Computer Science · 11th Grade

Active learning ideas

Introduction to Data Structures: Graphs

Graphs are abstract and visual, which makes them perfect for active learning. Students need to physically and socially engage with nodes, edges, and relationships to move beyond memorizing vocabulary and start recognizing graphs in their daily lives.

• Common Core State Standards
• CSTA: 3B-AP-13

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Concept Mapping
• 20 min · Whole Class

Kinesthetic Activity: Human Graph Construction

Students each represent a node and use yarn or string to form edges based on relationships (who lives nearest, who shares a hobby). The class then analyzes properties: Is the graph directed or undirected? Weighted? Does everyone have a path to everyone else? This creates immediate intuition for graph vocabulary before formal definitions.

Explain what a graph is and identify its components (nodes/vertices, edges).

Facilitation Tip

During Human Graph Construction, assign roles like timekeeper and recorder to keep movement organized and purposeful.

What to look for

Provide students with a scenario, such as 'a city bus system'. Ask them to draw a small graph representing a few bus stops and routes. They should label the nodes and edges and indicate if the graph is directed or undirected, explaining their choices.

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Real-World Graph Identification

Students receive a list of 8 real-world systems (airline routes, power grids, Facebook friendships, course prerequisites) and individually identify which are best modeled as directed versus undirected graphs and why. Pairs compare and defend their reasoning before a class discussion surfaces interesting edge cases.

Analyze real-world examples that can be modeled using graphs (e.g., social networks, road maps).

Facilitation Tip

For Real-World Graph Identification, provide a mix of obvious and subtle examples to push students beyond surface-level connections.

What to look for

Present students with two different real-world examples: a family tree and a subway map. Ask: 'How are these similar in terms of their underlying structure? How are they different? What kind of graph representation (directed/undirected, weighted/unweighted) would best model each, and why?'

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

Activity 03

• Gallery Walk
• 30 min · Small Groups

Gallery Walk: Graph Representation Comparison

Groups create side-by-side posters showing the same small graph as a drawing and as an adjacency list. Other groups annotate which representation they would prefer for different operations (adding a node, finding all neighbors) and leave sticky-note reasoning on each poster.

Differentiate between various ways to represent a graph (e.g., drawing, adjacency list concept).

Facilitation Tip

In Gallery Walk, require each group to present one representation they found most challenging to interpret.

What to look for

Show students a visual representation of a graph (e.g., a simple drawing with dots and lines). Ask them to count and state the number of nodes and edges. Then, present a second graph and ask if it represents a directed or undirected relationship, and why.

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

Activity 04

• Case Study Analysis
• 25 min · Small Groups

Case Study Analysis: The Internet as a Graph

Groups analyze a simplified diagram of internet router connections and answer structured questions: How many hops does it take to travel from node A to node B? What happens if one node fails? What does edge weight represent here? Groups share findings and connect to real network design decisions.

Explain what a graph is and identify its components (nodes/vertices, edges).

Facilitation Tip

During The Internet as a Case Study, provide a simplified URL network so students can trace paths without feeling overwhelmed by scale.

What to look for

Provide students with a scenario, such as 'a city bus system'. Ask them to draw a small graph representing a few bus stops and routes. They should label the nodes and edges and indicate if the graph is directed or undirected, explaining their choices.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

A few notes on teaching this unit

Start with concrete, relatable examples before introducing formal definitions. Avoid overwhelming students with too many graph types at once. Use analogies carefully, as they can reinforce misconceptions if not precise. Research shows that students grasp abstract structures better when they first experience them through physical movement and social interaction.

Students will confidently identify and describe graphs using correct terminology, explain differences between graph types, and apply these concepts to real-world scenarios with clear reasoning.

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Watch Out for These Misconceptions

• During Human Graph Construction, watch for students who equate all graphs with trees because they see the connecting lines as hierarchical.

  After students build their human graph, ask them to identify any cycles or multiple paths between nodes. Then, have them modify their graph to remove cycles and designate a root to see how it changes into a tree structure.

• During Real-World Graph Identification, watch for students who assume every graph must have many connections between nodes.

  When analyzing sparse examples like a subway map, have students count the average connections per node and compare it to a family tree example to highlight the difference between dense and sparse graphs.

• During Gallery Walk, watch for students who assume all edges represent two-way relationships.

  At each station, ask students to check whether reversing an edge would make sense in the real-world context. For directed examples like web links, have them physically turn their bodies to demonstrate one-way relationships.

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Methods used in this brief

• Concept Mapping
• Think-Pair-Share
• Gallery Walk
• Case Study Analysis