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Chapter 2 · Period 1 of 12 · 50 min

Building algebraic expressions from everyday scenarios

Introduction · Inductive

This unit opens the chapter's study of algebraic expressions, so orient students to the chapter's central move: translating a real situation into an expression. A common error here is confusing degree with the number of terms, or reading the coefficient of x^2 as the coefficient of x — watch for both in Q3. Example 4, p.19 in section 2.2 is a clean self-study read that previews the next idea.

0-10Open with the pens-and-pencils scenario (Example 1, p.16): write the purchase expression on the board and ask students to identify each part — what changes, what is fixed, what scales with quantity. Name the parts: variable, coefficient, constant, term.
10-22Work through Example 2, p.16-17 (garden fencing and seeding) and Example 3, p.17 (wire bent into rectangle). For each, have students first write their own expression before comparing with the book. Use the think-and-reflect prompt: ask students to compare the three expressions for similarities and differences — number of variables, whether a term has a product of two variables, highest power present.
22-35Introduce polynomial vocabulary: degree as the highest power of the variable in a univariate polynomial, and the naming convention (constant, linear, quadratic, cubic) by degree. Students classify each expression from the examples by degree individually, then compare answers with a neighbour.
35-50Students attempt Exercise Set 2.1 Q1 (p.18) and Q3 (p.18) in writing. Take responses on the board for Q1; for Q3, highlight the distinction between the coefficient of a specific power and the degree. Students who finish early attempt Q2 (p.18) as a self-study extension.

Homework

Exercise Set 2.1 Q4, p.19 and Q5, p.19 — identify the coefficient of z and the constant term in given cubic polynomials.

Assessment

Competency (C-3.2). Model and solve real-world situations using linear expressions and equations.

Learning outcome. Students can identify the degree, coefficients, and constant term of a given univariate polynomial and classify it as constant, linear, quadratic, or cubic.

Consider the polynomial 5x³ − 7x² + 3x − 4. Which of the following correctly states its degree, the coefficient of x², and its constant term?

  • A Degree 2; coefficient of x² is −7; constant term is −4
  • B Degree 3; coefficient of x² is 7; constant term is −4
  • C Degree 3; coefficient of x² is −7; constant term is 3
  • D Degree 3; coefficient of x² is −7; constant term is −4

D. Degree 3; coefficient of x² is −7; constant term is −4

What each wrong option reveals

  • A Reads degree as the highest power present among the non-leading terms (x²) rather than the leading term (x³), confusing the degree of a named term with the degree of the polynomial.
  • B Drops the negative sign from the coefficient of x², treating the coefficient as the absolute value of the numeric factor rather than the signed value.
  • C Reads the coefficient of x (the term 3x) as the constant term, confusing the last variable term with the term that has no variable.
Chapter 2 · 12 periods of 50 min

Also saved as 7 periods or 10 periods.

  • 2Defining and evaluating linear polynomials as input-output functions
    Linear Polynomials
  • 3Solving word problems using linear equations
    Linear Polynomials
  • 4Deriving linear expressions from growing patterns
    Exploring linear patterns
  • 5Extending linear patterns to multi-step modelling problems
    Exploring linear patterns
  • 6Modelling linear growth and linear decay with tables and expressions
    Linear growth and linear decay
  • 7Deriving the linear relationship y = ax + b from two data points
    Linear Relationships
  • 8Plotting a linear equation and identifying its line on the coordinate plane
    Visualising linear relationships
  • 9Comparing families of lines: slope and y-intercept on shared axes
    Visualising linear relationships
  • 10Consolidating the role of slope and y-intercept through graph construction
    Visualising linear relationships
  • 11End-of-chapter problem set: integrating modelling, patterns, and graphing
    Visualising linear relationships
  • 12Whole-chapter synthesis: from scenario to expression to graph
    Synthesis
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