Grade Level

11th Grade (Independent Learning)

Duration

30 minutes

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Unit Context

Unit: Algebra to Calculus Journey
Lesson: 6 of 6
Topic: Project Presentation: Analyzing Change Through Algebra and Beyond

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Common Core State Standards (CCSS) Alignment

• CCSS.MATH.CONTENT.HSF-BF.A.1
  Write a function that describes a relationship between two quantities.
• CCSS.MATH.CONTENT.HSF-IF.C.7
  Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
• CCSS.MATH.CONTENT.HSF-LE.A.1
  Distinguish between situations that can be modeled with linear functions and with exponential functions.
• CCSS.MATH.CONTENT.HSF-IF.C.8
  Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

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Learning Objectives ("I can" statements)

• I can clearly explain my algebraic model and its real-world application.
• I can connect algebraic concepts to the beginnings of calculus, understanding how rates of change reveal deeper insights.
• I can reflect on my learning journey from algebra through calculus.
• I can give and receive constructive feedback to improve mathematical understanding.

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Success Criteria

• Presentation includes a defined real-world problem modeled algebraically.
• Explanation of how the algebraic model relates to rates of change or derivative concepts.
• Clear reflection on personal learning progress and understanding.
• Active participation in peer feedback with thoughtful, respectful questions/comments.

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Materials Needed

• Student’s prepared project (written report, presentation slides, or digital media)
• Notebook or digital device for notes and reflections
• A quiet presentation space
• Optional: graphing calculator or graphing software

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Lesson Structure & Timing

Time	Activity Description
0-3 min	Introduction & Lesson Overview — Student reviews lesson goals and success criteria. Set a positive tone for self-directed presentation.
3-15 min	Student Presentation — Student presents their project, explaining the algebraic model and connecting to calculus concepts (e.g., rate of change, slope as derivative).
15-22 min	Reflection Discussion — Student reflects aloud or writes about: What was challenging? How did algebra prepare me for calculus? What did I learn about analyzing change?
22-28 min	Peer Feedback Simulation / Self-Assessment — Since this is independent learning, student simulates peer questions or uses a checklist to self-assess presentation clarity and content.
28-30 min	Wrap-Up and Next Steps — Student sets personal goals for further exploration or review.

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Detailed Activity Breakdown

1. Introduction & Lesson Overview (3 min)

• Student reviews the "I can" statements and success criteria.
• Reflect briefly on expectations for the presentation, emphasizing independent control and reflection.
• Teacher (mom) encourages confidence and openness during presentation.

2. Student Presentation (12 min)

• Present real-world phenomenon analyzed (e.g., population growth, velocity of an object, economics data).
• Show algebraic model: function definition, equation form, and graph (if relevant).
• Discuss relevance of slope, rate of change, and preview connection to derivatives.
• Highlight key results and interpretations.

3. Reflection Discussion (7 min)

• Student answers reflection prompts:
  • What inspired my choice of project?
  • How do algebra concepts help me understand continuous change better?
  • What connections do I see between algebraic functions and calculus?
  • What challenges did I overcome when modeling and analyzing data?

4. Peer Feedback Simulation / Self-Assessment (6 min)

• Student imagines two or three critique questions peers might ask, then responds.
• Or, uses a self-assessment checklist based on success criteria:
  • Did I explain my function clearly?
  • Did I connect algebra to calculus?
  • Was my reflection honest and insightful?

5. Wrap-Up & Goal Setting (2 min)

• Student writes or states next learning goal regarding algebraic or calculus concepts.
• Teacher provides positive reinforcement and suggests resources if needed.

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Differentiation Strategies

Learner Need	Strategy
Visual learner	Incorporate graphs, sketches, or digital slides in the presentation.
Struggles with public speaking	Practice presentation aloud beforehand; record and play back for self-improvement.
Needs enrichment	Explore more complex algebraic models or a deeper calculus connection (e.g., limits or instantaneous rates).
Needs support with reflection	Provide sentence starters or guided questions for reflection portion.
Preference for written over oral expression	Allow presentation in video or written report format, supplemented with a brief oral summary.

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Notes for the Parent/Teacher

• Since your daughter controls the lessons, encourage her to lead discussions and feedback processes.
• Promote metacognitive awareness by having her self-assess often and consider her mathematical growth.
• Use questioning to push deeper understanding during reflection, but keep it supportive.
• Celebrate this culminating presentation as a strong synthesis of the unit’s journey from algebra to calculus.

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End of Lesson Plan