Computer Science · 10th Grade

Active learning ideas

Introduction to Graph Algorithms

Active learning works for graph algorithms because these concepts are inherently visual and kinesthetic. Moving from abstract diagrams to human-scale simulations helps students internalize how traversals work. By physically acting out BFS and DFS, tracing paths on paper, and debating algorithm choices, students build durable mental models instead of memorizing steps.

• Common Core State Standards
• CSTA: 3A-AP-14

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Role Play
• 25 min · Whole Class

Role Play: Human BFS and DFS

Students each receive a node number. For BFS, the teacher calls out nodes by layer: start node, then all its neighbors, then all their unvisited neighbors. For DFS, one path is followed as deep as possible before backtracking. Students stand when visited. The contrast in visiting order between BFS and DFS is immediate and memorable with 10-15 students.

Explain the components of a graph and their representation.

Facilitation Tip

During Human BFS and DFS, assign clear roles for 'explorers', 'queue trackers', and 'visited node markers' to avoid chaos and keep everyone engaged.

What to look for

Provide students with a small, labeled graph. Ask them to draw the order in which nodes would be visited using BFS starting from a specific node, and then repeat for DFS. Check for correct application of each algorithm's rules.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 02

• Inquiry Circle
• 35 min · Small Groups

Inquiry Circle: Trace the Traversal

Groups of 3 receive a drawn graph with 7-8 nodes and perform both BFS and DFS starting from the same node, writing out the order of visited nodes for each. Groups compare their BFS and DFS orderings and explain why they differ. Surfaces that the same graph yields different valid orderings and that algorithm choice determines what you find first.

Analyze the process of Breadth-First Search (BFS) on a given graph.

Facilitation Tip

During Trace the Traversal, have students work in pairs so one student traces with a colored pen while the other records the step-by-step order aloud.

What to look for

On an index card, have students define 'vertex' and 'edge' in their own words. Then, ask them to describe one scenario where BFS would be more appropriate than DFS, or vice versa.

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

Activity 03

• Think-Pair-Share
• 25 min · Pairs

Think-Pair-Share: Which Search Fits the Problem?

Present four real-world scenarios: finding the shortest path in a road network, checking if two users are connected in a social network, exploring all files reachable from a root directory, and detecting circular dependencies in software packages. Pairs match each to BFS or DFS and justify the choice, then share reasoning with the class.

Predict the path taken by Depth-First Search (DFS) from a starting node.

Facilitation Tip

During Which Search Fits the Problem?, circulate and listen for students using terms like 'shortest path' or 'depth-first exploration' to describe their reasoning.

What to look for

Pose the question: 'Imagine you are designing a game where players explore a dungeon. Which traversal algorithm, BFS or DFS, would be better suited for finding all hidden treasures, and why? Be ready to explain your reasoning using graph terminology.'

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

Activity 04

• Gallery Walk
• 40 min · Small Groups

Gallery Walk: Graph Representation Challenge

Post four graphs around the room, each shown in one format: adjacency matrix, adjacency list, edge list, or visual diagram. Students must create the other three representations for each graph they visit. Reinforces that the same graph has multiple valid representations and that algorithm implementation depends on knowing which to use.

Explain the components of a graph and their representation.

Facilitation Tip

During Graph Representation Challenge, provide blank grids and ask students to convert between visual diagrams and adjacency lists before moving to code.

What to look for

Provide students with a small, labeled graph. Ask them to draw the order in which nodes would be visited using BFS starting from a specific node, and then repeat for DFS. Check for correct application of each algorithm's rules.

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

A few notes on teaching this unit

Experienced teachers approach graph algorithms by balancing concrete experience with abstract generalization. Start with physical simulations to build intuition, then transition to paper-and-pencil tracing to internalize the rules. Emphasize the difference between linear structures and relational ones by repeatedly asking students to explain why visited tracking matters. Avoid rushing to code; students need to feel the algorithms in their bodies before they can debug them on a computer.

Successful learning looks like students explaining why BFS visits nodes by distance while DFS follows a single path, identifying which algorithm fits a given problem, and representing graphs accurately using both adjacency lists and matrices. Students should also justify their choices with clear graph terminology.

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Watch Out for These Misconceptions

• During Human BFS and DFS, watch for students believing BFS and DFS visit nodes in the same order.

  Use the human simulation to physically mark nodes with distance labels for BFS (like breadcrumbs) and show how DFS follows one path deep before backtracking, making the order difference visible.

• During Graph Representation Challenge, watch for students treating graphs as linear structures like lists or arrays.

  Have students compare their adjacency lists to their visual diagrams, pointing out cycles and multiple connections that lists cannot represent linearly.

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Methods used in this brief

• Role Play
• Inquiry Circle
• Think-Pair-Share
• Gallery Walk