Year 9: x as a variable in a relationship
Ākonga solve equations with variables on both sides and interpret x as a quantity that varies, not just a hidden number.
- Year 9 move: Variables on both sides, with interpretation
- Evidence it produces: A solution plus a statement of what x represents in the relationship
Starter (10 mins)
The Covered Number
Write a simple equation on the board like "5 + ? = 12". Cover the question mark with a card. Ask students what number is hidden. Repeat with different operations (e.g., "10 - ? = 3", "3 x ? = 15"). Explain that in algebra, we use letters instead of a question mark or a box.
Main Activity (25 mins)
Translating to Algebra
Introduce the term 'variable'. Use the "Variable Vocabulary" handout to define key terms. Work through the first few examples together as a class. Students then work in pairs to translate word problems into simple algebraic expressions.
Example: "I have some apples, and my friend gives me 3 more. Now I have 8." How can we write this using algebra? (a + 3 = 8).
View HandoutPlenary (15 mins)
Algebra in Real Life
Brainstorm situations where we might not know a value. Examples: the cost of an item before you see the price tag, the number of people who will come to a party, the temperature tomorrow. Discuss how we could use a variable to represent these unknown quantities in planning or discussion.
Media Anchor (8-10 mins)
Video anchor: Variables as unknown values
Use this clip to strengthen understanding that letters stand for values that can change.
Pause and discuss: Why is using a variable more powerful than writing a blank box?
Transfer task: Students apply one method from the clip to the first equation in the next task set.
Resources Needed
- "Variable Vocabulary" Handout
- Whiteboard or projector
- Mini-whiteboards for students
Curriculum alignment
- 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…
- Statistics — Knowledge: - algebraic notation - expanded form - formulae - like terms - linear equation - linear patterns.
- Statistics — Practices: - ordered pairs - origin - rearrange - substitution - variable - value.
- Algebra — Practices: - Rearranging known formulae using one or two steps (e.g. making w the subject of A = lw) - Simplifying expressions involving any of the four operations by collecting like ter…
- Algebra — Practices: - Identifying and plotting points in the four quadrants of the coordinate plane, using ordered pairs and values from a table - Using tables, graphs in the coordinate plane, an…
📋 Teacher Planning Snapshot
📐 Year 9 — A variable is a changing quantity, not a hidden number
Year 7–8 meets x as a box with one answer in it. Year 9 needs both meanings: in 2x + 3 = 11 x is an unknown to solve for, but in c = 2n + 3 the letter is a quantity that varies — the same symbol behaving differently. Ākonga state, for each expression they meet, which kind it is and how they can tell. Confusing the two is the most common Year 9 algebra error.
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.
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.