Expanding Resource Bundles

Overview

In lesson 7 of 10 in Algebra for Kapa Haka, students connect multiplication with the distributive property. They use arrays, algebra tiles and area models to expand brackets, then explain why expressions such as (3(n+2)) are equivalent to (3n+6). Use generic resource bundles, avoiding names, prices or depictions of taonga, costumes or instruments unless guided by local Marau ā-Kura.

Learning intentions

• WALT use the distributive property to expand brackets.
• WALT connect area models and grouping models with algebraic expressions.
• WALT explain and check an expansion using algebraic and visual representations.
• WALT communicate mathematical reasoning clearly to others.

Success criteria

• I can identify the factor outside the brackets.
• I can distribute that factor to every term inside the brackets.
• I can expand accurately and collect the resulting terms where needed.
• I can explain expansion using an area or grouping model.

Curriculum links

• Pāngarau: Tau me te Taurangi — representing, manipulating and explaining algebraic expressions.
• Pāngarau: Ine me te Āhuahanga — connecting area representations with symbolic expressions.
• Te Ao Māori: learning through meaningful mathematical contexts and localised knowledge where appropriate.
• Marau ā-Kura: adapt the resource-bundle context to local iwi, hapū or kura aspirations, following local guidance.

Lesson structure (60 minutes)

1. 0–8 min · Retrieval with arrays. Display an array such as 3 rows of (n+2) objects using the retrieval and array hook slides; students sketch or build it, write (3(n+2)), and show on mini-whiteboards how many objects there are altogether. Prompt: “What does the 3 represent? What does each row contain?” Quickly revisit multiplication as repeated addition and check responses before moving on.

2. 8–18 min · Model with tiles and rectangles. Use algebra tiles and the expanding brackets area model grid to model (3(n+2)). Teacher draws a rectangle with side lengths 3 and (n+2), partitions it into (3n) and 6, and writes one transformation per line: (3(n+2)=3\times n+3\times2=3n+6). Use colour-matched arrows from the outside factor to both terms, large bracket symbols and oral rehearsal: “Three times n, three times two.” Students copy the model and complete a mini-whiteboard check for (2(x+4)).

3. 18–35 min · Team build: resource bundles. In teams of three or four, students use algebra tiles, cards and grid paper to build generic resource bundles represented by expressions such as (3(n+2)), (4(x+3)), (2(2m+5)) and (5(p+1)). Open the team task and station instruction slides and distribute the expansion recording worksheet. Each team records the expression, labels the outside factor and bracket terms, draws an area model, writes the expanded expression and photographs the finished model. Rotate roles: builder, recorder, checker and explainer. Use build-and-move stations, a visible timer and a clear stop signal.

4. 35–48 min · Expand, compare and explain. Teams place one model where another team can inspect it. Pairs use the worksheet peer checklist to verify that the factor has reached every term, the partial products are correct and the written expression matches the model. Students explain one example orally, then improve their written explanation. Ask selected students: “Why is (3(n+2)) not (3n+2)?” and “How does the rectangle show the two products?”

5. 48–55 min · Error analysis. Display three common errors through the error-analysis and discussion slides: (3(n+2)=3n+2); (4(x+5)=4x+5); and (2(3y+1)=6y+1). Students identify the error, rebuild or sketch the correct model, and write a corrected line. Use mini-whiteboards for rapid responses and question individuals to reveal whether the difficulty is identifying the factor, distributing, or multiplying.

6. 55–60 min · Exit ticket and close. Students complete the final question on the expansion recording worksheet: expand (4(a+3)), draw or describe an area model, and explain why the 4 multiplies both terms. Invite one concise oral explanation, collect the worksheet, and note which students need further support before lesson 8.

Resources

• the complete lesson slide deck
• the expansion recording worksheet
• the expanding brackets area model grid
• Algebra tiles, including positive and negative tiles if available
• Generic resource-bundle cards
• Grid paper and pencils
• Mini-whiteboards, pens and erasers
• Digital algebra tiles or interactive whiteboard
• Timer and camera/tablet for photographing models

Assessment

• Use mini-whiteboard responses during retrieval, modelling and error analysis to check understanding in real time.
• Observe team models and questioning, recording whether students identify the factor, distribute it to every term and connect the model to the expression.
• Collect the photographed model, worksheet explanation and exit ticket as evidence of symbolic fluency and mathematical communication.

Differentiation

• For dyslexic learners, provide large, clearly spaced equations; one transformation per line; colour-matched arrows; manipulatives; read-aloud or audio instructions; and time for oral rehearsal before writing.
• For students with ADHD, provide build-and-move stations, timed challenges, choice of materials, defined team roles, a visual sequence and a consistent stop signal.
• Support students with partially completed area models, highlighted brackets, sentence frames such as “The factor ___ multiplies ___ and ___ because…”, and a worked example available at the station.
• Extend advanced learners by expanding a double-bracket expression such as ((x+2)(x+3)) with an area model, collecting like terms and verifying equivalence by substituting a chosen value.