Algebra Showcase

Overview

In this final unit lesson, students independently demonstrate their algebra skills, then apply and communicate their thinking through a paired challenge. They consolidate prior learning by simplifying, substituting, checking and solving, before reflecting on progress and identifying a next step.

Learning intentions

• WALT demonstrate our understanding of algebra.
• WALT apply algebra skills to unfamiliar problems.
• WALT explain, compare and justify mathematical reasoning.
• WALT reflect on our progress and choose a next step.

Success criteria

• I can simplify expressions and substitute values correctly.
• I can check number sentences and solve one- and two-step equations.
• I can rearrange a formula and explain why my steps work.
• I can communicate my reasoning clearly and respectfully.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: applying relevant algebra knowledge in connected and challenging contexts.
• Mathematics and Statistics — Additional resources for advanced learners: reasoning, justification, flexible problem-solving and communication.
• Mathematical practices in the refreshed curriculum: represent, reason, communicate, connect and reflect.

Lesson structure (45 minutes)

1. 0–5 min · Welcome and learning focus. Display the opening challenge and learning intentions and pose: “Which algebra mistake could look convincing at first?” Briefly revisit the unit’s key skills and explain that today is a showcase of thinking, not just answers. Students discuss one skill they feel confident with and one they want to check.

2. 5–17 min · Individual mixed-skills check. Distribute the algebra showcase check and read each question aloud, allowing quiet processing time. Students independently simplify expressions, substitute values, check a number sentence, solve one- and two-step equations, and rearrange a simple formula; they show working or record spoken/visual reasoning as appropriate. Circulate and note strategies, misconceptions and students ready for extra challenge.

3. 17–20 min · Choose a pathway. Use the pathway instructions and success criteria to introduce three choices: Explain it—create a clear worked solution; Spot it—identify and correct an algebra error; or Stretch it—solve an open-ended problem in more than one way. Students choose a pathway, with teacher guidance to ensure an appropriate level of challenge.

4. 20–32 min · Paired application task. Pair students strategically and provide formula/reference cards where needed. Students select or receive a problem involving an expression, equation or formula, solve it, check the result, and prepare a short presentation using a poster, mini-whiteboard, annotated worksheet or oral explanation. Partners must agree on the reasoning, compare methods where possible, and practise explaining each step. Encourage MANA: Manaaki by supporting a partner, Aroha through respectful listening, Niwha through persistence, and Atamai through thoughtful problem-solving.

5. 32–40 min · Algebra showcase. Display the showcase prompts and audience response routine. Each pair presents for up to one minute, while the audience records one “数学 move” they noticed—such as a useful representation, efficient step or effective check—and one question or commendation. Invite presenters to explain how they know their answer is correct. Where time is limited, students can complete a gallery walk and leave spoken or written feedback.

6. 40–45 min · Reflection and next steps. Return to the reflection prompts. Students complete the final reflection on the worksheet: “At the start of the unit I…”, “Now I can…”, “A strategy that helps me is…”, and “My next algebra step is…”. Finish with a brief self- and peer-acknowledgement: each student names one example of MANA they demonstrated or noticed. Collect the worksheet and invite two or three students to share a useful insight.

Resources

• the Algebra Showcase slide deck
• the algebra showcase check
• Mini-whiteboards and pens
• A4 paper or small poster paper
• Pencils, rulers and highlighters
• Formula/reference cards
• Timer
• Optional devices for presenting or recording explanations

Assessment

• Confer with students during the individual check and application task, recording evidence of accuracy, strategy choice, checking and mathematical language.
• Use pair presentations and audience responses to assess whether students can communicate and justify reasoning, not merely state an answer.
• Use the completed reflection and mixed-skills check to identify individual strengths, misconceptions and next teaching steps.

Differentiation

• Read questions aloud, use an accessible uncluttered layout, enlarge text where required, and provide extra processing time.
• Offer formula/reference cards, worked-example prompts, vocabulary support and mini-whiteboards for students who benefit from rehearsal before writing.
• Accept written, spoken, diagrammatic or annotated visual reasoning where this provides a valid demonstration of understanding; scribe or record responses when appropriate.
• Pair students thoughtfully and allow students to choose a presentation format. Advanced learners complete the open-ended pathway, find multiple valid methods, and compare their efficiency, clarity and risk of error.