Lesson 2: The Mystery of 'x'
Learning Intention: We Are Learning To use symbols and letters to represent unknown values.
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 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: - algebraic notation - expanded form - formulae - like terms - linear equation - linear patterns.
- Statistics ā Practices: - ordered pairs - origin - rearrange - substitution - variable - value.
- Algebra ā 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 terā¦
- Algebra ā 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, anā¦
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.