Problem Sequence Designer
A Problem Sequence is a structured learning cycle built around a non-routine anchor problem. It helps students make meaning first, develop formal mathematical language, and generalise their understanding across contexts.
The Problem Sequence Designer automatically creates ready-made sequences—so teachers can focus on teaching, discussion, and noticing student thinking rather than building resources from scratch.
The Philosophy Behind Problem Sequences
Five principles that guide how sequences are designed
Concepts Before Labels
Students enter the mathematics without needing formal words first. Sequences move from everyday language (anchor problem) to formal language (explicit teaching + variation problem).
Structure Shapes Thinking
The same content can demand different reasoning depending on the problem's structure. Sequences surface the structure so students learn transferable ways of thinking.
Productive Struggle
Non-routine problems create a need for strategy choice, representation, and justification. Teachers respond by prompting, selecting, and comparing strategies.
Variation Builds Transfer
A second problem with the same structure—but different numbers and context—helps students see what stays the same mathematically and apply concepts flexibly.
Consolidation Makes Learning Visible
Students generalise, justify, and reflect. Teachers capture evidence of learning and identify next steps for continued growth.
"Teach less telling, more meaning-making."
Generate a sequence, try it once, and refine based on what your students show you.
The Problem Sequence Components
Each component serves a specific purpose in the learning cycle
1. The Hook
Orient attention and create curiosityHooks orient attention to the mathematical concept and create curiosity without teaching a method.
What it includes:
- 3 concept-aligned hooks of different types (WODB, Would You Rather, Same & Different, etc.)
- One picture book relevant to the concept (title + author + rationale)
Teacher Intent
Use a hook to launch noticing and wondering so students enter the anchor problem ready to attend to important relationships. The hook activates prior knowledge without revealing the solution pathway.
2. Anchor Problem
Create productive struggleA non-routine problem where the method is not obvious, multiple strategies are viable, and students must justify and convince.
Language Rule:
Written in everyday language, avoiding formal terms that will be taught later. Example: "same amount, different number of pieces" instead of "equivalent fractions"
Reduce barriers while keeping structure
Increase depth without changing structure
Surfacing Student Thinking
The anchor problem is designed to surface what students bring rather than explicitly teaching before students have the opportunity to problem solve. Teachers observe, prompt, and gather evidence of student reasoning.
Enabling prompts simplify numbers, provide representations, or narrow choices while preserving the concept. Extending prompts add constraints, ask for all solutions, or require proof.
3. Explicit Teaching
Consolidate meaning, name the mathematicsTeaching starts from student work: What did they notice? What strategies emerged? Where did misconceptions appear?
Key terms introduced as they become meaningful—simple language first, formal terms added once concepts are grounded
The key relationships, invariants, and mathematical structure behind student solutions
Compare approaches for efficiency, clarity, and generality
Concrete modelling to make the structure visible
Responsive Teaching
Explicit teaching is responsive, not scripted. It emerges from what students showed during the anchor problem. The teacher's role is to select, sequence, and connect student strategies to the mathematical goal.
A central move is helping students evaluate approaches: compare two student strategies, discuss efficiency, and prompt students to choose what they would try next.
4. Variation Problem
Generalise the structureA second problem with the same underlying structure but different context, numbers, and surface features.
Variation Rules:
- Same structure and concept
- Different context, numbers, materials
- Not a "reskin" of the anchor problem
Building Transfer
The variation problem helps students see what stays the same mathematically when surface features change. This builds flexible, transferable understanding rather than context-dependent procedures.
Students apply their refined strategies and newly acquired language, demonstrating growth from the anchor problem experience.
5. Consolidation
Secure learning, capture evidenceStudents generalise, justify, and reflect. Teachers capture evidence and identify next steps.
Concept-focused discussion
Apply beyond context
Build conceptual boundaries
Capture individual thinking
Demonstrating Understanding
Consolidation offers ways for students to demonstrate their conceptual understanding. Through reflection, generalisation, and justification, students make their learning visible.
Students leave with:
- Clearer conceptual understanding
- Stronger strategy use
- Improved ability to justify and generalise
What the Designer Produces
- Year level + concept tags
- Australian Curriculum alignment
- 3 curiosity hooks + picture book
- Non-routine anchor problem
- Enabling & extending prompts
- Explicit teaching guidance
- True variation problem
- Consolidation prompts
3 free sequences to try
One deck. Endless thinking possibilities.
This powerful deck includes four card types: Strategy, Challenge, Scaffold, and Reflect — designed to build problem-solving capabilities in any classroom.
Use them during rich tasks to nudge thinking, prompt decisions, or make learning visible.
Four Card Types
Each card type serves a specific purpose in developing problem-solving skills
Strategy
Provides thinking prompts and problem-solving approaches
Challenge
Encourages deeper exploration and extension of thinking
Scaffold
Offers support and guidance when students get stuck
Reflect
Promotes metacognition and learning reflection
Free Sample Pack
Get a taste of our problem-solving cards with this free sample pack. Includes 1 example from each of our four card types.
1
Strategy Card1
Challenge Card1
Scaffold Card1
Reflect CardSee what the cards look like • Check back soon
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