Date: February 10, 2026

Class Duration: 90 minutes
Class Size: 35 students
Grade Level: Algebra 1
Curriculum: International Baccalaureate (IB) Middle Years Programme (MYP) Mathematics Year 3/4

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Unit Context within IB MYP Framework

This lesson aligns with MYP Mathematics Criterion B: Investigating Patterns and Criterion C: Communicating. It fosters student inquiry and communication through polynomial operations, underpinning algebraic fluency essential for further mathematical reasoning and real-world applications.

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Learning Objectives

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

• Add and subtract polynomials with confidence and accuracy. (MYP Criterion B: Apply mathematical methods to investigate patterns)
• Substitute numerical values into polynomial expressions and evaluate them correctly. (MYP Criterion B)
• Multiply polynomials using distributive property and binomial expansion techniques. (MYP Criterion B & C)
• Explain their steps clearly and reflect on the accuracy of their work. (MYP Criterion C: Construct mathematical arguments)

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Key Concept & Related Concepts

• Key Concept: Relationships
• Related Concepts: Patterns, Models

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Statement of Inquiry

Understanding polynomial operations reveals patterns and relationships that model real-world phenomena.

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Essential Question

How do we use polynomial operations to simplify and evaluate expressions correctly?

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Class Agenda

Time	Activity	Description
5 min	Bell Ringer	Simplify combined polynomials to activate prior knowledge and set purpose.
10 min	Mini Review	Teacher-led focused review of adding, substituting, and multiplying polynomials.
10 min	Guided Practice	Collaborative problem-solving with immediate feedback.
15 min	Desmos Activity	Interactive polynomial operations review using Desmos platform to foster inquiry and visual learning.
40 min	Collaborative Stations	Station rotations involving differentiated tasks elucidating addition, substitution, and multiplication of polynomials; promotes peer learning.
5 min	Exit Ticket	Formative assessment to check knowledge acquisition and readiness for next lesson.

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Detailed Lesson Breakdown

1. Bell Ringer (5 minutes)

• Prompt: Simplify the expression below by combining like terms:
  ( 3x^2 + 5x - 2 + 4x^2 - 3x + 6 )
• Purpose: Stimulate recall of polynomial terminology and basic operations.
• Student Engagement: Individual written response on whiteboards, volunteers share solutions.
• IB Link: Activates prior knowledge, fostering inquiry linked to the key concept "Relationships."

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2. Mini Review (10 minutes)

• Focus Areas:
  • Adding polynomials (combine like terms, sum coefficients)
  • Substituting values into polynomial expressions (evaluate with correct order of operations)
  • Multiplying polynomials (distributive property, FOIL method for binomials)
• Teaching Strategies:
  • Use clear, stepwise example problems projected on board.
  • Highlight common pitfalls (e.g., forgetting to multiply every term).
  • Connect algebraic operations to real-life situations (e.g., area of composite rectangles).
• IB Link: Integrates Criterion B by practicing mathematical methods with symbolic expressions.

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3. Guided Practice (10 minutes)

• Format: Through teacher-led examples modeled on the whiteboard, students solve problems alongside.
• Examples:
  1. Add ( (2x^2 + 3x + 1) + (4x^2 - x + 7) )
  2. Substitute ( x = 2 ) into ( 3x^2 - 5x + 4 )
  3. Multiply ( (x + 3)(2x - 5) )
• Feedback: Immediate verbal and written feedback on student responses; encourage step explanation aloud.
• IB Link: Supports Criterion C by fostering clear communication of mathematical reasoning.

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4. Desmos Activity (15 minutes)

• Objective: Reinforce polynomial operations through interactive graphing and manipulation.
• Activity Outline:
  • Students access a teacher-created polynomial operations Desmos activity tailored to scaffold inquiry:
    • Add/subtract polynomials and graph results
    • Substitute values and observe corresponding points on the graph
    • Multiply binomials and visualize resulting polynomial curves
  • Use real-time classroom display for group predictions and discussions.
• Benefits:
  • Links algebraic and graphical representations (MYP Criterion A: Knowing and Understanding).
  • Engages digital literacy aligned with MYP global contexts (Scientific and Technical Innovation).
• Classroom Management: Students work in pairs to encourage collaboration. Circulate for formative assessment.

