Algebraic Expressions Start

Overview

This lesson introduces how algebraic expressions use variables to represent unknown numbers. Students will practise creating, expanding using distributive ideas, and simplifying basic linear expressions with integer coefficients and constants, building toward later equation and inequality work.

Learning intentions

Students will:

• understand that letters (variables) can represent unknown values in expressions
• create algebraic expressions from simple written situations
• expand and simplify linear expressions using basic algebra rules and operations
• check that expressions are equivalent by substituting values

Success criteria

Students can:

• write an expression for a given statement using correct algebraic notation
• simplify expressions like (2x+4) to an equivalent form using grouping and distributive reasoning
• expand and combine like terms to reach a simplified linear expression
• verify equivalence by substituting a value for the variable

Curriculum links

• Algebra — create, expand, factorise, rearrange and simplify linear expressions using associative, commutative, identity, distributive and inverse properties
• Algebra — solve linear equations and one-variable inequalities using graphical and algebraic techniques (preview by preparing accurate expression skills)
• General capability: numeracy (using variables, structure, and equivalence)

Lesson structure (30 minutes)

1. 0–4 min · Hook (variables as placeholders). Teacher writes: “A number plus 5” and asks students to show possible answers for the number 3, 7, and 10, then introduces a symbol for the unknown (e.g., (n)). Students propose expressions (e.g., (n+5)) and give quick example substitutions.

2. 4–10 min · Direct teach (from words to expressions). Teacher models translating short statements into expressions:

• “Twice a number decreased by 3” (\rightarrow 2n-3)
• “A number plus 4 more than another number” (\rightarrow a+(b+4)) Teacher highlights that brackets matter and that variables stand for any number. Students copy two models and complete three “words to algebra” examples on their mini-whiteboard.

3. 10–16 min · Guided practice (equivalence using distributive idea). Teacher shows the connection between equivalent forms using tiles/area reasoning with one worked example: (2(x+2)=2x+4) Teacher narrates: multiply everything inside the bracket by 2, then simplify. Students do two similar tasks with support:

• (3(a-b)=3a-3b)
• Expand then simplify: (4(x+3)-2x) (teacher prompts about distributing and combining like terms)

4. 16–24 min · Independent practice (simplify linear expressions). Teacher gives a short set of expression simplification questions (choose the middle two if time): A. Expand and simplify: (5(m+2n)+3m-4n) B. Simplify: (7x+2x-5) C. Simplify: (9-2(3x-1)) Teacher circulates, checking for correct distribution, signs, and like-term collection. Students work to simplify each expression fully and show one line of working (not just the final answer).

5. 24–28 min · Verification check (substitution). Teacher asks: “How do we know two expressions are the same?” and models a quick substitution check using an example pair (e.g., (2(x+2)) and (2x+4) with (x=3)). Students verify equivalence for one pair from their own work by substituting a value (teacher chooses the value to keep arithmetic manageable).

6. 28–30 min · Exit ticket (quick diagnostic). Teacher collects responses: one “words to expression” and one “simplify” question. Students complete independently:

• Write an expression for “(x) increased by 6, then multiplied by 2.”
• Simplify: (2(3x+1)-x)

Resources

• Mini-whiteboards and markers (or worksheet + pencil)
• Algebra tiles or area model diagrams (optional but helpful)
• Scaffolding card: “Step 1 distribute, Step 2 combine like terms, Step 3 check brackets”
• Teacher-made word-to-expression question set
• Exit ticket slips
• Calculator only for checking (not for core expansion)

Assessment

• Formative: teacher listens for correct interpretation of variables and checks distribution/sign accuracy during guided practice.
• Formative: observe written steps for expanding brackets and combining like terms (identify common errors).
• Summative-in-form: exit ticket (translation + simplification) to confirm understanding and next lesson readiness.

Differentiation

• Support: provide a “brackets/reminder” scaffold and sentence starters (e.g., “First distribute the 2, then…”, “Like terms are …, so we combine…”).
• Support: pre-printed examples of correct sign handling (especially for expressions like (3(a-b))).
• Extension (if finished early): ask students to create their own expression from a short scenario and provide an equivalent expanded form.
• EAL/SEN: allow oral explanation recorded by the teacher or student using simple phrases; keep numbers small to reduce arithmetic load so the focus stays on algebra structure.