Mathematics · Year 6 · Problem Solving and Investigations · Term 4

Exploring Problem Solving Strategies

Exploring and applying various problem-solving strategies such as working backwards, drawing diagrams, and looking for patterns.

• ACARA Content Descriptions
• AC9M6N07
• AC9M6A03

About This Topic

In Year 6 mathematics, students explore problem-solving strategies such as working backwards, drawing diagrams, and looking for patterns. They apply these methods to multi-step word problems, compare strategy effectiveness, design step-by-step plans, and justify their choices. This work supports AC9M6N07 on efficient calculation strategies and AC9M6A03 on equivalent algebraic expressions, while developing core reasoning skills.

These strategies build flexibility and perseverance, as students recognise that different problems demand different approaches. For instance, working backwards suits finding missing values in sequences, while diagrams clarify spatial relationships in resource allocation tasks. Classroom discussions reveal how patterns simplify complex calculations, linking to broader number and algebra proficiencies.

Active learning benefits this topic greatly, as students experiment with strategies on shared problems during group challenges. Collaborative trials and peer feedback make abstract methods concrete, boost confidence in justification, and highlight real-world applications like planning events or solving puzzles.

Key Questions

1. Compare the effectiveness of different problem-solving strategies for a given problem.
2. Design a step-by-step approach to solve a multi-step word problem.
3. Justify the choice of a particular strategy for a specific mathematical challenge.

Learning Objectives

• Compare the effectiveness of working backwards, drawing diagrams, and looking for patterns for solving specific multi-step word problems.
• Design a step-by-step problem-solving plan for a given multi-step word problem.
• Justify the choice of a particular problem-solving strategy for a specific mathematical challenge.
• Create a new word problem that can be effectively solved using the 'look for a pattern' strategy.

Before You Start

Four Operations (Addition, Subtraction, Multiplication, Division)

Why: Students need a solid understanding of basic arithmetic operations to apply them within problem-solving strategies.

Introduction to Word Problems

Why: Students should have prior experience interpreting and solving single-step word problems before tackling multi-step challenges.

Key Vocabulary

Working Backwards	A strategy where you start with the final answer and reverse the steps to find the initial value or unknown.
Drawing Diagrams	A strategy that involves visually representing the problem using pictures, charts, or graphs to understand relationships and find solutions.
Looking for Patterns	A strategy where you identify repeating sequences or relationships within the data of a problem to predict or solve for unknowns.
Multi-step Word Problem	A mathematical problem that requires more than one operation or logical step to find the solution.

Watch Out for These Misconceptions

Common Misconception

One strategy works for every problem.

What to Teach Instead

Students often assume trial and error suffices universally. Group comparisons during relay activities reveal context-specific strengths, like patterns for sequences versus diagrams for spatial tasks. Peer debates build metacognition on strategy selection.

Common Misconception

Diagrams are only for geometry problems.

What to Teach Instead

Many view diagrams as geometry-exclusive. Hands-on gallery walks expose their value in word problems like sharing resources. Students redraw peers' diagrams, seeing versatility firsthand.

Common Misconception

Working backwards is too slow for simple problems.

What to Teach Instead

Learners dismiss it for quick tasks. Timed pair swaps demonstrate its efficiency for unknowns in chains. Justification discussions affirm when speed trades for accuracy.

Active Learning Ideas

Pairs Challenge: Strategy Swap

Pairs solve the same multi-step word problem using different strategies, such as one drawing a diagram and the other working backwards. They swap papers after 10 minutes, explain the approach used, and evaluate its strengths. Discuss as a class which worked best and why.

30 min·Pairs

Small Groups: Pattern Hunt Relay

Divide a sheet of pattern-based problems among group members. Each solves one using a chosen strategy, passes to the next for verification and pattern extension. Groups race to complete and justify their full solutions.

45 min·Small Groups

Whole Class: Diagram Gallery Walk

Students create posters showing diagrams for various problems. Display around the room. Class walks, notes strategies, and votes on most effective visuals. Debrief on when diagrams outperform other methods.

50 min·Whole Class

Individual: Strategy Journal

Students tackle three problems solo, recording strategies tried, successes, and adjustments. Share one entry with a partner for feedback. Compile class insights on versatile strategies.

25 min·Individual

Real-World Connections

• Logistics planners use 'working backwards' to schedule delivery routes, starting from the final drop-off time and calculating departure times for each stop.
• Architects and engineers use diagrams extensively to visualize complex structures, plan spatial arrangements, and identify potential design challenges before construction begins.
• Financial analysts look for patterns in market data to predict stock trends or identify investment opportunities, using historical information to inform future decisions.

Assessment Ideas

Quick Check

Present students with two different word problems. Ask them to write down which strategy (working backwards, drawing diagrams, looking for patterns) they would use for each problem and briefly explain why.

Exit Ticket

Give students a multi-step word problem. On their exit ticket, they should show their chosen strategy, the steps they took, and write one sentence explaining why their strategy was a good choice for this problem.

Discussion Prompt

Pose a complex word problem to the class. Ask: 'What are two different strategies we could use to solve this? How would the steps differ for each strategy? Which strategy do you think is more efficient and why?'

Frequently Asked Questions

How do I teach working backwards in Year 6 maths?

Start with concrete examples like reversing subtraction steps in money problems. Model on the board: from final amount, subtract to find start. Pairs practise on age or distance puzzles, then justify steps aloud. Progress to abstract number sequences, linking to AC9M6N07 fluency.

What activities build pattern recognition for problem solving?

Use relay races with growing patterns in tiles or numbers. Groups extend sequences, test predictions, and verify with diagrams. This reinforces AC9M6A03 equivalents while showing patterns simplify multi-step work. Follow with class pattern-sharing to spot common errors.

How does active learning help students master problem-solving strategies?

Active approaches like strategy swaps and gallery walks let students test methods hands-on, compare outcomes in real time, and refine through peer input. This builds justification skills via discussion, makes failures learning moments, and connects strategies to authentic challenges, far beyond worksheets.

How can students justify strategy choices effectively?

Prompt structured reflections: state problem, chosen strategy, why it fits, evidence of success. Role-play defences in pairs. Rubrics score clarity and reasoning. Link to key questions by analysing class data on strategy wins, fostering metacognitive habits for AC9M6N07 and beyond.