Equivalent Expressions

Overview

This is lesson 19 of 26 in Linear Patterns and Algebra. Students build and simplify equivalent linear expressions by grouping like terms with algebra tiles, then connect the concrete model to symbolic notation and independent practice.

Learning intentions

Students will:

• identify terms, coefficients, variables, and constants in linear expressions
• combine like terms using algebra tiles and symbolic notation
• explain why two expressions are equivalent
• practise simplifying expressions accurately and independently

Success criteria

• I can identify which terms are like terms.
• I can group like terms and combine their coefficients.
• I can simplify an expression and check that it is reasonable.
• I can justify why two expressions are equivalent using tiles, calculations, or an oral explanation.

Curriculum links

• Patterns and Relations — understanding oral and written patterns and their corresponding relations
• Patterns and Relations — representing algebraic expressions in multiple ways
• Preservation of equality and explaining the difference between an expression and an equation
• Mathematical processes: communication, connections, mental mathematics and estimation, problem solving, reasoning, and visualization

Lesson structure (50 minutes)

1. 0–5 min · Hook and retrieval. Display the opening question in the hook and retrieval slides: “Are (3x+2x+4) and (5x+4) the same expression?” Teacher briefly revisits variable, coefficient, constant, and term using colour-coded examples. Students make a prediction, then identify the terms in two expressions on mini-whiteboards.

2. 5–14 min · Explicit modelling. Teacher uses the Algebra Tiles: Linear Expressions Pack to build (3x+2+2x+4), placing blue (x)-tiles together and green unit tiles together; teacher records (5x+6) beside the model and explains that only like terms can be combined. Students copy the model into the equivalent expressions worksheet and use the colour key to mark (x)-terms and constants.

3. 14–22 min · Guided practice and video observation. Play a short, age-appropriate algebra-tiles combining-like-terms video selected from the provided search results, using the guided example and viewing prompt to pause and ask: “What was grouped? Why could these terms be combined?” Students complete the partially finished examples in their guided notes and explain one step to a partner.

4. 22–32 min · Hands-on grouping. Teacher gives each student expressions from the Algebra Tiles: Linear Expressions Pack and provides tiles or drawn tile representations. Students physically build, sort, and regroup expressions such as (2x+3x+5), (7+4x+2), and (6x+2+3x+1), recording the simplified form on the recording section. Teacher circulates, prompting: “Which terms have the same variable part?” and checks that students do not combine (x) and constants.

5. 32–40 min · Symbolic connection and Mathology. Teacher completes one example in the worked-example and error-analysis slides, modelling the sentence: “I combine the coefficients of like terms and keep the variable.” Students finish the Mathology worksheet questions in the equivalent expressions worksheet, first with a partner and then independently. Discuss the error (3x+4=7x) and ask students to correct and justify it.

6. 40–47 min · Mathletics and independent checkpoint. Students complete a short assigned combining-like-terms activity in Mathletics, with tile drawings or guided notes available. Each student then independently simplifies two expressions on the evidence checkpoint in the independent checkpoint and justifies one equivalence with tiles, a calculation, or an oral explanation recorded by the teacher.

7. 47–50 min · Exit reflection. Finish with the retrieval practice exit ticket slips. Students simplify (4x+3x+2), state one rule for combining like terms, and rate their confidence from 1–3. Teacher previews that the next lesson will apply expressions to linear patterns.

Resources

• the Equivalent Expressions slide deck
• the equivalent expressions worksheet
• the Algebra Tiles: Linear Expressions Pack
• the retrieval practice exit ticket slips
• Physical algebra tiles or coloured paper tiles
• Mini-whiteboards and markers
• Guided notes with partially completed examples
• Mathology access
• Mathletics access
• Projector or interactive display

Assessment

• Knowledge and Understanding: During retrieval, modelling, and guided practice, record whether each student identifies terms, coefficients, variables, constants, and like terms accurately. Progress is shown by correctly naming and grouping the parts of at least three expressions.
• Mental Mathematics: Listen for efficient combining of small integer coefficients and ask students to estimate or mentally check whether (3x+2x) should become (5x). Progress is shown by combining coefficients accurately without recounting every tile.
• Problem Solving: Use the independent checkpoint to document whether students simplify two expressions and justify one equivalence. Progress is shown by a correct representation and a clear tile, calculation, or oral explanation.
• Collect the worksheet and exit slip; note misconceptions for Friday’s review and for PowerSchool evidence under Knowledge and Understanding, Mental Math, and Problem Solving.

Differentiation

• Provide colour-coded terms, large high-contrast tiles, a term-identification checklist, partially completed examples, and sentence starters: “These are like terms because…” and “The expressions are equivalent because…”
• For students with dyslexia or reading difficulties, read instructions aloud, use a clear sans-serif font with generous spacing, reduce written copying, and accept labelled diagrams or oral explanations.
• For students with a math disability or modified programme, use fewer terms, begin with positive coefficients, offer one expression at a time, and allow physical tiles throughout independent work.
• Seat distractable students close to the modelling area, assign a tile manager or explainer role, use short timed tasks, and provide immediate feedback. Students ready for challenge can simplify expressions with four or more terms and explain why (2x+3+4x+1) is equivalent to (6x+4).