Identifying Sub-problems and Dependencies

Active learning works because abstraction and pattern recognition are skills best developed through concrete, hands-on experiences. Students need to practice filtering details and spotting relationships with real materials and scenarios, not just listening to explanations.

• Year 6
• Technologies
• 3 activities
• 15 min–40 min

Learning Objectives

1. Analyze the dependencies between different components of a complex system, such as a school event planning process.
2. Justify the logical sequence for completing tasks within a project by evaluating their interdependencies.
3. Deconstruct a familiar daily routine into its constituent sub-problems and represent these relationships visually.
4. Identify critical sub-problems in a given scenario that, if not solved, would prevent the overall project from succeeding.

Gallery Walk

⏱ 30 min·Whole Class

Gallery Walk: The Map Challenge

Students are shown three different 'maps' of the same area: a satellite photo, a street map, and a simplified transit map. They move around the room and use sticky notes to identify what information has been 'abstracted' (removed) from each one and why.

Prepare & details

Analyze the dependencies between different sub-problems in a larger project.

Facilitation Tip: During the Gallery Walk, position yourself near one map station to listen for students who are using vague language like 'stuff' or 'things' and gently ask them to point to the exact part of the map they mean.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Inquiry Circle

⏱ 40 min·Small Groups

Inquiry Circle: Pattern Detectives

Groups are given a set of different board game rules. They must find the 'patterns' that all the games share (e.g., 'taking turns,' 'having a goal,' 'using a dice') and create a 'Master Rule Set' that could work for any new game.

Prepare & details

Justify the order in which sub-problems should be addressed.

Facilitation Tip: In Collaborative Investigation, circulate and ask pairs to explain how the pattern they found in one system (e.g., music) connects to a second system (e.g., code), ensuring they articulate the 'repeat' or 'loop' relationship.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: Emoji Abstraction

Students are asked to draw an emoji for a complex emotion like 'disappointed but hopeful.' They share their drawings in pairs and discuss which facial details they kept and which they ignored to make the meaning clear. This is a perfect example of abstraction.

Prepare & details

Construct a flow chart showing the decomposition of a daily routine.

Facilitation Tip: During Think-Pair-Share, listen for students who only describe emojis literally and guide them to explain what the emoji represents or how it functions in a sequence.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Experienced teachers approach this topic by modeling how to break problems into smaller parts and showing how dependencies create order. Avoid rushing to solutions; instead, slow down to emphasize the process of identifying what depends on what. Research suggests that students learn abstraction best when they physically manipulate or rearrange materials to highlight what matters and what can be ignored.

What to Expect

Successful learning looks like students identifying sub-problems and dependencies clearly, explaining their reasoning with examples, and applying these concepts to new situations. They should move from vague ideas to precise, actionable steps in their thinking.

Watch Out for These Misconceptions

Common Misconception

During Gallery Walk, watch for students who think abstraction simply means 'making something smaller or easier.'

What to Teach Instead

Use the map stations to redirect them: ask them to compare a highly detailed map to a simplified one, then have them explain which one works better for giving directions and why.

Common Misconception

During Collaborative Investigation, watch for students who struggle to connect patterns across subjects like music and code.

What to Teach Instead

Have them physically clap or tap the rhythm of a song while another student traces a loop in a simple code example, then ask them to describe how the two actions represent the same pattern.

Assessment Ideas

Quick Check

After the Gallery Walk, ask students to write down one sub-problem and one dependency from the map challenge scenario you provided (e.g., 'Finding the fastest route from Central to Circular Quay depends on knowing the train lines'). Collect and review these to check their understanding of functional abstraction.

Discussion Prompt

During Collaborative Investigation, listen for pairs to explain how a pattern they found in one system (e.g., a repeating chorus in a song) is similar to a pattern in another (e.g., a loop in a code snippet). Note which pairs can articulate the 'repeat' or 'loop' relationship clearly.

Exit Ticket

After Think-Pair-Share, provide an exit ticket with a simple sequence of emojis (e.g., 🍎🍏🍎🍏) and ask students to identify the pattern and create a second sequence that follows the same rule. Collect these to assess their ability to recognize and apply patterns.

Extensions & Scaffolding

• Challenge students to create their own abstraction of a complex real-world system (e.g., a school cafeteria) and present it to the class, explaining what they filtered out and why.
• Scaffolding: Provide partially completed flowcharts with missing steps or dependencies for students to fill in, using familiar routines like making toast.
• Deeper exploration: Have students research how a profession like urban planning or software development uses abstraction and pattern recognition in their daily work.

Key Vocabulary

Sub-problem	A smaller, more manageable part of a larger, more complex problem. Breaking down a big task makes it easier to solve.
Dependency	A relationship where one task or sub-problem cannot be started or completed until another one is finished.
Decomposition	The process of breaking down a complex system or problem into smaller, simpler parts.
Critical Path	The sequence of sub-problems that must be completed on time for the overall project to be completed by its deadline. Any delay on this path delays the whole project.