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Grade Level

Algebra 1 (approximate age 14-15 years)

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Duration

90 minutes

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Class Size

30 students

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IB Curriculum Alignment

IB MYP Mathematics Objectives (MYP Year 4 - equivalent to Algebra 1 level)

• Criterion B: Investigating patterns
  • B2: Explain patterns using mathematical vocabulary and representations.
• Criterion C: Communicating
  • C1: Use appropriate mathematical language, notation, and terminology to communicate effectively.
• Criterion D: Applying mathematics in real-life contexts
  • D1: Select and apply mathematical problem-solving techniques and technologies appropriately.

Key Concept: Relationships
Related Concepts: Variables, Functions
Global Contexts: Scientific and technical innovation — Understanding how mathematical principles underpin real-world problems in science and technology.

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Learning Objectives

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

1. Calculate the slope between two points and interpret its meaning in a linear context.
2. Differentiate between linear and quadratic functions based on their algebraic expressions and graphs.
3. Identify and classify polynomial expressions (focus on addition, subtraction, and multiplication of polynomials).
4. Apply polynomial operations to solve problems and communicate their reasoning clearly.
5. Explain why a linear function has a constant rate of change and understand how quadratic functions differ graphically and algebraically.

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Materials Needed

• Whiteboard + markers
• Graph paper
• Scientific calculators/tablets (optional)
• Student notebooks
• Handout with bell ringer questions and polynomial practice problems
• Colored pencils for graphing
• Interactive polynomial manipulative (physical or digital) if available

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Lesson Breakdown

1. Bell Ringer – 10 minutes

Activity: Warm-Up Questions (from teacher’s provided instructions)

• Find the slope between (2, 4) and (6, 12)
• Identify linear or quadratic for given equations
• Choose TRUE statement about linear vs quadratic graphs

Method:

• Students answer individually in notebooks showing all work fully.
• Teacher circulates, providing formative feedback and noting common difficulties.

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2. Review and Discussion – 15 minutes

Objective: Solidify understanding of slope and functions from Bell Ringer, linking to IB learner profile attributes (Thinkers and Communicators).

• Teacher explains slope calculation:
  [ m = \frac{y_2 - y_1}{x_2 - x_1} ]
  Using (2, 4), (6, 12).
• Discuss constant rate of change as a defining property of linear functions.
• Contrast linear and quadratic functions:
  • Linear: degree 1, straight line, constant slope.
  • Quadratic: degree 2, parabolic curve, slope changes.

IB Inquiry Prompt:
“How does the way a function looks graphically relate to its algebraic form? Why do you think slope changes in quadratic functions?”

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3. Exploration of Polynomial Operations – 30 minutes

Objective: Students apply and practice adding, subtracting, and multiplying polynomials.

• Mini-Lecture (10 min):
  Review polynomial terminology (degree, terms, coefficients). Demonstrate:

  • Addition & Subtraction of polynomials
  • Multiplying polynomials (introduce distributive property and FOIL for binomials).

• Activity (20 min):
  Students work in pairs to solve targeted polynomial operation problems on handout that gradually increase in complexity (MYP Criterion B).

• Example Problem:
  [ (3x^2 + 2x - 5) + (x^2 - 4x + 7) ]
  and
  [ (x + 3)(2x - 1) ]

• Differentiation: Advanced pairs challenge themselves further with multiplying trinomials.

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4. Graphing and Interpretation – 15 minutes

Objective: Connect polynomial expressions to their graphs (IB Criterion C: communicating concepts through multiple representations).

• Students sketch graphs of given linear and quadratic functions from the Bell Ringer and polynomial activity.
• Use colored pencils to highlight key features: intercepts, vertex, slopes at various points.
• Use graph paper or graphing tools.

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5. Real-World Application and Reflection – 15 minutes

Objective: Apply polynomial operations and function concepts to real-life contexts (IB Criterion D).

• Present a STEM scenario where modeling with polynomials is necessary, e.g., calculating revenue or area functions.
• Students write a short paragraph explaining how polynomial operations help solve this problem.
• Share reflections aloud with class, promoting IB traits of communicators and reflective learners.

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6. Exit Ticket (Formative Assessment) – 5 minutes

Students Write:

• Define “slope” in their own words and give an example from today’s activities.
• State one difference between linear and quadratic functions.
• Solve a quick 2-term polynomial addition problem independently.

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Assessment and Feedback

• Formative:

  • Bell Ringer responses reviewed to identify misconceptions.
  • Observation during polynomial activity with timely questioning.
  • Graphing accuracy and explanations.
  • Exit Ticket to assess retention and understanding.

• Summative Suggestions (Post-Lesson):

  • Quizzes on polynomial operations and functions.
  • Project incorporating function modelling in real-world contexts.

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Differentiation and Inclusion

• Provide step-by-step scaffolding handouts for students needing extra support.
• Encourage peer tutoring within pairs for practice tasks.
• Use digital graphing tools to support visual/spatial learners.
• Challenge extension with higher-degree polynomial operations for gifted learners.

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Reflection and Teacher Notes

Encourage teachers to reflect on student engagement with polynomial operations and graphical interpretations, looking to embed more inquiry-based activities in future lessons. Consider integrating technology to allow students to explore dynamic graphs interactively.

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Summary

This 90-minute lesson blends IB philosophy with Algebra 1 core concepts exploring slope, function types, and polynomial operations. It fosters inquiry, communication, and application skills, ensuring students grasp both procedural fluency and conceptual understanding aligned with the IB framework.