Year Level: 9-10 | Subject: Mathematics | Duration: 50 minutes
Curriculum Links: Algebra 5.1, Cultural Connections
Whakataukī: "He tangata takahi manuhiri, he mauri kino" - A person who mistreats guests has a bad life force.
Traditional pounamu (greenstone/jade) trading was central to Māori commerce and relationships between iwi. Trade routes connected communities across Te Waipounamu (South Island) and Te Ika-a-Māui (North Island), with complex mathematical relationships governing fair exchange.
Mātauranga Māori lens: Pounamu exchange was not merely transactional — it was governed by tikanga and embedded in whanaungatanga. The mathematical precision of fair trade reflects the deeper values of manaakitanga (care for others) and reciprocity that structured inter-iwi relationships. Use this lesson to affirm that mathematical thinking is not culturally neutral: te ao Māori has always included sophisticated quantitative reasoning.
Paearu Angitu — Success Criteria: students can write a linear equation from a verbal trading scenario, solve it showing working, and explain how word choice (e.g., "exchange" vs. "fair trade") connects to cultural values.
Readiness signal: Use the opening 10-min scenario as a diagnostic — students who cannot set up the simple substitution problem need concrete manipulatives before moving to simultaneous equations in Activity 2.
Inclusion guidance: ESOL / ELL learners benefit from the bilingual vocabulary cards and visual trading charts already listed in resources. For neurodiverse learners / ADHD, provide a step-by-step worked example on the board and allow token manipulatives (pounamu = tokens) throughout. UDL: accept oral explanations for the cultural connection component of the exit ticket.
Setup: Students work in pairs representing different iwi
Scenario: "Your iwi has 3 large pounamu pieces and 5 small ones. Another iwi offers 2 woven mats for each large piece and 1 mat for each small piece. How many mats will you receive?"
Extension: "If mats are worth 4 kūmara each, and you need 50 kūmara for winter, was this a good trade?"
Problem 1: The Balanced Exchange
Two iwi want to make a fair trade. Iwi A has pounamu worth different values:
Iwi B offers: 2L + 5S = 31 units of value
Question: If they trade 3L + 2S, what value should Iwi B offer to maintain fairness?
Problem 2: Multi-iwi Trading Network
Three iwi are trading. Create equations to represent:
Where x = large pounamu pieces, y = small pounamu pieces
Solve: How many of each type of pounamu do they have?
Scenario: Your marae is planning a hui and needs to trade pounamu for kai.
Success Criteria: Equation is realistic, solution is correct, cultural connection is meaningful
Interview a Family Member: Ask whānau about any trading, bartering, or exchange they've done. Create a linear equation to represent one of these exchanges.
Alternative: Research pounamu types (kawakawa, inanga, etc.) and create trading equations based on their relative values.
| Criteria | Excellence | Merit | Achieved |
|---|---|---|---|
| Mathematical Accuracy | All equations solved correctly with clear working | Most equations correct with minor errors | Basic equation solving attempted |
| Cultural Understanding | Deep understanding of cultural context and values | Good cultural connections made | Basic cultural awareness shown |
| Problem Solving | Creative approaches, multiple strategies used | Clear problem-solving process evident | Basic problem-solving attempted |
Use this space to note what worked well, what could be improved, and student responses to the cultural integration...