Simplifying Algebra

Overview

In this lesson (15 of 20) students learn techniques to simplify algebraic expressions by combining like terms. Students build on prior work with expanding and rearranging expressions, using properties to justify steps.

Learning intentions

• Students will simplify linear expressions by combining like terms.
• Students will explain their simplification using correct mathematical language (like terms, factor, coefficient).
• Students will check results by substituting a value for the variable.
• Students will choose an efficient order of operations for algebra (collect like terms, then simplify).

Success criteria

• I can identify like terms in an expression (same variable and same power).
• I can combine coefficients of like terms to produce a simpler equivalent expression.
• I can simplify expressions involving integers and constants without mistakes in signs.
• I can verify a simplified expression by substitution.

Curriculum links

• Algebra: create, expand, factorise, rearrange and simplify linear expressions using associative, commutative, identity, distributive and inverse properties.
• Algebra: solve and verify linear relations by substitution (used here as a checking strategy after simplification).
• Number/Operations: use efficient strategies with integers when combining terms with positive and negative signs.

Lesson structure (30 minutes)

1. 0–3 min · Retrieval starter (prior knowledge). Teacher writes two small expressions on the board: 2x + 3x and 5 - 2 + 7. Students respond on paper: what can be combined and what the simplified form would be.

2. 3–9 min · Direct teach: What “like terms” means. Teacher models an expression on the board (e.g., 3x + 2y + 5x - y + 4) and underlines like terms, then combines them to get 8x + y + 4 (showing sign care). Students copy a short “rule” in their notes:

• Like terms have the same variable and power.
• Combine coefficients; keep the variable part the same.
• Constants combine as like terms too.

3. 9–15 min · Guided practice using a worked example. Teacher guides through one expression step-by-step: Example: Simplify 4a - 3a + 2 - 5 + 7a. Teacher prompts: “Which terms are like? What happens to the coefficients? What do we do with constants?” Students work in pairs/independently: they write each simplification line neatly, ensuring the final line has all like terms combined.

4. 15–24 min · Independent practice (fluency with sign accuracy). Teacher hands out a short worksheet with 6 expressions, increasing difficulty. Students simplify each one and circle answers that they are confident about. Suggested set:

• 6x + 2x - 9x
• -3m + 4m + 5m
• 7 - 2 + 3x - x
• 5y - 2y + 4 - 9
• -a + 6a - 3a + 2
• 2(3x + 1) + 4x - 5 (teacher reminds: first distribute, then combine like terms) Teacher moves around checking correct identification of like terms and correct handling of negative coefficients.

5. 24–28 min · Verification by substitution (quick check). Teacher selects one student expression from the worksheet that commonly causes errors (e.g., 2x(… ) type or sign issues) and models checking: Choose a simple value, such as x = 2, substitute into the original and simplified expressions, and compare results. Students do the same check on one of their answers (original vs simplified) using their chosen value.

6. 28–30 min · Exit ticket (teacher gathers evidence). Students complete one final task: simplify -2x + 5x + 3 - 7. They also write one sentence: “These terms were like because…” (e.g., same variable power).

Resources

• Board/marker or digital equivalent
• “Like terms” mini-poster or class notes template
• Worksheet: 6 simplification expressions plus space for working
• Student scrap paper for substitution checks
• Exit ticket slips
• Optional: algebra tiles or counters to represent coefficients (if available)
• Calculator allowed only for checking, not for the main simplification

Assessment

• Formative checks during guided practice: teacher listens for correct identification of like terms and correct sign handling.
• During independent work, teacher uses a quick checklist: “Correct like terms grouped? Combined coefficients? Simplified constants? Neat working?”
• Exit ticket: simplified expression plus one justification sentence about like terms.

Differentiation

• Support: provide a worked “group and combine” example template with sentence starters:
• “These are like terms because…”
• “So I add/subtract the coefficients to get…”
• Support: reduce quantity of terms on first two practice questions; ensure at least one expression is constants-only plus one is variable-only.
• Challenge/extension within the same task: ask students to simplify an extra expression that includes negatives and requires careful regrouping (e.g., -4x + 3x + 2 - 6 + x).
• EAL/SEN: allow use of highlighting (colour-coding like terms) and encourage verbal explanation before writing the final line.

Extension (optional)

• SKIP