Simplifying Algebraic Thinking

Overview

This lesson is designed for Year 10 students in accordance with the Australian Curriculum: Mathematics – Level 10 (ACMNA190). The focus is on developing fluency in simplifying algebraic expressions and substituting into these expressions to solve problems. This lesson uses collaborative activities, real-life applications, and differentiated strategies to ensure all learners engage meaningfully with the material. The teacher is encouraged to foster a supportive and dynamic classroom environment while challenging students to think critically.

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Learning Objectives

By the end of the lesson, students will:

1. Simplify algebraic expressions by combining like terms and applying the distributive property.
2. Substitute numerical values into algebraic expressions to solve problems.
3. Understand the real-life applications of algebra in problem-solving.

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Lesson Structure

Warm-Up Activity (10 minutes)

Objective: Activate prior knowledge to build confidence and map connections to the topic.

1. Problem of the Day (Written on the board as students enter):

   Simplify: 3x + 5 + 2x - 4  
   Evaluate when x = 2.
   

   • Students complete it independently while you mark attendance.
   • As a class, discuss the steps and solution, ensuring students understand key terms ("like terms," "simplify," "substitute").

2. Ask warm-up questions to probe real-life relevance:

   • "When might we need to simplify an expression in real life?"
   • "Can anyone guess a career that might require algebra skills?"
     (Steer the discussion toward engineering, coding, and personal budgeting.)

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Explicit Instruction (25 minutes)

Objective: Demonstrate techniques for simplifying expressions and substituting values.

1. Simplifying Expressions:

   • Write the following on the board:

     Simplify: 4a + 3b - 2a + 5 + b + 3  
     

   • Show step by step:
     • Identify like terms.
     • Combine coefficients of the same variable.
     • Simplify constants.
   • Emphasise common errors like forgetting to include the sign of a term.

2. Substitution into Expressions:

   • Example shown step by step:
     Expression: 2x + 3y - 5, with x = 2 and y = 4.
     • Replace variables with their values.
     • Calculate step-by-step, following the order of operations.
   • Reinforce the use of brackets when substituting negative numbers.

3. Provide a real-world example:
   *“You’re buying movie tickets for $15 per person and ordering snacks for $10. Write an expression for the total cost for ‘x’ people, then calculate the cost for 4 people.”

   Expression: 15x + 10.

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Collaborative Activity: Algebraic Bingo (15 minutes)

Objective: Make learning interactive and reinforce substitution concepts.

• Preparation: Create Bingo cards with simplified algebraic expressions in each square (e.g., 4a + 2b). Write corresponding substitution values (e.g., a = 2, b = 3) on slips of paper.
• How to Play:
  1. Call out substitution values (e.g., “a = 2, b = 3”).
  2. Students calculate the value of all expressions on their Bingo cards.
  3. If a student finds a match, they call out “Bingo!” and explain the substitution process to win.

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Individual Practice (15 minutes)

Objective: Develop mastery through independent work with scaffolded support.

• Distribute a worksheet with three sections:
  1. Simplify basic expressions (e.g., 5x + 3 - 2x + 7).
  2. Substitution problems (e.g., Evaluate 4a + 2b when a = 3, b = -1).
  3. Real-world application:
     “You are designing a new garden. Write an expression for the total perimeter when the width is ‘w’ metres, and the length is 2w + 3 metres. Then calculate when w = 5.”
• Circulate to provide one-on-one help as required.

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Reflection and Exit Ticket (9 minutes)

1. Class discussion (4 minutes):

   • Ask students to share one thing they learned and one question they have.
   • Prompt them with discussion questions:
     • “How can simplifying expressions help you solve problems faster?”
     • “What was the trickiest part of today’s lesson?”

2. Exit Ticket (5 minutes): On a slip of paper, students answer:

   Simplify: 6c - 2 + 3c + 5  
   Evaluate when c = 3.
   

   Give them additional substitution problems if they finish early.

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Differentiation

1. For struggling students:

   • Pair them with a “study buddy” during practice activities.
   • Provide simpler examples with immediate feedback.

2. For advanced students:

   • Challenge them with problems that involve fractions or negative coefficients.
     Example: Simplify 3a - 5 + 4b - 2/3a + 7 when a = -3 and b = 2.

3. For visual learners: Use colour-coded examples (e.g., highlighting terms, constants, and operations).

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Assessment

1. Ongoing formative assessment through observation during activities.
2. Review exit ticket responses to gauge understanding and identify topics for follow-up.

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Resources Needed

• Whiteboard and markers.
• Algebra Bingo cards.
• Pre-prepared worksheets.
• Slips of paper for Exit Tickets.
• Calculator (optional, for substitution).

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Homework

Assign the following question:
“The angles in a triangle are represented by x, 2x - 10, and 3x + 20. Write and simplify an equation to find the value of x. Then determine the angles.”

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Teacher’s Reflection Post-Lesson

• Did students effectively understand simplification and substitution?
• Were students engaged with the collaborative and hands-on activities?
• What can be improved for next time?