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5. Collaborative Stations (40 minutes)

Divide students into 5 groups of 7, rotating through stations every 8 minutes:

Station	Task Focus	Description	IB Links
1	Adding Polynomials	Students simplify complex polynomial sums (some with three or more terms).	Apply Criterion B, practical task.
2	Substitution Challenge	Given different polynomials, students evaluate expressions at various values, then check answers via calculators/Desmos.	Promote Criterion C communication and accuracy.
3	Multiplying Binomials	Use algebra tiles and visual models to represent binomial multiplication.	Visual spatial reasoning, Criterion A exploration.
4	Word Problems	Solve real-life polynomial problems involving area, revenue, or motion. Students write out steps and reasoning.	MYP global context Connects math to real scenario.
5	Self-Reflection & Peer Review	Review own and peers’ solutions for correctness and clarity, provide constructive feedback.	Criterion C: Communicating, metacognition, and reflection.

• Teacher Role: Facilitate, support diverse learners, and prompt deeper thinking with scaffolded questions.
• Materials: Pre-printed task sheets, algebra tiles, calculators, Desmos open on tablets/laptops.

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6. Exit Ticket (5 minutes)

• Prompt:
  1. Add the polynomials ( (5x^2 - 2x + 3) + (3x^2 + 4x -1) ).
  2. Substitute ( x = -1 ) into ( 2x^2 - 3x + 5 ).
  3. Multiply binomials ( (x + 2)(x - 4) ).
• Format: Students complete on small cards, submit before leaving.
• Purpose: Quick formative check aligned with today's goals to inform next lesson’s pacing and support.
• IB Connection: Reinforces Criterion B & C; reflection on learning progress.

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Assessment & Feedback

Type	Description	IB Criterion Alignment
Formative: Bell Ringer	Evaluate prior knowledge and readiness.	Criterion B
Formative: Guided Practice	Monitor understanding and provide corrective feedback.	Criterion C
Formative: Desmos & Stations	Ongoing assessment through interactive tasks and observation.	Criterion A & B
Summative: Exit Ticket	Assess key skill mastery for addition, substitution, multiplication.	Criterion B & C

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Differentiation & Inclusion

• Support for struggling learners:

  • Use of algebra tiles at Station 3 for tactile understanding.
  • Step-by-step scaffolding and peer support during stations.
  • Visual aids during mini review and guided practice.

• Challenge for advanced learners:

  • Extension problems incorporating polynomial division or factoring offered at Stations 1 and 4.
  • Encourage explanation of reasoning aloud and peer teaching during Station 5 reflection.

• Language learners:

  • Vocabulary cards with polynomial terms and operations provided.
  • Sentence stems suggested for explaining steps (e.g., "First, I combine the like terms...").

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Resources Needed

• Whiteboards & markers for bell ringer and guided practice
• Projector or interactive board for mini review and Desmos activity
• Laptops/tablets with internet access for Desmos activity
• Algebra tiles (enough sets per group)
• Printed station task cards and reflection sheets
• Calculators

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Reflection & Connection to IB Philosophy

This lesson encourages inquiry-based learning, communication skills, and reflection aligned with the IB learner profile – fostering knowledge, principled reasoning, and open-mindedness. By using interactive technology alongside hands-on materials and peer collaboration, students experience a balanced, student-centered mathematical inquiry that highlights the interconnectedness of concepts and real-world applications.

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Teacher Notes

• Prepare Desmos activity in advance, ensure all student devices are charged and connected.
• Monitor time vigilantly to allow meaningful engagement at each station.
• Collect exit tickets promptly and review to identify individual and class-wide misconceptions.
• Encourage student verbalization of mathematical reasoning to deepen understanding.

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This detailed, IB-aligned plan will not only engage students in mastering polynomial operations but also develop their communication, critical thinking, and real-world application skills, embodying the holistic approach of the MYP Mathematics curriculum.