📚 Unit Plans → 🌍 Year 9 Algebra — Te Tātai Tauira → 📖 Lesson 5: The Two-Step Shuffle
Years 9–10 Pāngarau / Mathematics

Year 9 pitch · Lesson 5: The Two-Step Shuffle

Quick-fire questions for the class: What is the inverse of adding? Subtracting? Multiplying? Dividing? Emphasise that to solve equations, we undo them...

Year 9 pitch · Lesson 5

Year 9: rearrange the formula

Ākonga handle negative and fractional coefficients and rearrange a formula to make a different variable the subject.

Same topic at the other level: Years 7–8 pitch →

Starter (10 mins)

Inverse Operations Review

Quick-fire questions for the class: What is the inverse of adding? Subtracting? Multiplying? Dividing? Emphasise that to solve equations, we undo them in the reverse order of operations (reverse BEDMAS).

Main Activity (25 mins)

Solving Two-Step Equations

Model solving a two-step equation like 2x + 3 = 11. Explain that we undo the addition/subtraction first, then the multiplication/division. "We want to get 'x' on its own, so we first move the constant, then the coefficient."

Students work through the "Two-Step Equation Marathon" practice sheet, starting with the first level. Circulate and provide support.

View Practice Sheet

Plenary (15 mins)

Real-World Algebra Stations

Set up the "Real-World Algebra" station cards around the room. In small groups, students rotate through the stations, creating and solving a two-step equation for each real-world scenario. This demonstrates the practical application of their new skills.

View Station Cards

Media Anchor (8-10 mins)

Video anchor: Solving two-step equations clearly

Use this clip to reinforce reverse-order operations before station rotation work begins.

Pause and discuss: How do you check a two-step solution efficiently for accuracy?

Transfer task: Students apply one method from the clip to the first equation in the next task set.

Resources Needed

Curriculum alignment

📋 Teacher Planning Snapshot

📐 Year 9 — Test the claim — one counterexample settles it

Year 9 mathematics includes deciding whether a general claim is TRUE. Give ākonga claims such as “multiplying always makes a number bigger”, and ask them to prove or disprove. One counterexample is a complete disproof; a hundred examples is not a proof. That asymmetry is the idea, and it is worth more than another page of two-step solving.

Ngā Whāinga Ako — Learning Intentions

Students will develop algebraic thinking and pattern recognition (tātai tauira) through te ao Māori contexts, connecting mathematical reasoning to cultural and real-world problem-solving in Aotearoa.

Ngā Paearu Angitū — Success Criteria

  • ✅ Students can identify, describe, and extend patterns using algebraic notation.
  • ✅ Students can explain their mathematical reasoning and connect it to real-world contexts.

Differentiation & Inclusion

Scaffold support: Provide concrete materials and visual representations before moving to abstract notation. Offer entry-level tasks using number patterns, and extension challenges involving proof or generalisation for capable learners.

ELL / ESOL: Pre-teach key mathematical vocabulary (variable, expression, equation, pattern). Allow diagrams and tables as alternate representations. Bilingual glossaries recommended.

Inclusion: Neurodiverse learners benefit from structured step-by-step templates and multiple representations (visual, numeric, algebraic). Avoid time pressure on procedural tasks.

🌿 Mātauranga Māori Lens

Tātai (to reckon, count, calculate) reflects the deep mathematical tradition within te ao Māori — from whakapapa genealogy structures to wharenui proportional geometry, navigation, and seasonal calendars. Mātauranga Māori holds rich pattern-based thinking: tukutuku panel sequences, kōwhaiwhai scroll patterns, and fishing seasonal cycles all encode algebraic relationships. Algebra taught through these lenses makes abstract thinking visible and culturally grounded.