Computer Science · 10th Grade

Active learning ideas

Introduction to Trees and Graphs

Trees and graphs are abstract structures that become concrete when students manipulate physical or visual representations. Active learning works here because students must trace relationships with their hands and eyes, which builds mental models that lectures alone cannot. When students build or traverse these structures, they experience the immediate consequences of choices like branching factors or edge directions, making misconceptions harder to hold onto.

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

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Concept Mapping
• 35 min · Small Groups

Collaborative Modeling: Build a Tree

Give each small group index cards and string. Students receive a set of data values and must construct a binary search tree by placing values in the correct nodes according to insertion rules. Groups then perform an in-order traversal by reading cards aloud in sequence, verifying the result is sorted.

Explain the fundamental differences between linear and non-linear data structures.

Facilitation Tip

During Collaborative Modeling: Build a Tree, circulate and ask each group to explain their tree’s hierarchy to you before they add new nodes.

What to look for

Provide students with a scenario, such as organizing a family tree or planning a road trip. Ask them to draw a representation of this scenario using either a tree or a graph, labeling at least four nodes and two edges. They should also write one sentence explaining why they chose that data structure.

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

Activity 02

• Gallery Walk
• 40 min · Small Groups

Gallery Walk: Tree Type Museum

Set up stations around the room, each featuring a different tree type (binary tree, binary search tree, heap, trie, decision tree) with a diagram and two real-world applications. Students rotate through stations and record on a graphic organizer what access rule or property makes each type distinct.

Compare different types of trees (e.g., binary trees) and their applications.

Facilitation Tip

Before the Gallery Walk: Tree Type Museum, assign each student one tree type to research and present for 60 seconds at their station.

What to look for

Present students with two diagrams: one clearly representing a tree and another clearly representing a graph that is not a tree. Ask students to identify which is which and explain one key difference in their structure, focusing on parent-child relationships versus general connectivity.

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

Activity 03

• Simulation Game
• 30 min · Whole Class

Simulation Game: Graph Traversal Race

Students act as nodes in a graph drawn on the floor with tape. Each student-node holds a card with their neighbors' names. Two groups run breadth-first and depth-first traversal simultaneously, marking visited nodes with colored stickers. The class discusses which traversal found a target node faster and why.

Analyze how graphs can model relationships in complex systems.

Facilitation Tip

During Simulation: Graph Traversal Race, enforce a strict time limit for each traversal to highlight the difference between breadth-first and depth-first search.

What to look for

Facilitate a class discussion by asking: 'Imagine you are designing a system to recommend music based on listening habits. Would you use a tree or a graph? Explain your reasoning, considering how users and songs relate to each other.'

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 04

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Linear vs. Non-Linear Trade-offs

Students are given three data storage problems (contact list, org chart, city road map) and must individually decide whether a linear or non-linear structure fits best. They compare reasoning with a partner, then the class builds a shared decision framework on the whiteboard.

Explain the fundamental differences between linear and non-linear data structures.

Facilitation Tip

In Think-Pair-Share: Linear vs. Non-Linear Trade-offs, provide sentence stems like 'Linear structures work well when... but struggle when...' to guide the discussion.

What to look for

Provide students with a scenario, such as organizing a family tree or planning a road trip. Ask them to draw a representation of this scenario using either a tree or a graph, labeling at least four nodes and two edges. They should also write one sentence explaining why they chose that data structure.

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

A few notes on teaching this unit

Start with physical models to ground abstract concepts in tangible experiences, as research shows spatial manipulation improves understanding of hierarchical relationships. Avoid rushing to algorithmic details before students grasp the structural differences between trees and graphs. Use analogies carefully, as overused metaphors like family trees can reinforce the misconception that all trees are binary. Instead, let students discover the variety of tree structures through guided exploration.

Successful learning looks like students accurately distinguishing between trees and graphs, explaining parent-child relationships, and justifying their choice of structure for given scenarios. They should use correct terminology such as node, edge, parent, child, and root without prompting. Evidence of understanding includes clear labeling, correct edge drawing, and confident participation in discussions about trade-offs.

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Watch Out for These Misconceptions

• During Collaborative Modeling: Build a Tree, watch for students who arrange nodes in a straight line and call it a tree.

  Stop the group and ask them to define a parent-child relationship. Have them identify the root and trace paths downward, ensuring they physically demonstrate branching before continuing.

• During Gallery Walk: Tree Type Museum, watch for students who assume all trees are binary trees after seeing the binary tree example.

  Point to the multiway tree station and ask students to compare the number of children per node. Have them list two differences in structure or use between the binary and multiway trees.

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Methods used in this brief

• Concept Mapping
• Gallery Walk
• Simulation Game
• Think-Pair-Share