Mullins High School

Teacher: Ms. Cindy Graves
Course: Algebra 1
Date: February 11, 2027
Duration: 90 minutes
Class Size: 35 students

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Standards Addressed

• SC 2025 Algebra 1:

  • A1.PAFR.2.4 – Add, subtract, and multiply polynomials and interpret results in context.
  • A1.MPS.AJ.1 – Justify algebraic procedures using properties of operations.
  • A1.MPS.PS.1 – Make sense of problems and persevere in solving them.

• International Baccalaureate MYP Mathematics Objectives:

  • Criterion B: Investigating Patterns – Students develop algebraic reasoning by exploring polynomial multiplication and extending understanding through pattern recognition.
  • Criterion C: Communicating – Justify algebraic steps through verbal and written explanations, demonstrating command of mathematical language and notation.
  • Criterion D: Applying Mathematics in Real-Life Contexts – Model polynomial multiplication through area models reflecting realistic contextual problems.

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Objective (I Can Statement)

Students will be able to:

• Multiply two binomials using the distributive property (FOIL method).
• Multiply a binomial by a trinomial.
• Simplify polynomial expressions by combining like terms.
• Justify procedural steps mathematically using properties of operations.
• Interpret polynomial expressions in context of real-world scenarios.

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Essential Questions

• How does the distributive property apply to polynomial multiplication?
• Why is combining like terms essential after multiplying polynomials?
• How can polynomial multiplication model real-world problems such as areas of composite shapes?

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Lesson Overview & IB Learner Profile Integration

Time	Activity	Description	IB Learner Profile Focus
5–7 mins	Bell Ringer Activation	Simplify expressions, identify polynomial degree. Activate prior knowledge and vocabulary.	Thinkers, Knowledgeable
15 mins	Mini Lesson – Direct Instruction	Demonstrate FOIL on binomials and distribute over trinomials with justifications.	Inquirers, Communicators
15 mins	Guided Practice – Whole Group	Collaborative practice using whiteboards/Desmos, peer discussion to reinforce concepts.	Collaborators, Risk-takers
20 mins	Desmos Interactive Activity	Engage with area models, expand polynomials, error analysis task through structured slides.	Balanced, Reflective
25 mins	Independent Practice	Structured worksheet: 3 binomial×binomial, 3 binomial×trinomial, 1 challenge problem.	Principled, Communicators
8 mins	Exit Ticket & Reflection	Multiply and simplify (3x+2)(x+5); explain the use of distributive property.	Open-minded, Reflective

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Detailed Lesson Plan

Bell Ringer (5–7 minutes)

Purpose: Activate prior knowledge of distributive property and polynomial terms; reinforce terminology and degree identification.

• Simplify:
  1. (3x(2x+5))
  2. (x(x+4))
• Identify the degree of: (4x^2 + 3x - 7)

Expected Student Outcome:

• Recall how to distribute coefficients and variables.
• Recognize highest exponent as degree.

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Mini Lesson: Direct Instruction (15 minutes)

Goals: Model multiplication of polynomials step-by-step and justify each step, embedding mathematical language.

1. Example 1: Multiply Binomials using FOIL:
   [ (x + 3)(x + 5) ]

• F: Multiply First terms: (x \cdot x = x^2)
• O: Multiply Outer terms: (x \cdot 5 = 5x)
• I: Multiply Inner terms: (3 \cdot x = 3x)
• L: Multiply Last terms: (3 \cdot 5 = 15)

Combine like terms:
[ x^2 + 8x + 15 ]

2. Example 2: Multiply Binomial × Trinomial:
   [ (x + 2)(x^2 + 3x + 4) ]

• Distribute each term in binomial:
  [ x(x^2 + 3x + 4) + 2(x^2 + 3x + 4) ]
• Multiply out:
  [ x^3 + 3x^2 + 4x + 2x^2 + 6x + 8 ]
• Combine like terms:
  [ x^3 + 5x^2 + 10x + 8 ]

Teacher Notes:

• Emphasize the distributive property as the foundational concept.
• Highlight reasoning when combining like terms.
• Use precise vocabulary: coefficient, term, degree, exponent, distribute, combine.

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Guided Practice: Whole Group (15 minutes)

Activity: Students work on whiteboards or Desmos app with Ms. Graves facilitating. Students solve:

1. ((x + 7)(x + 2))
2. ((2x + 3)(x + 4))
3. ((x - 1)(x^2 + 5x + 6))

Teacher Support:

• Circulate to prompt justification using properties of operations.
• Encourage students to verbalize and write each step.
• Correct misconceptions immediately, focusing on combining like terms.

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Technology Integration: Desmos Activity (20 minutes)

Purpose: Incorporate multiple representations and error-spotting to deepen comprehension.

Activity Flow:

• Slide 1: Visualize multiplying binomials using an area model. Students shade regions corresponding to terms.
• Slide 2: Expand algebraic expression from model, simplify.
• Slide 3: Match expanded polynomial form to the original factors (multiple choice).
• Slide 4: Error analysis - identify and correct mistakes in polynomial multiplication.

IB Connections:

• Supports Criterion B through pattern investigation.
• Develops Criterion C by encouraging communication of reasoning.
• Builds Criterion D by relating algebraic expressions to spatial visualizations.

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Independent Practice (25 minutes)

Students independently complete problems with increasing difficulty.

Worksheet:

1. Multiply and simplify three binomial × binomial expressions.
2. Multiply and simplify three binomial × trinomial expressions.
3. Challenge: Multiply two trinomials or binomial×trinomial with a leading coefficient ≠ 1.

Example Challenge:
[ (2x + 1)(x^2 + 4x + 5) ]

Teacher Role:

• Provide differentiated support:
  • Remediation — Use area model and color-coding of like terms.
  • Extension — Students create real-world area problems modeled by their multiplication.

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Exit Ticket & Reflection (8 minutes)

Exit Ticket:

• Multiply and simplify:
  [ (3x + 2)(x + 5) ]

• Short answer: What property did you use when multiplying polynomials?

Expected responses:

• [ 3x \cdot x + 3x \cdot 5 + 2 \cdot x + 2 \cdot 5 = 3x^2 + 15x + 2x + 10 = 3x^2 + 17x + 10 ]
• Property: Distributive Property

Formative Assessment:

• Collect exit tickets for mastery check (goal ≥ 80%).
• Use responses to inform next lesson emphasis.

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Differentiation Strategies

Learner Support	Method
Remediation	Use the area model (box method) physically or digitally; provide color-coded worksheets highlighting terms to combine. Use stepwise question prompts to guide through FOIL.
Advanced Learners	Multiply two trinomials; challenge to compose a real-world problem solved by polynomial multiplication and justify solution steps in writing.

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IB Approaches to Learning (ATL) Skills Targeted

• Thinking Skills: Analyze polynomial structures and combine like terms correctly.
• Communication Skills: Justify each mathematical step verbally and in written form.
• Self-Management: Persevere through multi-step multiplication problems.
• Social Skills: Collaborate during guided practice and Desmos tasks.

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Reflection & Next Steps

• Collect student work to identify common errors.
• Plan for reinforcement on distributive property or introduce factoring polynomials next.
• Incorporate cross-disciplinary links for Math and Design Technology through area model projects.

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Ms. Graves actively models the IB learner profile traits throughout, encouraging curiosity, courage in mistake analysis, and precise communication—key to developing mathematically proficient and internationally minded students. This lesson plan not only meets state and IB standards but incorporates technology and real-world applications to inspire lasting understanding.