Simplifying Expressions

Overview

In this second lesson of the 10-lesson unit Algebra for Kapa Haka, students build on their understanding of variables, coefficients and constants. Through a fictional rehearsal plan, they identify like terms, simplify expressions and evaluate them for different numbers of participants, using algebra tiles before recording symbolic reasoning.

Learning intentions

• WALT identify and combine like terms.
• WALT simplify algebraic expressions accurately.
• WALT substitute a value and evaluate an expression.
• WALT explain why unlike terms cannot be combined.

Success criteria

• I can identify terms with the same variable and power.
• I can use algebra tiles or symbols to simplify an expression.
• I can substitute a given value and calculate correctly.
• I can explain why terms such as (x) and (y), or (x) and a constant, remain separate.

Curriculum links

• Pāngarau: Tau me te Taurangi — use algebraic representations, simplify expressions and reason about relationships.
• Te Reo Rangatira: Kōrero and Whakaatu — explain mathematical thinking orally and through symbolic or visual representations.
• Marau ā-Kura: connect mathematical modelling to a local context while using fictional, culturally safe rehearsal examples.
• Cross-curricular links: financial literacy through resource totals and digital technologies through structured symbolic processes.

Lesson structure (60 minutes)

1. 0–7 min · Retrieval quiz. Open with the retrieval quiz slides and distribute the simplifying and evaluating expressions worksheet. Students independently answer five short questions: identify the variable, coefficient and constant in an expression; write a repeated addition as multiplication; and interpret a simple rehearsal expression such as (4p+2). Review answers quickly, asking students to justify one response.

2. 7–17 min · Teacher modelling. Use the modelling slides and physical algebra tiles to represent a fictional rehearsal plan, for example (3p+2p+4), where (p) represents participant groups and 4 represents resource items. Model grouping (p)-tiles with (p)-tiles and unit tiles with unit tiles, then record (5p+4). Include a hinge question: “Can (5p) and 4 be combined? Why or why not?” Students rehearse an oral explanation with a partner before writing it on the worksheet.

3. 17–35 min · Collect-like-terms relay. Set up four task stations with algebra tiles, symbol cards and counters. Display the relay instructions on the relay instruction slides. In groups of four or five, students draw or receive an expression, build it, collect like terms, write the simplified form and have a peer check it before moving to the next station. Use short two- or three-minute rounds and assign roles such as builder, recorder, checker and runner. Confer with groups, asking, “What makes these terms alike?” and “How does your model prove your answer?”

4. 35–48 min · Evaluate for different values. Display the evaluation slides and direct groups to the evaluation section of the simplifying and evaluating expressions worksheet. Each group receives expressions connected to fictional rehearsal groups, such as (3p+5), (2g+4p+1), or (6p+2), and evaluates them for specified values of (p) or (g). Students first simplify where possible, substitute the value using brackets, calculate, and peer-check using a calculator only to verify. Ask groups to compare how the total changes when the number of participants increases.

5. 48–55 min · Error analysis. Show two worked examples on the error-analysis slides, including an error such as (3p+2p=5p) and an incorrect attempt to combine (4p+3) as (7p). Students identify the error, correct it on the worksheet and give a one-minute oral or written explanation. Invite several groups to share reasoning, emphasising that unlike terms represent different quantities.

6. 55–60 min · Self-assessment and exit check. Return to the plenary slides. Students complete the self-assessment on the simplifying and evaluating expressions worksheet by rating their confidence and completing: “I know terms are like terms when…” and “For (4p+3), when (p=5), the value is… because…”. Collect worksheets and invite selected students to record their explanation by voice if writing is a barrier.

Resources

• the simplifying expressions lesson deck
• the simplifying and evaluating expressions worksheet
• Algebra tiles, including positive and negative tiles if available
• Expression symbol cards and counters
• Four labelled task stations
• Calculators for checking only
• Visual timer and group-role checklist
• Large-print worked examples and audio instructions

Assessment

• Use retrieval responses, hinge questions and observation of tile models to identify misconceptions immediately.
• During the relay and evaluation task, use teacher conferencing and peer checking to assess identification of like terms, simplification and substitution.
• Assess the annotated worksheet and the final one-minute explanation for accurate calculation and reasoning about unlike terms.

Differentiation

• Support dyslexic learners with colour-coded terms, large-print examples, one example per line, reduced copying, read-aloud or audio instructions, manipulatives and oral rehearsal before writing.
• Support learners with ADHD through short relay rounds, movement between stations, a visible checklist, clear roles and a choice of standing or seated work.
• Provide a worked example, vocabulary prompts and sentence frames: “These are like terms because…” and “I substituted ___ for ___, so…”.
• Allow students to explain by voice, drawing or writing. Pair students thoughtfully and check that fictional examples do not require disclosure of cultural affiliation or reproduction of protected material.

Extension

• Students compare two expressions that model the same fictional rehearsal total, such as (3p+2p+4) and (5p+4), and prove their equivalence using algebra tiles and at least two values.
• Challenge students to create two different-looking expressions for the same total, then explain why they are equivalent algebraically and numerically.