Factorising Resource Plans

Overview

In lesson 8 of the 10-lesson unit Algebra for Kapa Haka, ākonga reverse the distributive property to factorise simple algebraic expressions. They connect algebraic grouping with organising resources for a fictional kapa haka plan, while checking that factorised and expanded forms are equivalent.

Learning intentions

• WALT factorise simple algebraic expressions by identifying a common factor.
• WALT write an expression as a product of factors.
• WALT check factorisation by expanding.
• WALT explain how factors can represent organised resource groups in a plan.

Success criteria

• I can find the greatest common factor in a simple expression.
• I can write an expression as a product using brackets.
• I can expand my answer to check that it is equivalent.
• I can explain what the factors mean in a fictional resource plan.

Curriculum links

• Pāngarau: Tau me te Taurangi, using algebraic expressions, factors, products and the distributive property.
• Te Reo Rangatira: Kōrero, whakarongo and whakaatu through mathematical explanation, peer teaching and presenting reasoning in te reo Māori or the kura’s agreed bilingual language practices.
• Marau ā-Kura: Connects mathematical organisation and planning to a fictional kapa haka context, using local language, narratives or resource examples where appropriate.
• Develops mathematical communication, reasoning, collaboration and problem-solving through hands-on representation and explanation.

Lesson structure (60 minutes)

1. 0–8 min · Retrieval: expand. Teacher opens the retrieval and lesson introduction slides and displays four quick expansions, such as (3(x+2)), (5(a+1)), (2(4y+3)) and (7m+14) written in expanded form; students solve the first three independently on whiteboards and explain how the fourth could be written with brackets. Check responses rapidly, asking: “What operation happened when the bracket was expanded?” Record factor, product and equivalent as they arise.

2. 8–18 min · Model the reverse distributive property. Teacher uses the next slides and a worked example, (6x+12=6(x+2)), thinking aloud: identify the greatest common factor, divide each term by it, place the remaining terms inside brackets, then expand to check. Model a second example, (4a+20=4(a+5)), using colour to highlight the common factor. Students copy one example, then complete (8p+24=) and show the check by expanding. Invite a student to explain the process using the sentence frame: “The common factor is ___ because ___.”

3. 18–35 min · Pair sort: factors and representations. Teacher forms 12 pairs and distributes factor cards, algebra tiles, sorting hoops and the factorising record and practice sheet; display the pair-sort instructions from the hands-on sorting and discussion slides. Each pair sorts expressions into “can factorise with a common factor”, “factorised form”, and “needs checking”, building selected expressions with tiles where useful. Students match examples such as (3x+9) with (3(x+3)), identify the greatest common factor, and record the match and an expansion check. Partners use roles: builder/reader and recorder/checker, changing roles halfway through. Teacher conferences with pairs, listening for whether students confuse a term with a factor.

4. 35–48 min · Collaborative factorise-and-check challenge. Teacher displays the challenge rounds from the collaborative challenge slides and gives each group a fictional kapa haka resource plan, for example: “Six groups each need (x+4) poi items. Represent the total as an expression and as a product.” Groups solve three progressively challenging expressions, including (5x+15), (4y+28) and (7n+21), then expand to verify each answer. Students place each completed solution on the group’s visible completion board and nominate one explanation showing what the outside factor and bracket could represent. Teacher pauses for an individual check question: “Factorise (9r+18) and expand your answer.”

5. 48–55 min · Peer teaching. Teacher assigns each student a partner from another group and displays the peer-feedback prompts. Students teach one example from their record, explaining the common factor and the check. The listener responds with: “I agree because…”, “I checked by…”, or “Please explain…”, then gives one specific piece of feedback. Teacher circulates, noting accurate vocabulary, clear reasoning and any need for a brief reteach.

6. 55–60 min · Exit ticket and close. Teacher distributes the final section of the factorising record and practice sheet and returns to the plenary and exit-ticket slides. Students independently complete: (a) factorise (6q+18), (b) expand their answer to check it, and (c) write one sentence explaining what the factors could represent in a resource plan. Collect responses as evidence for the next lesson. Close by revisiting the WALT and inviting two students to share a useful checking strategy.

Resources

• the algebra retrieval, modelling, activity instructions and plenary deck
• the factorising record and practice sheet
• Teacher-prepared factor cards with expressions and matching factorised forms
• Algebra tiles or equivalent tactile representations
• Sorting hoops or labelled floor/table areas
• Mini-whiteboards, pens and erasers
• Group completion boards or progress strips
• Check sheets and peer-feedback prompts
• Accessible printed directions and audio directions

Assessment

• Observe pair sorting and listen to explanations; assess whether students identify the greatest common factor rather than only a visible coefficient.
• Use the individual (9r+18) check question, teacher conferences and peer feedback to identify misconceptions.
• Collect the exit ticket and factorisation record, checking factorised form, expansion check and resource-plan explanation.

Differentiation

• For dyslexic ākonga, use uncluttered cards, accessible print, symbols and words together, colour-coded common factors, tactile tiles, reduced item sets, audio directions and the option to respond orally. Read instructions aloud and avoid unnecessary copying.
• For ākonga with ADHD, use movement-based sorting, short challenge rounds, partner roles, a visible completion board and clear one-step instructions. Provide a quiet workspace or brief reset option where needed.
• Support learners with a factorisation scaffold: “Find the greatest common factor → divide each term → write brackets → expand to check.” Begin with positive coefficients and two terms.
• Extension learners factorise expressions using a negative common factor, such as (-3x-12=-3(x+4)), or explain why an expression such as (x+5) cannot be factorised further at this level.