Algebraic Expressions

Inline Questions
Learning Objectives:
By the end of the unit, students will be able to:

  1. Understand the concept of variables, constants, coefficients, and terms.
  2. Identify and write algebraic expressions.
  3. Simplify algebraic expressions using addition and subtraction of like terms.
  4. Apply algebraic expressions in real-life word problems.
  5. Translate verbal statements into algebraic expressions.
  6. Develop confidence in discussing mathematical ideas in English.

Materials Required:

  • Whiteboard and markers
  • Flashcards with algebraic terms (variable, coefficient, constant, term)
  • Worksheets for practice
  • Charts with algebraic expressions examples
  • Manipulatives (tokens, cubes, or counters)
  • Laptops/tablets (optional) for interactive games
  • Visual aids for ESL students (color-coded expressions)

Teaching Strategies:

  • Visual Learning: Use color-coding for terms, coefficients, constants.
  • Scaffolding: Start with simple examples, gradually increase complexity.
  • Interactive Learning: Pair and group activities to encourage discussion.
  • ESL Support: Simplify language, repeat key vocabulary, provide sentence frames.
  • Formative Assessment: Inline questioning and quick exercises.

Week 1: Introduction and Identification of Algebraic Expressions

Day 1: Introduction to Algebra

Objective: Students understand the concept of variables, constants, and coefficients.
Activities:

  1. Begin with real-life examples (e.g., "I have 3 pens and x pencils").
  2. Introduce terms:
    • Variable (x, y, z)
    • Constant (numbers like 3, 5, 10)
    • Coefficient (number before variable, e.g., 3x)
  3. Show visual examples on the board with colors:
    • 3x + 5 → 3 (coefficient, blue), x (variable, red), 5 (constant, green)
  4. Inline Questions:
    • “What is the variable in 7y + 4?”
    • “Which part is the constant in 5x + 9?”
  5. Practice: Students underline terms in examples provided.

Homework: Write 5 expressions using numbers and variables from daily life.

Day 2: Terms and Types of Expressions

Objective: Identify different types of algebraic expressions (monomial, binomial, trinomial).
Activities:

  1. Explain monomial (1 term), binomial (2 terms), trinomial (3 terms).
  2. Use colored cards to represent each term and classify expressions.
  3. Group Activity: Students sort a list of expressions into monomial, binomial, trinomial.
  4. Inline Questions:
    • “Is 3x a monomial or binomial?”
    • “How many terms are in 5x + 7y + 2?”
  5. Quick Quiz: Show 5 expressions, students classify individually.

Homework: Write 3 expressions for each type and label terms.

Day 3: Simplifying Expressions (Introduction)

Objective: Simplify algebraic expressions using addition of like terms.
Activities:

  1. Introduce like terms: same variable with same power.
  2. Example: 3x + 5x = 8x
  3. Hands-on: Give students tokens representing variables and constants, combine like terms physically.
  4. Inline Questions:
    • “Can we combine 3x + 4y? Why or why not?”
    • “Simplify 2a + 5a + 3.”
  5. Group Activity: Simplify given expressions on the board together.

Homework: Simplify 5 expressions from the textbook.

Day 4: Simplifying Expressions (Subtraction)

Objective: Subtract like terms in algebraic expressions.
Activities:

  1. Explain subtraction of like terms with examples: 7x – 3x = 4x
  2. Practice problems: color-code terms to visually separate them.
  3. Pair Activity: Give a worksheet to simplify expressions with addition and subtraction.
  4. Inline Questions:
    • “What happens if we subtract 5y – 7y?”
    • “Simplify: 8a + 2b – 3a – b”
  5. Homework: Simplify 6 expressions using addition and subtraction of like terms.

Day 5: Translating Verbal Statements into Expressions

Objective: Convert word problems into algebraic expressions.
Activities:

  1. Model examples: “I have 5 more than x apples → x + 5”
  2. Provide structured sentence frames:
    • “___ more than ___” → “x + y”
    • “___ less than ___” → “x – y”
  3. Pair Activity: Students translate given sentences into expressions.
  4. Inline Questions:
    • “How would you write ‘three times a number decreased by 4’?”
    • “Translate ‘the sum of a number and 7’ into an expression.”
  5. Homework: Create 5 word statements and write algebraic expressions.

Week 2: Advanced Practice and Application

Day 6: Evaluating Expressions

Objective: Evaluate expressions for given values of variables.
Activities:

  1. Explain evaluation: replace variable with number and calculate.
  2. Example: If x = 3, evaluate 2x + 5 → 2×3 + 5 = 11
  3. Practice on board and in pairs.
  4. Inline Questions:
    • “If y = 4, what is 3y + 7?”
    • “Evaluate 5a – 2b for a = 2, b = 3.”
  5. Homework: Evaluate 5–6 expressions using given values.

Day 7: Word Problems

Objective: Apply algebraic expressions in solving word problems.
Activities:

  1. Model problem: “A shop sells x chocolates a day. How many in 5 days?” → 5x
  2. Students work in groups to create expressions from short word problems.
  3. Inline Questions:
    • “Translate this into an expression: A train travels y km per hour for 3 hours.”
    • “If I buy x pens and 2 pencils each, how to write it as expression?”
  4. Homework: Solve 5 word problems from the textbook.

Day 8: Combining Like Terms (Advanced)

Objective: Handle complex expressions with multiple variables.
Activities:

  1. Examples: 2x + 3y + 5x – 2y → combine like terms → 7x + y
  2. Guided practice in pairs using worksheets.
  3. Inline Questions:
    • “Simplify: 4a + 3b – 2a + 5b – 6”
    • “Why can’t we combine 2x + 3y?”
  4. Homework: Simplify 6–7 multi-variable expressions.

Day 9: Quiz & Peer Learning

Objective: Assess students’ understanding; reinforce learning through discussion.
Activities:

  1. Mini Quiz: Identify terms, simplify expressions, translate word problems.
  2. Peer teaching: Students explain solutions to each other.
  3. Inline Feedback: Teacher addresses misconceptions.
  4. Homework: Revise all expressions learned; prepare 3 self-created expressions.

Day 10: Real-Life Application & Project

Objective: Apply algebraic expressions in real-life scenarios.
Activities:

  1. Project Work: Students create a mini poster or presentation using 3–4 algebraic expressions from real life (shopping, money, school items).
  2. Discuss in class: “How algebraic expressions help us in daily life.”
  3. Inline Questions:
    • “How would you write your daily allowance as an algebraic expression?”
    • “Can we use expressions to calculate distance or cost? Give example.”
  4. Assessment: Evaluate project creativity and correctness of expressions.

Assessment & Evaluation:

  • Formative: Inline questioning, class participation, worksheets.
  • Summative:
    • Mini quiz (Day 9)
    • Final project (Day 10)
  • ESL Support: Evaluate both understanding of math concepts and ability to explain in English.

Differentiation & ESL Support:

  • Use visual aids and manipulatives for concrete understanding.
  • Color-coded expressions to differentiate terms.
  • Sentence frames to help students explain reasoning.
  • Pair strong and weak students for peer support.