Patterns of Change and Algebraic Reasoning · Term 1

Solving Linear Inequalities

Solving linear inequalities and representing their solutions on a number line.

Key Questions

  1. Explain why the inequality sign flips when multiplying or dividing by a negative number.
  2. Differentiate between a strict inequality and one that includes the boundary value.
  3. Construct a real-world problem that can be modeled and solved using a linear inequality.

ACARA Content Descriptions

AC9M10A03
Year: Year 10
Subject: Mathematics
Unit: Patterns of Change and Algebraic Reasoning
Period: Term 1

Suggested Methodologies

Four Corners

Move to corners to defend your position

20–35 min

Learn more about Four Corners

Problem-Based Learning

Tackle open-ended problems without predetermined solutions

35–60 min

Learn more about Problem-Based Learning

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Review of Algebraic Foundations

Revisiting fundamental algebraic concepts including operations with variables and basic equation solving.

2 methodologies

Expanding Binomials and Trinomials

Applying the distributive law to expand products of binomials and trinomials, including perfect squares.

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Factorizing by Common Factors and Grouping

Identifying and extracting common factors from algebraic expressions and applying grouping techniques.

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Factorizing Quadratic Trinomials

Mastering techniques for factorizing quadratic expressions of the form ax^2 + bx + c.

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Difference of Two Squares and Perfect Squares

Recognizing and factorizing expressions using the difference of two squares and perfect square identities.

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