Algebra Challenge Makers

Overview

In this ninth lesson of Algebra Detectives: Solve, Simplify, Share, students draw on earlier learning about sequences, expressions and equations to design a rigorous, multi-part algebra challenge. They will communicate reasoning, test whether others’ questions are valid, and revise their work using the class values of Manaaki, Aroha, Niwha and Atamai.

Learning intentions

• WALT communicate algebraic reasoning clearly.
• WALT create a valid multi-part challenge using at least two unit skills.
• WALT critique solutions respectfully and use feedback to improve mathematical thinking.
• WALT check that answers are valid by substituting, comparing or proving.

Success criteria

• I can create a clear, solvable challenge involving at least two algebra skills.
• I can provide a complete solution and explain my reasoning.
• I can give specific, useful feedback using Manaaki and Aroha.
• I can revise my challenge accurately and explain what I improved.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge questions with previously learned mathematical topics.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Mathematical communication, reasoning, problem solving and participation in collaborative learning are developed through creating, testing and defending solutions.

Lesson structure (45 minutes)

1. 0–5 min · Hook and revisit. Teacher opens with the provocative challenge hook and learning intentions and displays: “What makes an algebra problem clever rather than just difficult?” Students silently recall two skills from the unit, then share examples with a partner. Invite two or three responses and clarify that a strong challenge has clear information, a unique or explainable answer, and a way to check it.

2. 5–10 min · Unpack quality. Teacher models a short challenge such as: “The rule for a sequence is (3n+2). Find the 5th term, write the expression for the 10th term, and explain how you know.” Use the model challenge and success-criteria checklist to identify the skills, expected answer, reasoning and checking method. Students annotate the model orally or on the challenge blueprint and peer-feedback sheet, suggesting one feature that makes it effective.

3. 10–18 min · Research and plan. Teacher places students in three teams of three or pairs with one trio, and provides the sequence rule cards as a prompt for recalling sequence ideas. Revisit earlier unit work through books, notes or displayed examples, while conferencing with groups. Students choose at least two skills—such as finding a sequence rule, simplifying expressions, solving an equation, using an inequality or rearranging a formula—and complete the challenge blueprint: context, parts, difficulty, expected reasoning and checking method.

4. 18–28 min · Create and solve. Teacher directs teams to write a challenge card and a separate complete solution, checking that every part has enough information and that notation is accurate; use the design steps and equation bank for prompts. Students create an engaging presentation format, such as a detective case file, coded message, mini-poster or digital card, then solve their own challenge without skipping reasoning. Students who finish early add an inequality, rearranged formula or error-analysis question.

5. 28–36 min · Peer-test and revise. Teacher swaps challenges between teams and displays the respectful feedback protocol: “Notice…”, “Question…”, “Suggest…”. Students attempt another team’s challenge independently before discussing it. They record feedback on the challenge blueprint and peer-feedback sheet, identifying clarity, solvability, mathematical accuracy and one useful improvement. Teams return to their own work and revise in response, showing Niwha when a first version does not work.

6. 36–43 min · Gallery walk and share. Teacher displays the gallery-walk instructions and discussion prompts and assigns each team a presentation space. Students circulate, read at least two challenges and leave one specific Manaaki/Aroha comment or question at each; each team briefly presents its revised challenge and explains one design decision and one validity check.

7. 43–45 min · Exit reflection. Teacher returns to the WALT and asks students to complete the final reflection on the challenge blueprint and peer-feedback sheet: “One algebra idea I communicated well was…”, “Feedback changed my challenge by…”, and “I know my answer is valid because…”. Collect the sheets and invite one student to share an example of Atamai in action.

Resources

• the complete algebra challenge deck
• the challenge blueprint and peer-feedback sheet
• the sequence rule cards
• Unit books, worked examples and student notes
• A3 paper or card for challenge displays
• Coloured pens, pencils and sticky notes
• Mini-whiteboards and pens
• Timer
• Optional classroom devices for designing digital challenge cards

Assessment

• During planning, conference with each group: ask, “Which two skills are connected?”, “What makes the answer valid?” and “Could another answer fit?”
• Check peer-test evidence for mathematical accuracy, clarity, respectful feedback and meaningful revision.
• Use the exit reflection to assess students’ ability to communicate reasoning and identify a checking or proof strategy.

Differentiation

• Provide a challenge blueprint with sentence starters: “First find…”, “Then use this to…”, “To check, substitute…”. Offer the equation bank and a worked example without requiring students to copy it.
• Conference with groups needing support; reduce the number of parts while retaining two connected skills. Allow students to explain orally, visually, with manipulatives or in writing.
• Pair students strategically and assign roles such as question writer, solver/checker and presentation designer. Read instructions aloud, display key vocabulary and allow extra processing time.
• Advanced learners include an inequality, a rearranged formula and an error-analysis question, then provide a proof or substitution check showing that their answers are valid.

Extension

• Students create a second version of their challenge with a different answer or representation, then explain which version gives clearer evidence of algebraic reasoning.
• Students select the most powerful peer challenge and justify their choice using precision, originality, solvability and quality of explanation.