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Grade Level:

Algebra 1 (Typical age range: 14-15 years)

Duration:

90 minutes

Class Size:

25 students

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IB MYP Key Concepts:

• Relationships
• Logic

IB MYP Related Concepts:

• Patterns
• Functions

IB Approaches to Learning (ATL) Skills:

• Thinking: Critical thinking, Problem solving, Transfer
• Communication: Exchanging thoughts, Ideas, and Information
• Self-management: Organization, Reflection

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Learning Objectives (TSWBAT - They Should Be Able To):

• Solve multi-step linear equations accurately and verify solutions. (A.REI.3)
• Determine whether a relation is a function from mappings, tables, graphs, and equations. (A1.FIF.1)
• Evaluate functions using function notation, including substitution and order of operations. (A1.FIF.2)
• Classify parent functions (linear, quadratic, absolute value, exponential) by graph and equation features. (A1.FIF.3)
• Distinguish between rational and irrational numbers, providing mathematical justification. (A1.NSR.1)
• Apply mathematical reasoning and problem-solving perseverance throughout activities. (MP1, MP2)

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Essential Questions

• How do I know if a relation is a function?
• How do I correctly evaluate a function?
• How can different functions be classified?
• What distinguishes rational numbers from irrational numbers?
• How does review strengthen my mathematical understanding?

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Materials and Resources

• Whiteboard and markers
• Student notebooks and graph paper
• Projector for modeling (functions, graphs)
• Spiral review worksheets (equations focused)
• Function notation worksheets
• Parent function matching activity cards (graphs, tables, equations)
• Rational vs. irrational number classification worksheet
• Exit tickets (one per student)
• Calculator (optional, for support)
• Reference to Radical and Polynomial Review concepts from file (e.g., perimeter and area context for applying functions)

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Lesson Structure and Timing

Time (min)	Segment	Activity Description	Purpose
10	Bellringer & Intro	Bellringers: Multiple short starters to activate prior knowledge and set context. - Solve two linear equations. - Identify if relations are functions (from mapping/table). - Evaluate f(x)=2x+3 at x=4. - Match graphs to parent functions. - Classify numbers as rational or irrational.	Engage students & activate prior knowledge across all key standards.
15	Direct Instruction: Linear Equations (I Do)	Model solving multi-step linear equations with detailed attention on inverse operations and checking solutions. Use problems linked to perimeter and area examples from the reference file (e.g., fence problem). Emphasize key IB concepts of perseverance and reasoning.	Demonstrate problem-solving procedures and verification for accuracy (MP1, MP2).
15	Guided Practice: Linear Equations (We Do)	Solve a mixed set of linear equations together on the whiteboard, encouraging students to identify and correct common mistakes (e.g., distribution errors, sign errors). Use think-pair-share to deepen reasoning about solution checking.	Build confidence, reinforce conceptual understanding, and collaborative reasoning.
10	Independent Practice: Linear Equations (You Do)	Distribute spiral review worksheets with progressively challenging linear equations. Students solve individually with teacher circulating to provide support.	Consolidate independent mastery of equation solving and solution checking.
10	Small Group: Linear Equation Reteach	Targeted reteach for students struggling with inverse operations and multi-step equation solving. Use hands-on manipulatives or digital algebra tiles if available for kinesthetic support.	Differentiate instruction to support all learners’ conceptual development.
5	Exit Ticket #1	Solve one linear equation and explain every step in writing. Collect to assess mastery and misconceptions.	Formative assessment to inform ongoing instruction.
10	Direct Instruction: Functions (I Do)	Review the precise IB definition of a function: one input maps to exactly one output. Use mapping diagrams, tables, and graphs. Model function evaluation using substitution with step-by-step guidance on order of operations.	Build foundational understanding of functions and function notation aligned with IB.
10	Guided Practice: Functions (We Do)	In pairs, classify relations as functions or not from a variety of representations; evaluate functions at given x-values together. Use think-aloud protocols to verbalize reasoning.	Encourage analytical and quantitative reasoning (MP2) with peer collaboration.
10	Independent Practice: Functions (You Do)	Function notation worksheet containing various problems—evaluating functions, function identification from equations/tables. Include problems with negative inputs and powers for richer understanding.	Deepen individual understanding of function evaluation and recognition.
10	Small Group: Parent Function Classification	Hands-on matching activity: students work in groups to match graphs, tables, and equations to parent function categories (linear, quadratic, absolute value, exponential). Emphasize features like shape, intercepts, domain, range. Use digital graphing calculators/demos if possible for engagement.	Enhance conceptual clarity of function types through active exploration.
5	Quick Check	Individually identify a parent function from a given graph and justify the reasoning in one or two sentences. Provide immediate verbal feedback.	Check conceptual understanding for IB criterion “communicating mathematical reasoning.”
10	Direct & Guided Instruction: Rational vs Irrational Numbers	Review definitions and properties of rational and irrational numbers using examples from the Radical and Polynomial Review and beyond (e.g., decimals, square roots). Classify various numbers as rational or irrational with justification.	Connect number system classification to prior learning; develop reasoning and justification skills.
5	Mastery Check Quiz	Short individual quiz on classification of rational/irrational numbers and function concepts.	Summative formative check aligned with standards and IB learner profile traits: reflective and knowledgeable.
5	Reflection and Closing	Whole class reflection: Students write or discuss the strongest concept they mastered today and one area they want to improve. Tie back to essential questions and IB attributes like persistence and being principled.	Promote metacognition and IB learner profile development.

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Differentiation and Inclusion Strategies

• Use visual aids (mapping diagrams, graphs, color-coded notes) and manipulatives where possible.
• Provide sentence starters for written explanations on exit tickets and quizzes.
• Offer calculator support only for checking work, not during initial computation, to promote conceptual understanding.
• Flexible grouping (pairs, small groups) to encourage peer support.
• Extra scaffolding for ELL (English Language Learners) and students with IEPs: glossaries of terms, chunking instructions, one-on-one check-ins.

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Assessment and Feedback

• Formative: Exit tickets, quick checks, spiral review answers monitored through observation and collected work.
• Summative/Formative: Mastery check quiz on rational/irrational numbers and function concepts.
• Ongoing: Teacher observation during group and partner work, taking note of questioning techniques to prompt deeper thinking.
• Peer and self-assessment encouraged during reflection phase to develop learner autonomy and IB attributes.

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Connection to IB MYP Criteria

• Criterion A (Knowing and Understanding): Accurately solving equations and classifying functions aid knowledge acquisition.
• Criterion B (Investigating Patterns): Evaluating functions and classifying parent functions foster pattern recognition and generalization.
• Criterion C (Communicating): Explaining reasoning on exit tickets and quizzes encourages clear mathematical communication.
• Criterion D (Applying Mathematics in Real-Life Contexts): Applying equations to the fence perimeter and area problem links learning to real-world contexts, a core IB emphasis.

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Teacher Reflection and Next Steps

• Evaluate exit ticket common errors to target reteaching in subsequent lessons.
• Use quiz data to identify students needing further support in rational vs irrational number concepts before moving into polynomial operations as per Radical and Polynomial Review file.
• Design follow-up lessons integrating function transformations and application problems, emphasizing IB learner profile traits such as inquirer and thinker.

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Additional Notes

• The integration of the Radical and Polynomial Review file’s context-based problems (perimeter and area fence exercises) enriches linear equations instruction with real-life applications, critical for IB’s concept-driven learning goals.
• Emphasize IB Approaches to Learning by encouraging students to articulate their thought processes, reflect on their learning, and set goals for mastery.

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End of Plan.