the lesson, the learner will be able to:
- Plot ordered pairs from a table on a coordinate plane.
- Identify the domain and range of a function shown in a table or graph.
- Find and interpret the x-intercept and y-intercept.
- Describe the end behavior of a linear function using words or arrows.
- Connect each key feature to a Roblox-related situation.
Success Criteria
I am successful when I can:
- Correctly plot at least 4 ordered pairs.
- Identify the domain and range from the given data.
- Locate and label the intercepts, when they appear in the displayed domain.
- Explain what an intercept and end behavior mean in the Roblox context.
- Use correct vocabulary: domain, range, x-intercept, y-intercept, and end behavior.
Introduction: Bell Work and Hook — 2 Minutes
Bell Work: Reconnect to Prior Knowledge
Imagine that a Roblox player earns 10 coins each time they complete an obby stage. The table shows the number of coins earned.
| Stages Completed, x | Coins Earned, y |
|---|---|
| 0 | 0 |
| 1 | 10 |
| 2 | 20 |
| 3 | 30 |
- Write the ordered pairs.
- What pattern do you notice?
- Predict the number of coins earned after 4 stages.
Quick check: The expected ordered pairs are (0, 0), (1, 10), (2, 20), and (3, 30). The pattern is an increase of 10 coins for every additional stage.
Hook: “If this pattern continued, how could we use a graph to predict a player’s coins at any point in the obby?”
Body: Gradual Release of Responsibility
I Do: Teacher Modeling — 4 Minutes
Use the bell-work table to model each step aloud.
- Plot the points: Plot (0, 0), (1, 10), (2, 20), and (3, 30). Connect the points with a straight line if the number of stages can include fractional values.
- Identify the domain: The domain is the set of input values. For the table, the domain is {0, 1, 2, 3}. In context, it represents the stages completed.
- Identify the range: The range is the set of output values. For the table, the range is {0, 10, 20, 30}. In context, it represents coins earned.
- Find the y-intercept: The graph crosses the y-axis at (0, 0). This means the player has 0 coins after completing 0 stages.
- Find the x-intercept: The graph crosses the x-axis at (0, 0). This means the player earns 0 coins when 0 stages are completed.
- Describe end behavior: As the number of completed stages increases, the number of coins increases. Symbolically, as x increases, y increases.
Teacher language: “The domain tells us the possible inputs. The range tells us the possible outputs. Intercepts show where the graph crosses an axis. End behavior describes what happens as the input moves farther to the left or right.”
Formative check: Ask, “Which quantity is the input: stages or coins? Which quantity is the output?”
We Do: Guided Practice — 4 Minutes
Work through the following Roblox scenario together. The player begins with 50 coins and earns 15 coins per completed stage.
Equation: y = 15x + 50
Complete the table and graph the function.
| Stages Completed, x | Coins, y |
|---|---|
| 0 | 50 |
| 1 | 65 |
| 2 | 80 |
| 3 | 95 |
Use the following prompts:
- What ordered pairs should we plot?
- What is the domain shown in the table?
- What is the range shown in the table?
- Where is the y-intercept? What does it mean?
- Does the x-intercept appear in the table or graph? Explain.
- As the number of stages increases, what happens to the number of coins?
Expected responses:
- Ordered pairs: (0, 50), (1, 65), (2, 80), and (3, 95).
- Domain: {0, 1, 2, 3} stages.
- Range: {50, 65, 80, 95} coins.
- Y-intercept: (0, 50), meaning the player starts with 50 coins.
- The x-intercept is not shown in the practical domain because a player cannot complete a negative number of stages. Algebraically, the x-intercept is approximately (-3.33, 0), but it is not meaningful in this Roblox situation.
- The function increases as stages completed increase.
You Do: Independent Roblox Challenge — 3 Minutes
A Roblox shop charges 25 coins for each special power-up. A player has 100 coins and spends 25 coins on each power-up.
Equation: y = 100 - 25x
Answer the questions below. The learner may use paper, a graphing tool, or a verbal explanation.
- Complete the table for x = 0, 1, 2, 3, 4.
- Plot the ordered pairs and connect them with a line segment.
- State the domain and range for this Roblox situation.
- Identify the x-intercept and explain its meaning.
- Identify the y-intercept and explain its meaning.
- Describe the end behavior as the number of power-ups purchased increases.
Answer check:
- Ordered pairs: (0, 100), (1, 75), (2, 50), (3, 25), and (4, 0).
- Domain: {0, 1, 2, 3, 4} power-ups, or 0 ≤ x ≤ 4 for the practical situation.
- Range: {100, 75, 50, 25, 0} coins.
- X-intercept: (4, 0), meaning the player has no coins left after buying 4 power-ups.
- Y-intercept: (0, 100), meaning the player starts with 100 coins before buying any power-ups.
- End behavior: As x increases, y decreases. The player’s coins go down as more power-ups are purchased.
Conclusion: Closure and Recap — 2 Minutes
Three-Sentence Recap
Have the learner complete these statements orally or in writing:
- “The domain is the set of __________, and the range is the set of __________.”
- “The y-intercept tells me __________, and the x-intercept tells me __________.”
- “End behavior describes what happens to __________ as __________ changes.”
Exit Ticket
For the function y = 5x + 20, answer:
- What is the y-intercept?
- What does it mean in a Roblox game where x is the number of completed levels and y is the player’s score?
- Is the function increasing or decreasing?
Expected answer: The y-intercept is (0, 20), meaning the player begins with a score of 20. The function is increasing because the score rises by 5 points for each completed level.
Assessment Plan
- Formative assessment: Bell-work responses, ordered-pair questioning, graphing checks, and guided-practice discussion.
- Summative assessment: Independent Roblox Challenge and exit ticket.
- Feedback: Give specific feedback such as, “Your domain correctly lists the inputs. Now label what those inputs represent in the game.”
Differentiation and Choice
Support for Learners Who Need More Scaffolding
- Provide a labeled coordinate plane with the axes already named.
- Use a vocabulary guide: domain = inputs, range = outputs, y-intercept = starting amount, x-intercept = amount when output reaches zero.
- Allow the learner to identify features from the table before graphing.
- Use only nonnegative values because they fit the Roblox context.
- Complete the first two independent questions together, then release the learner to finish.
Extension for Advanced Learners
- Create a Roblox coin function with a positive slope and another with a negative slope.
- Write an equation from a table and explain the meaning of the slope and y-intercept.
- Compare two power-up plans and determine which one leaves the player with more coins after 3 purchases.
- Explain why a mathematical x-intercept may not always make sense in a real-world context.
Choice of Final Product
The learner may demonstrate understanding by completing a graph, explaining the answer aloud, creating a short Roblox-style challenge card, or entering the equation into a digital graphing tool and labeling the key features.