Unlocking Algebra Plans

Overview

This is lesson 5 of 10 in Algebra for Kapa Haka. Students build on one-step equations and substitution by solving two-step linear equations, rearranging and using simple formulae in fictional planning contexts involving transport, rehearsal blocks and equipment quantities. Teaching and discussion should be supported through te reo Māori, with local terms or contexts confirmed by kaiako and the kura.

Learning intentions

• WALT solve two-step linear equations using inverse operations.
• WALT rearrange and use simple formulae to find an unknown quantity.
• WALT explain logical steps and verify that a solution is correct.
• WALT communicate mathematical reasoning in a collaborative planning task.

Success criteria

• I can undo operations in the correct order.
• I can show clear, logical steps.
• I can substitute my answer to verify a solution.
• I can use a formula to find an unknown quantity and decide whether the answer makes sense.

Curriculum links

• Pāngarau — Tau me te Taurangi: solve and explain linear equations, use variables and formulae, and connect symbolic mathematics with meaningful situations.
• Te Reo Rangatira — Kōrero, Whakarongo, Pānui and Tuhituhi: listen to mathematical instructions, discuss reasoning, read concise problem cards and record explanations.
• Marau ā-Kura: use fictional planning contexts only; authentic kapa haka planning, budgets, protocols or performance details should be co-designed with relevant whānau, kaumātua or kaiako.
• Links to financial capability and health and physical education through transport planning, time allocation and safe equipment quantities.

Lesson structure (60 minutes)

1. 0–8 min · Retrieval and mistake-spotting. Display retrieval questions through the retrieval and mistake-spotting slides: solve a one-step equation, substitute into a formula and identify an inverse operation. Students complete the short retrieval section of the two-step equations and formulae worksheet, then annotate a deliberately incorrect solution, explaining where the reasoning changed direction. Briefly review answers and listen for misconceptions about order of operations.

2. 8–20 min · Explicit modelling. Model (3x+5=20), first representing the equation with the algebra balance mat or algebra tiles, then recording aligned symbolic steps: subtract 5, then divide by 3. Model verification by substitution. Next demonstrate a simple formula such as (C=4n+2), finding (n) when (C) is known. Use the modelling and vocabulary slides to highlight variable, inverse, rearrange, formula and verify. Students copy one worked example and solve a parallel example independently.

3. 20–23 min · Hinge check. Present the hinge question on the hinge-question slide: “What is the first operation to undo in (4x-7=25), and why?” Students show A/B/C response cards or fingers, then justify their choice to a partner. Use responses to form a quick support group or provide an additional worked example before the puzzle.

4. 23–38 min · Collaborative ‘Unlock the Plan’ puzzle. Organise five groups of five. Give each group an envelope of concise, dyslexia-friendly fictional clue cards from the unlock-the-plan puzzle pages and assign roles: reader/audio reader, equation builder, calculator checker, recorder and movement runner. Clues involve a transport total, rehearsal blocks and equipment quantities; students translate each situation into a two-step equation or use a formula, solve it, verify it and collect the next clue. Students may move between clue stations. Confer with groups, asking: “What does the variable represent?” and “How do you know your answer is sensible?”

5. 38–50 min · Create a solution card. In pairs, students invent a fictional planning situation with one two-step equation or simple formula, ensuring all quantities are realistic and clearly defined. They write the problem, show aligned calculations, verify the answer and state the unit. Students use the creation frame in the pair solution-card page. Remind them not to present invented details as actual local kapa haka practice or protocol.

6. 50–56 min · Feedback and peer marking. Pairs swap cards and mark using the four success criteria shown on the peer-feedback slides. Partners identify one strength and one improvement, checking the operation order, reasoning, verification and contextual sense. Invite two pairs to explain different solution methods; peers may challenge or confirm the verification.

7. 56–60 min · Reflection and exit problem. Students complete the final exit problem on the reflection and exit-ticket section: solve (5x+8=33), verify the answer and state what (x) could represent. They finish the sentence, “The most important step when solving a two-step equation is …” Collect responses at the door.

Resources

• the full algebra teaching deck
• the two-step equations and formulae worksheet
• the algebra balance mat
• Equation puzzle cards and envelopes
• Algebra tiles
• Formula cards
• Calculators
• Role cards
• A/B response cards or mini-whiteboards
• Coloured pens and timer

Assessment

• Use retrieval work, the hinge question and teacher conferences to identify whether students understand inverse operations and order.
• Assess marked reasoning, not only final answers: equation representation, logical steps, verification and contextual interpretation.
• Use the exit problem to group students for the next lesson: secure, developing or requiring targeted support.

Differentiation

• Provide dyslexic learners with step-by-step strips, aligned calculation spaces, reduced visual clutter, highlighted operation words, audio instructions and speech-to-text for explanations. Keep puzzle cards concise, with one instruction per line and no dense paragraphs.
• Support learners who need additional processing time with a worked example, formula card, algebra tiles and a reduced number of clues. Read cards aloud without requiring students to read publicly.
• Support ADHD learners through defined puzzle roles, chunked problems, movement between clue stations, a visible countdown and choice of challenge. Allow students to stand or use a quiet workspace when appropriate.
• Extend advanced learners by requiring an equation with a negative or fractional solution and an explanation of whether that answer is contextually sensible. They may also rearrange a formula before substituting values.

Extension

• Solve and explain a planning equation with a negative or fractional solution; discuss whether the result is mathematically valid but contextually sensible.
• Rearrange a formula such as (T=3n+6) to make (n) the subject, then create a verified context for it.