Build, Balance, Explain

Overview

Students use algebra tiles and cooperative reasoning to connect concrete models with algebraic expressions. They build, write, simplify and evaluate expressions, extending prior learning about number properties, inverse operations and order of operations.

Learning intentions

• WALT identify variables, coefficients, constants and like terms.
• WALT represent and simplify linear expressions using algebra tiles.
• WALT substitute values into expressions and explain each step.
• WALT communicate and justify mathematical thinking when working cooperatively.

Success criteria

• I can identify the parts of an algebraic expression.
• I can build an expression and write its symbolic form.
• I can collect like terms to simplify an expression.
• I can substitute a value for a variable and check whether my answer is reasonable.

Curriculum links

• Number and Algebra — identify variables and find the value of an expression or formula when values are given.
• Number and Algebra — simplify algebraic expressions involving sums, products, differences and single brackets.
• Number and Algebra — use properties of operations, including commutative and distributive properties, to rewrite equivalent expressions.
• Mathematics and Statistics — use mathematical language, representations and reasoning to solve higher-order problems and explain thinking.

Lesson structure (60 minutes)

1. 0–5 min · Hook and pre-assessment. Teacher displays the learning intentions and asks, “Can two expressions look different but have the same value?” Open with the visual hook and learning-intention slides and invite students to compare 3 + 4 and 4 + 3, then x + x + 2 and 2x + 2. Students make an individual prediction, then briefly discuss their reasoning with a partner.

2. 5–15 min · Explicit teaching. Teacher models the meaning of a variable, coefficient, constant and like terms using a large algebra-tile representation; introduce an x-tile as one unknown amount and a unit tile as 1. Use the vocabulary and worked-example slides to model x + x + 3 = 2x + 3, highlighting that only like terms can be combined. Students annotate a quick sketch and respond to hinge questions using fingers or mini-whiteboards: “How many x-tiles are in 4x + 2?” and “Can 3x + 2 become 5x? Explain.”

3. 15–30 min · Cooperative build-and-write. Teacher places students in five mixed-readiness groups of five and assigns roles: facilitator, resource manager, builder, recorder and reporter. Distribute the Algebra Tiles Printable Pack and provide tile materials; display the group-task instruction slide. Call out or display expressions such as 2x + 4, 3x + 1, x + x + x + 5 and 4x + 2x + 3. Students build each expression, draw or photograph the model, write its symbolic form and simplify by collecting like terms. The reporter prepares one explanation for the group.

4. 30–42 min · Match, justify and challenge. Teacher gives each group a small set of expression prompts from the Algebra Tiles: Linear Expressions Pack and asks groups to match models, words and symbolic expressions. Students complete a “convince me” routine: one student states the answer, a second points to the tiles, a third checks the use of like terms, and a fourth explains why the expressions are equivalent. Groups then create one expression with two different-looking but equivalent forms for another group to solve.

5. 42–54 min · Independent application. Teacher models substitution with 3x + 2 when x = 4, explicitly replacing every x and using order of operations. Refer to the substitution and practice slides before distributing the algebra expressions practice worksheet. Students complete questions independently, then compare one answer with a partner and correct it in a different colour. Include expression identification, simplifying, substitution and one explanation question. Circulate and ask, “What does the x represent here?” and “How can you check your answer?”

6. 54–60 min · Plenary and exit check. Teacher returns to the hook using the discussion and plenary slides and invites two groups to explain equivalent expressions. Students complete the final question on the algebra expressions practice worksheet: simplify 3x + 2 + 2x + 4, then find its value when x = 2; they add one sentence explaining how they know their answer is correct. Collect responses for next-lesson grouping.

Resources

• Slide deck covering the hook, vocabulary, modelling, group instructions, substitution, discussion and plenary
• Algebra tiles or prepared x, positive-one and negative-one tiles
• the Algebra Tiles Printable Pack
• the Algebra Tiles: Linear Expressions Pack
• the algebra expressions practice worksheet
• Mini-whiteboards or scrap paper
• Pencils, coloured pens and group role cards
• Five trays or envelopes of tiles

Assessment

• Listen to hinge-question responses and inspect group models for correct identification of variables, coefficients, constants and like terms.
• During cooperative work, question students individually and note whether they can explain why expressions are equivalent rather than only state an answer.
• Use the worksheet exit response to identify students needing support with combining like terms or substitution, and students ready for two-step expressions.

Differentiation

• Support learners with colour-coded tiles, a vocabulary bank, partially completed examples and the sentence starters: “I combined ___ because they are like terms” and “I substituted ___ for x.”
• Read all worksheet instructions aloud, use a clear sans-serif font with generous spacing, avoid crowded pages and allow students to respond by drawing, speaking or writing. Pair students strategically and provide a quiet working position for learners who need reduced distraction.
• For students developing English, pre-teach variable, term, coefficient, constant, equivalent and substitute with gestures, visuals and partner rehearsal. Accept labelled diagrams before requiring full written explanations.
• Extend advanced learners by asking them to create three different expressions equivalent to 5x + 7, include brackets using the distributive property, and prove their expressions work for two different values of x.