Collaborative Problem-Solving

Unit: Algebra in Everyday Life

Lesson 25 of 30

Duration: 45 minutes

Year Levels: 7–10 (support unit students working approximately at Year 2 to Year 7 levels)

Class Size: 20 students

NSW Curriculum Links

Mathematics — Number and Algebra

MA5.1-18SP (Year 7) to MA5.3-18SP (Year 10) – Use algebraic expressions to represent practical situations, solve simple linear equations, and model everyday situations.
MA5.2-19SP (Year 8) – Develop fluency with algebraic skills, including solving simple equations and describing relationships between variables.
MA5.3-9NA (Year 9) and MA5.4-9NA (Year 10) – Solve real-life problems involving linear equations, substitutions, and collaborative problem-solving.

General Capabilities

Critical and creative thinking
Personal and social capability (collaboration, empathy, communication)
Literacy (dyslexia- and language-accessible presentation of algebra problems)
Numeracy (connecting algebra to authentic, everyday contexts)

Learning Objectives

By the end of the lesson, students will:

Collaboratively solve algebraic problems grounded in everyday life contexts.
Apply basic algebraic concepts previously learned in the unit to authentic group tasks.
Use problem-solving strategies such as making tables, substitution, and simple equations.
Communicate mathematical thinking clearly, respectfully, and patiently within their group.
Develop confidence in working with peers, sharing diverse ideas, and supporting each other’s understanding.

Lesson Structure and Timing

Time (minutes)	Activity	Details & Differentiation
0 – 5	Warm-Up: Algebra Puzzle Recap	Quick whole-class interactive recap using simple fill-in-the-blank algebra statements related to everyday items (e.g., “If x represents the number of apples, then 2x + 3 is how many fruits you have if you add 3 bananas.”). Use large print, dyslexia-friendly fonts, and verbal cues. Teacher models thinking aloud.
5 – 10	Explain Collaborative Task	Present the challenge: solving a real-world algebra problem as a cooperative group. Emphasise respect, turn-taking, and helping behaviors – model this explicitly. Use visual cue cards as reminders.
10 – 30	Group Problem-Solving Activity	Groups of 4-5 students are given different authentic, scaffolded algebra problems related to everyday scenarios, such as budgeting, sharing money, shopping discounts, or time management. Provide manipulatives (counters, number lines), graphic organisers, and example problems. Teacher circulates offering assistance and prompting thinking. Integrate roles within groups: recorder, presenter, checker, encourager – to support structure and confidence. Advanced learners get extension challenge problems (e.g., multi-step substitutions or forming equations from word problems).
30 – 40	Group Presentations & Discussion	Each group presents their solution and explains their thinking process simply. Use sentence starters to support expressive language. Peers give positive feedback with provided sentence frame cards. Teacher highlights collaborative strategies and celebrates effort and teamwork.
40 – 45	Reflection and Individual Exit Slip	Students complete a simple “I feel confident about…” / “I found challenging…” exit slip, with sentence starters or symbols for those with literacy difficulties. Teacher collects to inform upcoming lessons.

Detailed Collaborative Problem-Solving Activity Examples

Scenario 1: Shopping Budget

Problem: You have $x. You want to buy 3 chocolates each costing $4 and a drink costing $2. Write an algebra expression for the total cost and find how much money you will have left if x = $20.
Supports: Use counters as dollars; substitution template; guide questions (What is the total cost? How do you find money left?).

Scenario 2: Sharing Pizza

Problem: There are x pizzas with 8 slices each. 5 friends share the slices equally. How many slices will each friend get? (Form an expression and substitute x=4)
Supports: Visual slices, sharing cutouts, guided talk.

Scenario 3: Time Management

Problem: Homework takes x minutes. Break time adds 10 minutes. If total time = 40 minutes, calculate x.
Supports: Number line, writing and solving a simple equation, teacher scaffolding.

Differentiation Strategies

For diverse learners including students with autism, behaviour, and mental health issues:
Structured group roles and clear rules for turn-taking to manage behaviour.
Break tasks into smaller, manageable steps.
Frequent positive reinforcement for participation and cooperation.
Visual supports and checklists for process steps.
For students working below expected Year 7 level:
Provide concrete manipulatives and visuals to represent algebraic concepts.
Use simple language and repeat instructions.
Scaffold tasks with worked examples and sentence starters.
Allow extra think-time and encourage peer support.
For dyslexic students:
Use dyslexia-friendly fonts, short clear sentences, and avoid clutter on handouts.
Provide instructions orally and visually.
Use coloured overlays if helpful.
Use graphic organisers and highlight key terms.
Extension for advanced learners:
Challenge to form and solve two-step equations related to the task.
Introduce simple inequalities (e.g., “If a total budget is less than $30, how many chocolates can you buy?”)
Explore creating their own word problems to present to others.

Assessment

Formative: Observation of group work and collaborative behaviours, participation in discussion, use of algebra strategies.
Exit Slip: Quick written or pictorial feedback on confidence and challenges with the problem-solving process.
Teacher notes: Use reflections and work samples to plan targeted interventions or extensions for upcoming lessons.

Teacher Notes

Emphasise real-world relevance of algebra to careers and everyday problem solving, linking to the teacher’s expertise as a Careers Advisor to foster meaningful learning.
Encourage respect, kindness, and maturity in group interactions reflecting workplace expectations.
Use authentic examples students can relate to from daily life or potential jobs.
Maintain predictable routines and visual supports to reduce anxiety and enhance focus.
Celebrate small successes to build self-esteem and motivation.

This carefully scaffolded collaborative problem-solving lesson builds not only algebraic skills but also critical social and emotional capabilities necessary for post-school success, truly embracing the diverse needs of your unique students.

If desired, I can also provide printable versions of materials, visual cue cards, or sentence starter sheets tailored for dyslexia and social-emotional support.

Teaching Instructions