Lesson 4: Balancing Act
Learning Intention: We Are Learning To write and solve simple linear equations.
Starter (10 mins)
Think of a Number
Play a "think of a number" game. "I'm thinking of a number. I add 5, and the answer is 13. What's my number?" Students work backwards. Explain that this is what we do when we solve equations: we perform the "inverse operation".
Main Activity (25 mins)
The Equation Balancer
Introduce the idea of an equation as a balanced scale. What you do to one side, you must do to the other. Use physical balance scales with weights if available, or draw them.
Use the "Equation Balancer" handout. Students work through a series of one-step equations, showing their working by applying the inverse operation to both sides.
View HandoutPlenary (15 mins)
Create Your Own Problem
Students write their own simple word problem that can be solved with a one-step equation. They translate it into algebra and solve it. For example: "There were some birds on a wire. 5 flew away, and now there are 8 left. How many were there to start with?" (b - 5 = 8).
Students can share their problems with a partner to solve.
Media Anchor (8-10 mins)
Video anchor: Solving equations with balance logic
Use this clip as a worked-example routine before students solve one-step equations independently.
Pause and discuss: What operation must be undone first, and why?
Transfer task: Students apply one method from the clip to the first equation in the next task set.
Resources Needed
- "Equation Balancer" Handout
- Balance scales and weights (optional)
- Mini-whiteboards
Curriculum alignment
- Algebra ā Knowledge: - A variable can be used to represent:an unknown number, often in formulae (e.g. s in s2)a quantity that can vary or change (e.g. y = 3x + 4; A = bh)a specific unknown value tā¦
- Number ā Knowledge: - Finding equivalent fractions and representing fractions in their simplest form - Adding and subtracting fractions, including improper fractions and mixed numbers, and represā¦
- Measurement ā Knowledge: - Finding equivalent fractions and representing fractions in their simplest form - Adding and subtracting fractions, including improper fractions and mixed numbers, and represā¦
- Statistics ā Knowledge: - Finding equivalent fractions and representing fractions in their simplest form - Adding and subtracting fractions, including improper fractions and mixed numbers, and represā¦
- Algebra ā Knowledge: - Finding equivalent fractions and representing fractions in their simplest form - Adding and subtracting fractions, including improper fractions and mixed numbers, and represā¦
š Teacher Planning Snapshot
NgÄ WhÄinga Ako ā Learning Intentions
Students will develop algebraic thinking and pattern recognition (tÄtai tauira) through te ao MÄori contexts, connecting mathematical reasoning to cultural and real-world problem-solving in Aotearoa.
NgÄ Paearu AngitÅ« ā Success Criteria
- ā Students can identify, describe, and extend patterns using algebraic notation.
- ā 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.
TÄtai (to reckon, count, calculate) reflects the deep mathematical tradition within te ao MÄori ā from whakapapa genealogy structures to wharenui proportional geometry, navigation, and seasonal calendars. MÄtauranga MÄori holds rich pattern-based thinking: tukutuku panel sequences, kÅwhaiwhai scroll patterns, and fishing seasonal cycles all encode algebraic relationships. Algebra taught through these lenses makes abstract thinking visible and culturally grounded.