Balance and Simplify

Overview

Students build on prior learning about variables, coefficients and inverse operations. They use movement, algebra tiles and balance models to simplify linear expressions and solve two-step equations, explaining why each step preserves equality.

Learning intentions

• WALT identify like terms and simplify linear expressions.
• WALT use inverse operations to solve two-step equations.
• WALT check solutions by substituting them back into the original equation.
• WALT explain algebraic thinking using mathematical language, including appropriate kupu Māori.

Success criteria

• I can identify terms, coefficients, constants and like terms.
• I can combine like terms accurately.
• I can undo operations in the correct order to solve a two-step equation.
• I can check my answer and explain whether both sides are equal.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: connected challenge that extends relevant textbook learning.
• Mathematical reasoning, problem solving and communication through explaining equivalent expressions and justifying solution steps.
• Te Mātaiaho classroom practice: inclusive, collaborative learning that supports learners to communicate mathematical ideas in different ways.

Lesson structure (45 minutes)

1. 0–5 min · We Do — Active hook. Display the question “Are 3x + 2x + 4 and 5x + 4 always equal?” on the opening hook slide. Teacher frames the learning and invites students to move to one side of the room for “yes” and the other for “no”. Students briefly justify their choice to a partner using “I think… because…”. Transition: teacher connects students’ ideas to the vocabulary and examples that follow.

2. 5–12 min · I Do — Vocabulary and modelling. Teacher uses the vocabulary and worked-example slides to introduce term, coefficient, variable, constant, like terms and equivalent expressions; model 3x + 2 + 4x − 5 by grouping like terms and thinking aloud. Students echo key terms, identify the like terms in two examples, and use gestures or mini-whiteboards to show whether terms can be combined. Transition: teacher explains that students will now build expressions together using concrete materials.

3. 12–20 min · We Do — Build and simplify. Teacher places students in six groups of five and distributes the Algebra Tiles: Linear Expressions Pack. Teacher calls an expression such as 2x + 3x + 4; students physically group matching tiles, write the simplified expression on a mini-whiteboard, and hold it up. Repeat with subtraction and negative constants, pausing to address common errors such as combining x with a number. Transition: teacher links the grouped tiles to the balance model and explains that the class will apply the same reasoning to equations.

4. 20–30 min · I Do, then We Do — Model two-step equations. Teacher revisits the equation modelling slides and demonstrates 2x + 3 = 11 using a balance model: remove 3 from both sides, then divide both sides by 2. Students stand and mime each inverse operation. Teacher then prompts students to solve 3x − 4 = 14 on whiteboards, asking, “What must we undo first, and why?” Students show their working and answers; teacher checks responses and addresses misconceptions before the independent application. Transition: teacher explains the solver-and-checker roles and the support available during practice.

5. 30–40 min · You Do — Paired practice and teacher workshop. Teacher distributes the simplifying and solving worksheet and sets clear solver-and-checker roles. Students work in pairs, taking turns as solver and checker: simplify four expressions, solve four two-step equations, and check at least two answers by substitution. Teacher circulates, uses the balance language with learners needing support, and runs a short guided group using the Algebra Balance Mat for students who need a concrete representation. Early finishers attempt the challenge questions and create an equation with a chosen solution. Transition: teacher gives a brief time warning, then brings students together for movement-based reflection and the exit check.

6. 40–45 min · You Do, with We Do sharing — Movement plenary and exit check. Teacher displays the plenary and reflection slides. Students rotate to a partner and explain one step from solving 4x + 5 = 21, then complete the exit prompt: “Simplify 6x + 2x − 3. Solve 2x + 7 = 19. Show one check.” Teacher collects responses as students leave and uses them to identify next steps.

Resources

• the algebra introduction and modelling deck
• the simplifying and solving worksheet
• the Algebra Tiles: Linear Expressions Pack
• the Algebra Balance Mat
• Mini-whiteboards, pens and erasers
• Large room space or clear movement pathways
• Group tables arranged for six groups of five

Assessment

• Use movement choices, vocabulary responses and mini-whiteboards to identify misconceptions about like terms and inverse operations.
• During paired practice, check that students preserve equality, use the correct operation order and explain their reasoning rather than only recording answers.
• Use the exit prompt to identify who can simplify, solve and verify independently; group students for the next lesson based on the result.

Differentiation

• Support: provide a worked example, colour-code matching terms, read instructions aloud, and offer sentence frames such as “I removed ___ from both sides because ___.”
• Neurodivergent learners: use the movement-based responses, hands-on tiles, short timed sections and purposeful partner roles; allow standing, fidgeting or working at a standing space where appropriate.
• Bilingual Māori unit: invite students to explain ideas in English, te reo Māori or both; display agreed classroom kupu alongside English and accept oral, drawn or symbolic explanations.
• Extension: students solve equations involving brackets or negative coefficients, compare two different solution methods, and write a Mathsteaser-style equation with a deliberate common error for a partner to find and explain.