Algebra Basics Today

Overview

Today students begin Unit 1/6: “Unlocking Algebra: Year 9”. They will build a clear meaning for algebra, variables, and algebraic expressions, and connect these ideas to real-life situations.

Learning intentions

WALT:

• Understand what algebra is and why we use it.
• Identify variables and describe what they represent.
• Recognise and interpret simple algebraic expressions (e.g., (x+7), (2x), (x-3)).

Success criteria

Students can:

• Explain in their own words what a variable is.
• Point out the variable(s) and the numbers in an algebraic expression.
• Give one real-world example where algebra could help predict or generalise.

Curriculum links

• Algebra — AC9M9A02: simplifies algebraic expressions and works with algebraic expressions as a foundation for later expanding and factorising.
• Algebra — AC9M9A04 (future connection): uses graphs and solving, building from understanding expressions and variables now.
• Number/System skills (foundation for later work) — AC9M9N01: uses real numbers and representation with accuracy later when substituting values into expressions.

Lesson structure (55 minutes)

1. 0–6 min · Hook: “What’s missing?”

• Teacher shows 3 short word statements on the board (e.g., “A number plus 7”, “Twice a number”, “A number less 3”) with one blank symbol (a box) where the number should be.
• Students think-pair-share what the box could mean, then share ideas with the class.

2. 6–16 min · Direct teach: What algebra does

• Teacher uses a simple “rule” example: “If the number is (n), then the answer is (n+7)” and shows how a rule becomes a shorter general statement.
• Students copy a printed mini-notes template: “Algebra = using symbols/rules to describe patterns and relationships,” then underline the “rule” part and circle the variable.

3. 16–26 min · Guided practice: Variables as placeholders

• Teacher draws a substitution table: if (x=4), then (x+7=11); if (x=10), then (x+7=17). Emphasise that the variable changes.
• Students complete two more substitutions on their sheet (choose (x=3) for (x+5) and (x=6) for (x-2)) and check answers with a partner.

4. 26–40 min · Real-life modelling activity (science link)

• Teacher presents a science scenario: “A container heats up. Starting temperature is (x). After 5 minutes it increases by 6°C. Write the temperature after 5 minutes.”
• Students work in pairs to write an expression, then share as a class. Teacher prompts: “What is changing? What stays the same?” and records the expression clearly (e.g., (x+6)).
• Quick check: teacher asks a student to identify the variable(s) and the constants.

5. 40–50 min · Expression recognition sort

• Teacher shows 8 cards (mix of expressions and non-expressions). Examples: (x+7), (2x), (x^2) (optional as “later”), “(7+\square)” and a sentence like “twice the number”.
• Students sort into two columns: “Algebraic expression” and “Not an expression yet” (or “needs a variable”). Teacher circulates, using verbal prompts for students who struggle.

6. 50–55 min · Exit ticket

• Students answer 2 short questions on the printed exit ticket:

1. Define “variable” in one sentence.
2. Write an expression for “a number less 9”.

• Teacher collects for quick formative data.

Resources

• Printed mini-notes with clear headings and bullet points (dyslexia-friendly, large font)
• Substitution table worksheet (x-values and answers)
• Algebra expression card set (paper cards) for sorting
• Coloured highlighters or markers (one colour for variables, one for constants/numbers)
• Whiteboard/markers
• Optional: simple algebra tiles/arrow cards (variable “x” tiles and number tiles like 7)

Assessment

• Ongoing formative checks: teacher listens for correct variable meaning during discussion and substitution work.
• Expression recognition: observe sorting accuracy and ask targeted “Which part is the variable?” questions.
• Exit ticket: defines variable and writes one correct expression (used to group students for Lesson 2).

Differentiation

• Visual aids: variable and numbers highlighted in different colours; teacher models variable as a “label on a changing number.”
• Manipulatives: use tiles/arrows where a variable tile “x” can combine with number tiles (+7, −3, ×2) to form an expression.
• Scaffolds for struggling learners:
• Sentence starters: “A variable is a symbol that…”, “In (x+7), (x) is the…”
• Reduced set of cards for the sorting task (fewer options).
• Extension for advanced learners:
• Ask students to rewrite the expression in two ways using words (e.g., (x+6) as “(x) plus 6” and as “six more than (x)”).
• Challenge: create a real-life scenario for an expression (e.g., “starting mass is (x); after removing 3g…”).
• Optional mini-research direction: name a historical figure in mathematics connected to algebra (e.g., al-Khwarizmi) and write one sentence about their contribution (due next lesson or as homework).
• EAL/Diverse learners:
• Provide bilingual/extra simplified wordings where available for “constant”, “variable”, “expression”.
• Allow oral responses first, then translate to symbols with teacher support.
• Dyslexia-friendly reading options:
• Teacher reads instructions aloud once; students follow along with the printed notes.
• Use short lines per sentence on worksheets and highlight key words (“variable”, “expression”, “less than”, “more than”).

Extension (optional)

• Research task (for advanced students): Choose one historical figure in mathematics linked to algebra, then write 3 bullet points about what they contributed to algebra and how it connects to symbols/rules today.