Algebra Checkpoints

Overview

In lesson 18 of the Year 9 Maths 2026 Plan, students consolidate algebraic problem-solving before the Tuesday class test and Thursday Common Assessment Task (CAT). They select and connect expressions, equations, tables and graphs, then verify solutions and explain what they mean in context.

Learning intentions

• WALT choose and use suitable algebraic representations for unfamiliar problems.
• WALT simplify, substitute and solve accurately.
• WALT identify patterns and represent relationships in tables and graphs.
• WALT communicate, justify and check mathematical reasoning.

Success criteria

• I can decide whether an expression, equation, table or graph is the most useful representation.
• I can simplify, substitute and solve, showing logically ordered steps.
• I can check an answer and explain whether it makes sense in the original context.
• I can describe a pattern or relationship and justify my conclusion using mathematical evidence.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: problem-solving topics are connected to relevant textbook learning.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: extension through unfamiliar, non-routine problems.
• Mathematical competencies: using representations, reasoning, communicating ideas, and selecting tools strategically.

Lesson structure (60 minutes)

1. 0–5 min · Hook and retrieval. Open with the algebra checkpoint introduction slides and display: “A taxi fare is $4 plus $2 per kilometre. What does the expression (4+2k) tell us, and how could we check it?” Students complete a silent think, then explain one interpretation to a partner.

2. 5–12 min · Model strategy selection. Teacher models a short unfamiliar problem, thinking aloud through: understand the context, choose a representation, solve, check and interpret. Students annotate the algebra problem-solving checkpoint worksheet and identify where an expression, equation, table or graph could be useful.

3. 12–37 min · Mixed problem-solving stations. Set up five groups of five; each group spends five minutes at each station, using the worksheet and the task prompts on the station instruction and timer slides. Students solve and record reasoning at:

• simplification and collecting like terms;
• substitution into formulae and expressions;
• forming and solving linear equations;
• continuing patterns and generalising the rule;
• creating or interpreting tables and graphs. Teacher circulates, questions strategy choice, and records misconceptions for the review.

4. 37–47 min · Review misconceptions. Teacher presents two or three anonymous errors from the stations, such as treating (3(x+2)) as (3x+2), reversing an inequality of meaning in a context, or plotting an incorrect scale. Students use mini-whiteboards to correct each error, explain why it occurred, and state a checking method.

5. 47–56 min · Checkpoint rehearsal. Students complete one integrated problem independently: generalise a context, form an equation, solve it, represent selected values in a table or graph, and justify the conclusion. They use the solution-planning prompts on the independent checkpoint problem. Students must include a substitution check and one sentence explaining the solution in context.

6. 56–60 min · Reflection and next steps. Display the reflection prompts on the plenary and reflection slides. Students write: “The representation I chose was… because…”, “My checking method was…”, and “Before the test/CAT I need to practise…”. Collect the worksheet for targeted feedback and corrections.

Resources

• the algebra checkpoint introduction slides
• the algebra problem-solving checkpoint worksheet
• Five station task cards or projected station prompts
• Mini-whiteboards and pens
• Graph paper
• Calculators
• Formula sheet
• Timer
• Test and CAT papers, rubric and marking schedule for teacher preparation

Assessment

• Question students during stations: “Why did you choose that representation?”, “How do you know your answer is reasonable?” and “Can you verify it another way?”
• Use mini-whiteboard responses to identify misconceptions in simplification, substitution, equations, patterns, tables and graphs.
• Mark the integrated problem using the CAT emphasis: representation 25%, algebraic accuracy 30%, generalisation/problem solving 30%, and communication 15%. Provide individual feedback and require corrections. The Tuesday test should be approximately 25 marks, balancing procedural fluency and reasoning; the Thursday CAT should be approximately 30 marks.

Differentiation

• Support students with tiered station questions, worked examples, colour-coded like terms, a vocabulary bank for expression, equation, variable, coefficient, relationship and gradient, and a structured “understand–represent–solve–check–interpret” planner.
• Offer dyslexia-friendly reading options: clear sans-serif font, uncluttered pages, short instructions, generous spacing, symbols alongside key words, and the option to have questions read aloud or displayed one at a time.
• Pair students strategically and allow oral rehearsal before written explanations. Provide graph paper, pre-labelled axes or a partially completed table where appropriate.
• Extend advanced learners with problems requiring two different representations or methods, evaluation of assumptions and constraints, comparison of solution efficiency, or explanation of when a model may not apply.