Overview

This 60-minute lesson for a class of 25 Grade 6 students focuses on evaluating algebraic expressions with whole numbers and decimal tenths. It follows the Ontario Curriculum expectations for Grade 6 Mathematics, specifically under the strand Number Sense and Algebra, addressing the learning goals related to algebraic expressions and variable evaluation. This is the second lesson in the 4-lesson unit titled "Mastering Variables and Expressions."

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Curriculum Connections

• Ontario Curriculum 2023, Grade 6 Mathematics
  Strand: Number Sense and Algebra
  Overall Expectation:

  • 3. Demonstrate an understanding of variables, expressions, and equations.

• Specific Expectations:

  • 3.1 Describe, represent, and explain the meaning of variables in expressions.
  • 3.3 Evaluate algebraic expressions for given values of variables, including whole numbers and decimals to tenths.

• Mathematical Process Expectations:

  • Reasoning and Proving: Develop and apply strategies for evaluating expressions.
  • Reflecting: Check and verify the answers for reasonableness.

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Learning Goals

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

1. Evaluate algebraic expressions involving whole numbers and decimal tenths by substituting values.
2. Simplify expressions step-by-step using order of operations.
3. Apply evaluating strategies to solve real-world problems.
4. Use guided notes to support systematic substitution and error checking.

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Materials Needed

• Whiteboard and markers
• Printable guided notes with evaluation tips
• Student math notebooks
• Calculators (optional but encouraged for decimal calculations)
• Expression cards with algebraic expressions (whole numbers and tenths)
• Real-world word problem worksheets
• Exit tickets with evaluation problems

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Lesson Outline

1. Introduction (10 minutes)

• Begin with a brief review of Lesson 1's content: identifying variables and expressions.
• Discuss the day's learning goals and explain the importance of correctly evaluating expressions in math and everyday situations.
• Model a simple algebraic expression evaluation on the whiteboard, showing substitution with whole numbers.

Teacher Script Example:
"Today, we're going to dive deeper into algebraic expressions by evaluating them when variables have specific values, including decimals. This skill builds your confidence and prepares you for many real-world math problems."

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2. Guided Notes and Strategy Teaching (15 minutes)

• Distribute guided notes comprising:

  • Steps for evaluating expressions (substitution, order of operations).
  • Tips:
    • Substitute values carefully and write intermediate steps.
    • Use parentheses to avoid mistakes with decimals.
    • Check calculations by re-evaluating or reverse reasoning.

• Work through 2-3 progressively challenging examples as a class, first with whole numbers, then decimals (e.g., Evaluate 3x + 4.5 when x = 2.3).

• Emphasize reasoning and systematic work to avoid common pitfalls.

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3. Collaborative Practice (15 minutes)

• Divide the class into small groups of 4-5 students.

• Provide expression cards and real-world worksheets where they substitute values and evaluate expressions covering whole numbers and decimal tenths.

• Encourage groups to explain their reasoning aloud, supporting Ontario’s focus on communication and mathematical argument.

• Circulate and provide targeted feedback, ensuring vocab like "variable," "coefficient," and "evaluate" are used correctly.

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4. Real-World Application (10 minutes)

• Present two real-world problems requiring evaluating expressions—such as calculating cost with taxes or distance with speed and time.

• Students complete problems independently, applying evaluation strategies, and show all steps on their guided notes.

Example:
"A taxi charges $3.50 plus $1.25 per kilometre. If you travel 4.2 km, evaluate the expression 3.50 + 1.25d where d = 4.2."

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5. Assessment & Reflection (10 minutes)

• Students complete an exit ticket with 3 expressions to evaluate (including decimal tenths).

• Prompt a quick reflection:

  • What step helped the most?
  • How do you check your work?

• Review answers briefly to address misconceptions.

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Differentiation Strategies

• For students needing extra support: Provide templates with step prompts or use manipulatives for substitution.
• For advanced learners: Challenge with expressions involving multiple variables or require evaluation of expressions inside parentheses first.
• Use of Technology: Encourage some students to use calculators for decimal computation to focus on substitution and strategy mastery.

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Assessment and Evaluation

• Formative assessment through guided practice participation, group discussions and exit ticket completion.
• Use exit ticket results to inform whether students need more practice with decimals or order of operations in expressions.
• Observe student explanations during group time to assess conceptual understanding and use of mathematical language per Ontario curriculum requirements.

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Teacher Reflection (Post-Lesson)

• Did students effectively use the guided notes and strategies?
• Were decimal substitutions a noticeable challenge?
• What real-world examples generated the most engagement?
• How can we integrate technology further to support understanding?
• Plan for adjusting lesson 3 based on observed student needs and misconceptions.

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Wow Factor Tips for Teachers

• Use colour-coded substitution sheets for decimals versus whole numbers to help visual learners.
• Incorporate real objects (e.g., money, measuring tapes) to “act out” expressions for kinesthetic learners.
• Create an “Expression Evaluation Wall” where students post tricky examples for peers to solve.

This lesson plan integrates Ontario's curriculum expectations with practical, engaging strategies to develop confident evaluation skills in algebraic expressions—a foundational step in mastering algebra for Grade 6 learners.