Like Terms Lab

Overview

In this fourth lesson of Algebra Detectives: Solve, Simplify, Share, students investigate why some algebraic terms can be combined and others cannot. They move between concrete algebra-tile models, symbolic expressions and explanations, building on prior learning about variables, coefficients, constants and equivalent expressions.

Learning intentions

• WALT identify like and unlike terms.
• WALT simplify expressions by collecting like terms.
• WALT use algebra tiles and symbols to explain equivalent expressions.
• WALT communicate a clear rule for simplifying algebraic expressions.

Success criteria

• I can identify terms with the same variable and exponent as like terms.
• I can combine coefficients while keeping the variable unchanged.
• I can explain why (3a+a+a=5a) and (3b-2b=b).
• I can justify each step when simplifying an expression.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge tasks connect with classroom mathematics content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, explanation and non-routine problem solving.
• Mathematical communication and reasoning: students represent, justify and share algebraic thinking using materials, symbols and oral explanation.

Lesson structure (45 minutes)

1. 0–5 min · Hook and recall. Display the opening question in the Like Terms Lab introduction deck: “Can (3a+a+a) really become (5a)?” Students independently predict an answer, then explain what they remember about terms, coefficients and variables to a partner. Briefly revisit the WALT and invite students to listen for an explanation that proves, rather than merely states, the answer.

2. 5–13 min · Model with tiles. Use the Algebra Tiles: Linear Expressions Pack and the matching modelling slides in the Like Terms Lab introduction deck to build (3a+a+a), using one colour for (a)-tiles and another for unit tiles. Teacher groups the five identical (a)-tiles and records (5a), then models (3b-2b) by removing two (b)-tiles to show one (b) remains. Students narrate the model using the words “term”, “coefficient”, “like” and “equivalent”; check that the variable has not changed.

3. 13–23 min · Card-sort investigation. In pairs or a group of three, students use the expressions and prompts in the Algebra Tiles: Linear Expressions Pack and follow the sorting instructions on the Like Terms Lab introduction deck. They sort terms into like/unlike groups, then match selected expressions to their simplified forms. Teacher circulates and asks: “What makes these terms alike?” “What does the coefficient tell us?” and “Why can’t (3a) and (3b) be combined?” Students record two matches and a written justification on the collecting like terms investigation sheet.

4. 23–32 min · Guided symbolic practice. Reveal the worked examples and misconception check in the Like Terms Lab introduction deck. Model the routine: circle like terms, combine the coefficients, retain the variable, and check by substituting a simple value. Work through (4x+2x), (7p-3p+ p), and (5+2a+3+ a), inviting students to explain each decision. Students complete the first section of the collecting like terms investigation sheet individually, then compare one answer with a partner. Address the common error of adding variables, such as writing (3a+a=4).

5. 32–40 min · Create and share a “How to simplify” poster. Pairs use the poster frame and prompts in the collecting like terms investigation sheet to create a concise mini-poster: a definition of like terms, a four-step method, one tile example and one symbolic example. They must include explanations of (3a+a+a=5a) and (3b-2b=b), using words, symbols or a labelled sketch. Each pair gives a one-minute explanation to another pair. Listeners identify one clear mathematical idea and ask one “Why?” question, demonstrating manaaki and aroha through respectful mathematical discussion.

6. 40–45 min · Plenary and exit check. Use the final discussion slide in the Like Terms Lab introduction deck to revisit the hook and ask students to improve their original explanation. Students complete the final three questions on the collecting like terms investigation sheet: simplify (6m+2m), identify whether (4x) and (4y) are like, and explain one reason terms may be combined. Collect the sheets and invite two students to share different valid explanations.

Resources

• the Like Terms Lab introduction deck
• the collecting like terms investigation sheet
• the Algebra Tiles: Linear Expressions Pack
• Coloured pencils or highlighters
• A3 paper or cardboard for pair posters
• Marker pens
• Whiteboard and board pens
• Optional counters or linking cubes for students needing an additional concrete model

Assessment

• Listen during modelling and sorting for accurate use of “like term”, “coefficient”, “variable” and “equivalent”.
• Check pair explanations and worksheet reasoning, not only final answers; identify whether errors arise from combining unlike terms or mishandling coefficients.
• Use the exit check to group students for the next lesson: secure understanding, needs further modelling, or ready for extension.

Differentiation

• Support learners with algebra tiles, matching colours, partially completed models, a word bank and sentence starters such as “These terms are like because…” and “I combined the coefficients by…”.
• Offer simplified numerical analogies, such as (3 apples+1 apple=4 apples), before connecting the structure to (3a+a=4a). Read instructions aloud and allow students to explain orally before writing.
• Pair students thoughtfully and provide enlarged expressions, reduced writing demands or a scribe where appropriate for learners with dyslexia, fine-motor needs or language-processing difficulties.
• Extension learners simplify expressions with negative coefficients and several variables, such as (-3a+5a-2b+b), then justify every step and explain why terms involving different variables remain separate. They may create a deliberately incorrect expression for another pair to diagnose.