Rate of Change

Overview

Grade: 8
Time: 30 minutes
Class size: 9 students
Unit: Exploring Functions in Depth (Lesson 1 of 8)
Lesson Title: Understanding Rate of Change
Common Core Standard:

• CCSS.MATH.CONTENT.8.F.A.3
  Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

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Learning Objectives (I can statements)

• I can define the rate of change in a function.
• I can identify the rate of change from different types of representations (table, graph, verbal scenario).
• I can compare two functions and explain which one changes faster using a sentence frame.

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Success Criteria

• I can correctly find the rate of change from a table or graph.
• I can write a comparative sentence using:
  “Function A changes ___ times faster than Function B because ___.”
• I can express my reasoning clearly, supported by data from the given examples.

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Materials Needed

• Whiteboard and markers
• Pre-prepared function tables for two scenarios
• Graph paper and ruler for students
• Printed copies of sentence frames and dyslexia-friendly fonts (e.g., OpenDyslexic or Comic Sans)
• Visual aids (color-coded charts, arrows showing change)
• Timer or stopwatch (optional)

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Lesson Outline

1. Introduction (5 minutes)

• Activate Prior Knowledge: Ask students if they have ever noticed how fast or slow something changes — like the speed of a car or the filling of a water bottle.
• Explain: Introduce the concept of rate of change as “how fast one quantity changes compared to another.” Show a simple example: "If a car travels 60 miles in 1 hour, the rate of change is 60 miles per hour."
• Link to Functions: Explain that in math, rate of change helps us understand how quickly the y-values in a function change when x changes.

Dyslexia friendly tip: Use a clear font on the board with color highlights on key terms rate of change and function. Provide printed versions of key vocabulary with definitions.

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2. Guided Practice (12 minutes)

• Visual Example: Display two tables representing two real-world scenarios, e.g.,
  Function A: Water filling a tank over time

  Time (minutes)	Volume (liters)
  0	0
  1	3
  2	6

  Function B: Water filling a pool

  Time (minutes)	Volume (liters)
  0	0
  1	5
  2	10

• Task: Students compute the rate of change for both functions by calculating the change in volume divided by the change in time.

• Sentence Frame: Provide this prompt for students to compare the two:
  “Function ___ changes ___ times faster than Function ___ because ___.”

• Group Discussion: Let students share their answers and reasoning. Use visuals (e.g., arrows showing volume increase) to reinforce which function is faster.

• Differentiation: Students struggling may work with smaller numbers or use color-coded steps to calculate differences step-by-step.

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3. Independent Practice (8 minutes)

• Scenario Creation (Extension for advanced learners): Students create their own two real-world functions representing different rates of change (e.g., running speeds, filling different containers). They write a table of values and compare rates using the sentence frame.
• Simplified task (for diverse learners): Match pre-made pairs of functions with corresponding rate of change calculations and complete the sentence frame.

Dyslexia friendly tip: Allow students to write or type their sentences. Encourage the use of bullet points or drawings alongside text.

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4. Closing and Assessment (5 minutes)

• Exit Ticket: Students write one sentence aloud or on paper using the frame:
  “Function A changes ___ times faster than Function B because ___.”
• Review: Quickly discuss a few exit tickets to confirm understanding. Clarify misconceptions.
• Homework Suggestion: Observe two activities at home (e.g., cooking heating times, bike speeds) and describe which changes faster using the sentence frame.

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Differentiation

• Use visuals, step-by-step calculations, and sentence frames for structured support.
• Provide calculators for those struggling with arithmetic.
• Use color-coded notes and dyslexia-friendly fonts.
• Pair students strategically for peer support.

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Extension Activities

• Develop more complex comparisons involving negative or fractional rates of change.
• Investigate rate of change from graphs only (slope interpretation).
• Explore real data from sports, weather, or economics to compare functions.

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Reflection for Teachers

This lesson emphasizes conceptual understanding and language scaffolding to build mastery in rate of change. Encourage rich classroom conversation and real-life connections. Notice how students use the sentence frame to communicate math thinking clearly. Use formative assessment to inform pacing for upcoming lessons on deeper function properties.