Algebraic Language

Overview

Lesson 1 of 10 in Algebra for Kapa Haka. Students build shared algebraic language by modelling invented or class-agreed rehearsal scenarios. They connect changing quantities to variables and expressions while distinguishing the mathematical model from the cultural knowledge it supports.

Learning intentions

• WALT use the terms variable, constant, coefficient, term and expression accurately.
• WALT translate verbal statements into algebraic expressions.
• WALT explain what a letter represents in a mathematical model.
• WALT communicate mathematical ideas respectfully in a kapa haka preservation context.

Success criteria

• I can identify a variable and a constant.
• I can identify terms and coefficients in an expression.
• I can translate a verbal statement into an expression and explain my symbols.
• I can distinguish the mathematical model from the cultural knowledge it supports.

Curriculum links

• Pāngarau: Tau me te Taurangi, with a focus on algebraic thinking, changing quantities and mathematical modelling.
• Pāngarau: communicating and interpreting mathematical ideas through representations, symbols and explanations.
• Te Reo Rangatira: kōrero, whakarongo and whakaatu through mathematical discussion and presentation.
• Marau ā-Kura: use local contexts only where appropriate and approved by the kura, whānau or local experts.

Lesson structure (60 minutes)

1. 0–8 min · Mihi, safety and diagnostic. Welcome students, acknowledge the class and establish that kapa haka is not being treated as a data source or commodity; explain that scenarios are invented or class-agreed unless local permission has been given. Invite students to share what they already know about letters in maths, then use the opening question and cultural safety slides and a short diagnostic on the entry and exit worksheet. Students think-pair-share, complete two quick prompts on mini-whiteboards and agree to listen, ask respectfully and avoid using iwi, hapū, waiata, tikanga, names or movements without permission.

2. 8–18 min · Explicit teaching. Display the algebra vocabulary and worked-example slides. Model a scenario such as “There are (g) groups with (p) performers in each group”: total performers (= gp). Define variable, constant, coefficient, term and expression, using symbols alongside words and colour coding. Students repeat or explain each term orally, identify the parts of examples on mini-whiteboards, and show answers simultaneously for quick checking.

3. 18–35 min · Hands-on modelling. Place students in mixed-ability groups of four and open the group task instruction slide. Give each group counters, labelled cards, role cards and an invented, context-neutral rehearsal scenario. Students use counters to represent quantities, then match cards to the model; for example, “five groups with (p) performers in each group” becomes (5p). Assign roles such as facilitator, resource manager, recorder and speaker, with a visible timer and checkpoints at 25 and 32 minutes. Students must state what each letter represents and identify any constant, coefficient and term.

4. 35–48 min · Create and explain. Show the expression-creation and explanation prompts. Each group creates two expressions from different rehearsal scenarios, records them on the worksheet and prepares a brief explanation. At least one expression must include a variable and one must include a fixed number. Students explain the quantity being modelled, why the chosen letter is suitable, and which part is mathematical modelling rather than cultural knowledge.

5. 48–55 min · Gallery walk and feedback. Display the gallery-walk feedback prompts and set clear movement expectations. Students circulate, inspect two groups’ models and leave feedback using “I notice…” and “I wonder…”. They check whether each expression matches its verbal statement, whether symbols are defined and whether the explanation is respectful and appropriately separated from cultural knowledge. Groups respond to one useful question or correction.

6. 55–60 min · Exit ticket and reflection. Return to the plenary and exit-ticket prompt. Students complete the final section of the independent exit ticket: identify the variable and constant in (4n+2), translate “three groups with (x) performers in each” into an expression, and explain what (x) represents. Collect responses to inform Lesson 2 and briefly acknowledge the collaborative learning.

Resources

• the complete introduction, teaching and activity deck
• the entry, modelling and exit worksheet
• Counters or other small manipulatives
• Labelled algebra vocabulary and scenario cards
• Mini-whiteboards and pens
• Group role cards
• Visible timer
• Dyslexia-friendly vocabulary cards and printed instructions
• Invented or class-agreed, context-neutral rehearsal scenarios

Assessment

• Question students during explicit teaching and scan mini-whiteboards for accurate identification of variables, constants, terms and coefficients.
• Use an observation checklist during group work: defines letters, matches a model to a statement, uses vocabulary accurately and communicates respectfully.
• Use the exit ticket to diagnose whether students can identify algebraic components, translate language into symbols and explain a variable.

Differentiation

• For dyslexic learners, provide a teacher-read or slim-text version in OpenDyslexic or Arial 14–16 pt on a cream background, with uncluttered cards, audio directions, symbols alongside words and chunked instructions. Offer oral responses and do not require copying notes.
• For students with ADHD, use a visible timer, movement-based card sorting, defined group roles and brief task checkpoints. Provide a clear “now/next” instruction at each transition.
• Support learners with a worked example, colour-coded vocabulary, counters and sentence frames: “The letter ___ represents ___”; “The coefficient is ___ because ___.”
• Offer challenge through two equivalent expressions for a larger rehearsal model, with students justifying their choice of variable and explaining why both expressions represent the same quantity.
• Before using any iwi- or hapū-specific material, consult kaumātua, whānau or kaiako. Keep examples culturally safe and avoid presenting cultural knowledge as something to quantify or own.

Extension

• Create two equivalent expressions for a larger invented rehearsal model and justify the choice of variable.
• Write a new verbal statement for a partner to translate, then check and explain the partner’s model.