Streaming Growth Studio
Students model subscriber growth and determine whether scenarios represent functions and linear patterns.
Common Core standards covered
- 8.F.A.1Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
- 8.F.A.3Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
- 8.F.B.5Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Teacher-facing overview
Big idea: Define, evaluate, compare, and interpret functions.
Student target: “I can decide whether a relationship is a function, decide whether a function is linear, and describe or sketch how a quantity changes from the shape of its graph.”
Success criteria: I can state the function rule — each input has exactly one output — and use it to accept or reject a data set. · I can test a table for linearity by checking for a constant rate of change. · I can identify rate of change and initial value from a linear table and write y = mx + b. · I can sketch a graph from a verbal description, and tell a graph's story in words.
Essential question
A month number goes in, a subscriber count comes out. When is that a function — and when is it a lie waiting to crash your report?
Learning target: I can decide whether a relationship is a function, decide whether a function is linear, and describe or sketch how a quantity changes from the shape of its graph.
Success criteria
- I can state the function rule — each input has exactly one output — and use it to accept or reject a data set.
- I can test a table for linearity by checking for a constant rate of change.
- I can identify rate of change and initial value from a linear table and write y = mx + b.
- I can sketch a graph from a verbal description, and tell a graph's story in words.
Why this matters
The function rule is the quiet foundation of everything after Grade 8 — every formula, every graph, every spreadsheet column that computes from another. The linear test (constant differences) is the first honest tool for saying 'this trend is a line' versus 'this is something else', and story graphs train the skill every news reader needs: a graph is a sentence about change, not a picture of hills.
Students should already be able to
- Plot points and read coordinates.
- Slope as unit rate, and y = mx + b — Unit 3.
- Evaluate an expression for a given value.
Vocabulary to define explicitly
- Function
A rule assigning each input exactly ONE output.
Example: Each month has exactly one subscriber count: month 3 → 19 000.
Not an example: A log where month 2 shows both 16 000 and 21 000 is not a function — one input, two outputs.
🔒 3 more terms with examples and non-examples — Input and output, Linear function, Rate of change and initial value — are defined in the full lesson. See plans →
Where this shows up outside the classroom
Assessment plan
Formative — for feedback during the lesson
- The vending-machine asymmetry check in the warm-up.
- Audit tables during team work — the evidence column is the assessment.
- Story-graph gallery critiques: listen for slope-language, not scenery-language.
Summative — the graded evidence: The exit ticket (function decision, linearity with equation, story sketch), scored with the four-criterion rubric.
The task students work on
Your analytics team audits three streaming platforms before the quarterly report. StreamCo's table: month 0 → 10, 1 → 13, 2 → 16, 3 → 19 (thousands of subscribers). GoViral's: month 0 → 1, 1 → 2, 2 → 4, 3 → 8. And the Glitch file: a log where month 2 appears twice — once as 4 and once as 7. For each platform: is it a function? Is it linear? What equation or description honestly reports its growth?
Platform audit — complete a verdict per platform.
| Platform | Function? | Linear? | Evidence | Equation or description |
|---|---|---|---|---|
| StreamCo | ||||
| GoViral | ||||
| Glitch file |
Anticipated student strategies
Function first, then the linearity test, then the picture. Ending with plot-and-look ties the audit back to graphs just before the story-graph segment needs exactly that reading skill.
- Scan inputs for repeats. The student checks whether any input appears twice with different outputs — the Glitch file fails at month 2 and the audit stops there.
Share first: the function test comes before every other question, because the rest are meaningless without it.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
One button, one product, every time. A button that sometimes drops chips and sometimes soda is broken — not because the outputs are bad, but because the RULE broke. Name it: a function is a rule where each input gets exactly one output.
Listen for: No — two inputs may share an output. Only one input with two outputs breaks the rule.
Function? Each month appears once — yes. Linear? Differences 13−10, 16−13, 19−16: +3 every month — yes, and that constant IS the rate of change. Initial value: 10 at month 0. Equation: y = 3x + 10. Check month 3: 3(3) + 10 = 19 ✓.
- The difference column is the linearity test: constant differences (for equal input steps) means linear, period.
- Say the units every time: 3 thousand subscribers per month.
Listen for: Slope — the unit rate from the racing lesson. The difference column is slope wearing table clothes.
🔒 The remaining 4 steps — fully scripted with teacher-says lines, discourse questions, look-fors, and interventions — are in the full lesson. See plans →
Misconceptions and how to respond
- “Month 4 and month 7 both show 22 thousand — not a function!” Backwards: repeated OUTPUTS are fine. The rule breaks only when one INPUT has two outputs. Flat months happen.
- “Every growing table is linear.” — the teacher response is in the full lesson.
- “The initial value is the first row of the table.” — the teacher response is in the full lesson.
- “A graph without a formula isn't a function.” — the teacher response is in the full lesson.
- “The story graph should look like the thing in the story.” — the teacher response is in the full lesson.
🔒 Every misconception ships with a tested classroom response. See plans →
Scaffolded practice
The workbook follows gradual release rather than a page of blank prompts: 1 fully worked, 1 partially completed, then 3 independent.
- I doIs this log a function? Month 1 → 5, month 2 → 7, month 3 → 9, month 2 → 11.
🔒 4 more prompts across all three release tiers are in the full lesson. See plans →
Worked solutions and scaffolds for every prompt are in the downloadable kit, included with membership. See plans and pricing.
Exit ticket
- Is {(1, 5), (2, 7), (3, 9), (2, 11)} a function? One sentence of evidence.
🔒 2 more exit-ticket questions are in the full lesson. See plans →
Worked answers, the completed answer tables, and the scoring rubric are in the downloadable kit, included with membership. See plans and pricing.
Printable handouts in the kit
All handouts are in Printable_Handouts.pdf inside the kit download.
Materials and classroom resources
Student experience
Students enter through a low-floor prompt, build or sketch a model, test a strategy, revise their thinking, collaborate, and present a final solution. The task remains accessible while allowing for sophisticated reasoning.
Detailed facilitation notes
- Step 1: Review function notation and rate of change. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Analyze streaming-service growth scenarios. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Create graphs and compare patterns. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Produce a one-slide data story. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Use tables before equations; extend with nonlinear models.
Language support: “I started by…”, “My model shows…”, and “I know my answer is reasonable because…”.
Extension: Require a second solution, alter a condition, or have students write a challenge for another group.
Accessibility: Manipulatives, enlarged visuals, oral response choices, partner reading, and reduced-copy student pages.
Assessment plan
Formative checks: Strategy choice, accuracy, representation, collaboration, and explanation.
End evidence: Students interpret one function value and compare two rates.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.