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 = ___
Curriculum alignment
- Geometry ā Knowledge: - Triangles can be categorised by their angles.An acute triangle has three acute angles.A right triangle has one right angle.An obtuse triangle has one obtuse angle. - An acutā¦
- Geometry ā Knowledge: - The sum of the exterior angles of a polygon is 360Ā°. - In a regular polygon, all exterior angles are the same; an exterior angle can be found by subtracting the interior angā¦
- Statistics ā Practices: - ordered pairs - origin - rearrange - substitution - variable - value.
- 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¦
- Statistics ā Knowledge: - The response to a statistical question includes findings that are summarised and interpreted in context and using evidence. - The tapering sides of a data visualisation are ā¦
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.