Handout: The Equation Balancer

Keep the scales balanced by doing the same thing to both sides!

Example:

Solve for x:

x + 6 = 14

To get 'x' by itself, we do the opposite of '+ 6', which is '- 6'. We must do it to both sides.

x + 6 - 6 = 14 - 6

x = 8

Your Turn: Solve for the variable

a + 10 = 22

a = ___
b - 5 = 11

b = ___
3c = 18 (Remember, 3c means 3 x c)

c = ___
d / 4 = 5 (d divided by 4)

d = ___

Challenge Zone

Can you solve this two-step equation?

2x + 3 = 15

Hint: Get rid of the '+ 3' first!

x = ___

📋 Teacher Planning Snapshot

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.

Hononga Marautanga · Curriculum Alignment

Curriculum alignment for this handout has not yet been verified against the live curriculum statements. A generated placeholder that stood here was removed on 2026-08-29 because it matched no real statement.