Changes and Rates

Grade Level

8th Grade

Duration

30 minutes

Unit

Comparing Functions Effectively (Lesson 1 of 4)

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Common Core State Standards Alignment

• CCSS.MATH.CONTENT.8.F.A.3
  Interpret the equation ( y = mx + b ) as a linear function and compare properties of two functions each represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions).

• CCSS.MATH.PRACTICE.MP2
  Reason abstractly and quantitatively.

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Learning Objectives

By the end of this lesson, students will be able to:

• I can define rate of change in my own words.
• I can compare two functions to determine which changes faster using context clues and sentence frames.
• I can explain why one function changes faster than another using structured reasoning.

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Success Criteria

• I can identify which walking speed changes faster between two scenarios.
• I can use the sentence frame: “Function A changes faster than Function B because _______________.”
• I explain rate of change clearly with examples.

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Materials Needed

• Whiteboard and markers
• Printed visual aids (graphs showing walking speeds)
• Sentence frame handouts
• Scenario cards describing two characters walking at different speeds
• Dyslexia-friendly font worksheets & audio recording of instructions
• Timer or stopwatch

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Lesson Breakdown

1. Introduction and Hook (5 minutes)

• Begin by presenting two scenarios verbally:
  • “Tom walks 3 miles every hour.”
  • “Sara walks 5 miles every hour.”
• Ask: “Who is changing distance faster?”
• Show a quick graph sketch comparing the two distances over time.
• Define rate of change by connecting it to walking speed with simple language:
  Rate of change tells us how fast something is changing over time.

Strategy: Use a dyslexia-friendly font slide with key vocabulary highlighted. Provide audio support for the definition.

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2. Guided Practice: Comparing Rates (10 minutes)

• Present the two scenarios visually (side-by-side graphs and tables).
• Provide sentence frames on handouts:
  • “Function ______ changes faster because ______.”
• In pairs, students discuss which function changes faster using the sentence frame, with teacher circulating to support.
• Encourage use of numeric data (e.g., miles per hour) and visual cues (steeper lines on graphs).

Differentiation: For ELL students, display pictures of walking figures alongside graphs to support comprehension.

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3. Independent Practice: Sentence Frame Application (8 minutes)

• Individually, students write a short explanation using the sentence frame to compare new walking speed data on a worksheet.
• Example prompt:
  “Anna walks 4 miles every hour. Mike walks 6 miles every hour. Use the sentence frame to explain who changes faster.”
• The teacher provides dyslexia-friendly worksheets with plenty of spacing and a recorded prompt for auditory learners.

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4. Extension for Advanced Learners (Optional within independent practice)

• Challenge advanced students to create their own walking scenarios with different rates of change.
• They write a sentence using the sentence frame explaining which function changes faster.
• When done, these students can share their scenarios with the class or a partner.

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5. Closing and Formative Assessment (7 minutes)

• Invite several students to read their sentences aloud.
• Provide verbal feedback and reinforce the key vocabulary: rate of change, function, changes faster.
• Quick exit question: “In your own words, what does ‘changes faster’ mean?”
• Collect sentence frame handouts for review to assess understanding.

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Differentiation Strategies

• Visual aids (graphs, pictures) support conceptual understanding.
• Sentence frames scaffold language production for ELL and struggling writers.
• Dyslexia-friendly reading materials and audio instructions aid accessibility.
• Pairing and teacher-guided discussion reduce cognitive load.

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Extension Activities

• Students design their own function-based scenarios (e.g., biking speeds, pouring water rates) and compare rates.
• Use digital graphing tools (optional, if technology available) to visualize rates.
• Investigate non-linear rates of change for curious learners (prepare for future lessons).

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Teacher Reflection Prompts (Post-Lesson)

• Did all students meet the success criteria?
• Were sentence frames effective in helping students articulate comparisons?
• How well did the dyslexia-friendly supports aid learners?
• What adjustments are needed for the next lesson in this unit?

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This concise yet interactive lesson blends conceptual understanding, practical application, and language support while staying fully aligned with the Common Core standards. It sets a strong foundation for students to compare functions based on rate of change in engaging, student-centered ways.