Algebra Review Basics

Overview

Lesson 2 revisits core algebra skills needed for linear and simple non-linear relationships: simplifying expressions, transposing to solve equations, and evaluating using substitution (with calculator support). Students complete initial textbook exercises to consolidate routines from Lesson 1.

Learning intentions

• Students will simplify algebraic expressions by combining like terms and using basic index rules.
• Students will solve linear equations by transposing (maintaining balance) and checking solutions.
• Students will substitute numerical values into algebraic expressions and evaluate correctly, using a calculator efficiently.
• Students will record working clearly to communicate steps and avoid common errors.

Success criteria

• I can simplify an expression by collecting like terms correctly.
• I can solve for a pronumeral in a linear equation and verify by substitution.
• I can substitute values into an expression and get the correct evaluated answer using calculator methods appropriately.
• I can show my algebra steps clearly enough that another student can follow and check them.

Curriculum links

• Algebra (Linear and non-linear relationships): find the value of a pronumeral in linear and simple non-linear equations given other pronumerals, using transposing where necessary.
• Algebra (Linear and non-linear relationships): substitute numerical values into linear and simple non-linear algebraic expressions and evaluate.
• QCAA General Mathematics Unit 1 / Topic 4: consolidating algebra skills that underpin later equation solving and function-style evaluation.
• Technology use: calculator-based evaluation to support accuracy and checking.

Lesson structure (60 minutes)

1. 0–5 min · Retrieval warm-up. Teacher writes three “quick start” items on the board: (a) simplify (3x+5x), (b) solve (x/3=4) (just the rearrangement idea), (c) evaluate (2a-1) when (a=5). Students do silent first attempts, then share answers with a partner and identify one likely mistake to avoid.

2. 5–15 min · Mini-teach: simplifying & transposing. Teacher models two worked examples:

• Simplify: (4(2x-3)+3x) showing distribution and collecting like terms.
• Solve: (5x-7=3x+9) showing transposing (subtract (3x) both sides, then add 7 both sides, then divide by 2). Students copy the method headings, then complete two “guided” follow-ups on their own: simplify (2(3y+1)-y) and solve (4( x-2)=2x+6).

3. 15–25 min · Calculator and substitution routine. Teacher demonstrates a substitution routine for accuracy:

• Write the expression clearly.
• Substitute values carefully with brackets.
• Evaluate in one clean calculator sequence (and estimate quickly to confirm reasonableness). Example: evaluate (3p^2-2p) for (p=-2), emphasising order of operations and brackets. Students complete: evaluate (a^2+4a) when (a=1), and evaluate (b^2-9) when (b=3). Students check by quick mental reasoning (e.g., “if (b=3), then (b^2-9=0)”).

4. 25–40 min · Textbook: initial exercises (teacher-led pacing). Students work through the first set of textbook questions (chosen by the teacher) covering all three types:

• simplifying expressions (collect like terms),
• solving linear equations (transposing),
• substituting and evaluating (including at least one with a negative value and one requiring brackets). Teacher circulates with a focus checklist: correct algebra steps, correct sign handling, and checking solutions by substitution where appropriate. Students must show at least one line of working, not just answers.

5. 40–52 min · Error correction and short conferencing. Teacher selects 3 common errors from student work (e.g., incorrect distribution, sign error when transposing, forgetting brackets on substitution). Teacher rewrites the correct method on the board and asks targeted questions: “What did we change when we transposed?” and “How do brackets affect your calculator entry?” Students correct their own work (or a peer’s worked solution) in a different colour/pen and write one brief rule to remember.

6. 52–60 min · Exit ticket (5 questions, mixed). Students complete a short exit ticket under time pressure:

• Simplify: (6x-2x+3).
• Solve: (7-2x=3x).
• Solve: (4(x+1)=2( x+5)).
• Substitute & evaluate: (2k^2-5k) for (k=2).
• Substitute & evaluate: (m^2+4m) for (m=-3). Teacher collects to identify misconceptions before Lesson 3.

Resources

• Textbook (Lesson 2 exercise set) with pencil, eraser, and spare paper
• Board/markers and projector/screen
• Calculator (student devices) plus calculator habits prompt card (brackets, order of operations)
• Worked example printouts (simplifying + transposing + substitution routine)
• Coloured pen/pencil for error corrections
• Exit ticket sheet (printed or prepared slide)

Assessment

• Formative checks during the mini-teach guided tasks (simplification and transposing steps).
• Teacher observation during textbook work: accuracy of signs, correct transposing process, and evidence of substitution checking.
• Exit ticket marking for: (1) simplification accuracy, (2) equation solution method and correctness, (3) correct calculator substitution with brackets, (4) ability to handle negatives.

Differentiation

• Support: provide sentence starters for working (“First I expand…, then I collect like terms…”, “To transpose, I subtract/add … to both sides…”). Allow students to use a “bracket reminder” when entering expressions into the calculator.
• Support: for students needing it, offer a partially completed example worksheet for one equation and one substitution question.
• Extension: for faster students, include an extra textbook question that requires simplifying first before solving (e.g., an equation where distribution and collecting like terms are necessary before transposing).
• EAL/SEN considerations: emphasise careful language for operations (add/subtract/divide both sides; meaning of “collect like terms”); check understanding of negatives and brackets through quick oral questions.