Handout: Variable Vocabulary

Understanding the language of algebra.

Key Terms

Variable
A symbol (usually a letter like 'x' or 'y') that represents a number we don't know yet. It's a placeholder.
Expression
A mathematical phrase that contains numbers, variables, and operators (like +, -, x, ÷). Example: x + 5
Equation
A statement that two expressions are equal. It has an equals sign (=). Example: x + 5 = 10
Constant
A number on its own, whose value does not change. In "x + 5 = 10", the numbers 5 and 10 are constants.

Practice: Translate to Algebra

Read the sentence and write it as an algebraic expression or equation. Use 'n' as your variable.

  1. A number increased by 7.
    Answer: _________________________
  2. The product of a number and 4.
    Answer: _________________________
  3. A number decreased by 10 is 25.
    Answer: _________________________
  4. Five less than a number.
    Answer: _________________________
  5. A number shared between 3 people.
    Answer: _________________________

Curriculum alignment

  • Statistics — Knowledge: - algebraic notation - expanded form - formulae - like terms - linear equation - linear patterns.
  • Algebra — 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 t…
  • Number — Practices: - Locating negative and positive numbers on a number line - Comparing and ordering negative and positive numbers using a number line (e.g. −3.4 < −3) - Evaluating expressions …
  • Measurement — Practices: - Locating negative and positive numbers on a number line - Comparing and ordering negative and positive numbers using a number line (e.g. −3.4 < −3) - Evaluating expressions …
  • Statistics — Practices: - Locating negative and positive numbers on a number line - Comparing and ordering negative and positive numbers using a number line (e.g. −3.4 < −3) - Evaluating expressions …

📋 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.