Computing · JC 1

Active learning ideas

Non-Linear Data Structures (Trees and Graphs)

Active learning helps students grasp algorithm efficiency because they can see and feel the difference in speed and effort. By moving through each step of a sorting or searching process, students connect abstract concepts to concrete experiences, which builds lasting understanding.

• MOE Syllabus Outcomes
• 9569 1.3.3 Implement and traverse Binary Search Trees
• 9569 1.3.4 Represent graphs using adjacency matrices and lists

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

Activity 01

• Think-Pair-Share
• 35 min · Small Groups

Sorting Race: Bubble vs Selection Sort

Provide groups with identical sets of 10 numbered cards. Instruct them to sort using bubble sort first, counting swaps aloud, then repeat with selection sort and compare counts. Groups record results on a shared chart and discuss differences.

How is data organized in a Binary Search Tree?

Facilitation Tip

During Sorting Race, have students physically swap cards to mimic swaps in Bubble Sort, making the operation count visible and memorable.

What to look for

Present students with two simple algorithms (e.g., finding the largest number in a list of 5 items using two different methods). Ask them to count the operations for each and write down which is more efficient and why.

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

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Search Challenge: Linear vs Indexed

Give pairs printed lists of 8 names. Have them perform linear searches for three targets, counting comparisons, then create a simple index and repeat. Pairs graph step counts and predict for larger lists.

What are the different tree traversal methods?

Facilitation Tip

For Search Challenge, use sticky notes to label items in the array so students can physically point and count comparisons during Linear Search.

What to look for

Pose the question: 'Imagine you have a list of 3 names to sort alphabetically. Algorithm A takes 10 steps, and Algorithm B takes 20 steps. Which is better and why? Now imagine you have 1,000,000 names. Does your answer change? Explain.'

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

Activity 03

• Think-Pair-Share
• 40 min · Whole Class

Maze Path Competition: DFS vs BFS

Draw simple mazes on paper. Whole class divides into teams; one team traces depth-first paths counting steps, another breadth-first. Compare paths to shortest solutions and vote on efficiency.

How can graphs be represented using adjacency matrices and lists?

Facilitation Tip

In Maze Path Competition, mark each step taken on a whiteboard so students can tally operations for both DFS and BFS side by side.

What to look for

Ask students to describe a situation where choosing a slightly slower algorithm would be perfectly fine, and another situation where choosing the fastest possible algorithm is crucial. They should briefly explain their reasoning for each.

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

Activity 04

• Think-Pair-Share
• 30 min · Pairs

Step Counter Relay

Individuals trace algorithms on worksheets for small inputs, passing to partners for verification. Class tallies averages and debates why one algorithm wins for the dataset.

How is data organized in a Binary Search Tree?

Facilitation Tip

In Step Counter Relay, assign each team a different starting point in the algorithm to ensure all students participate in the step count.

What to look for

Present students with two simple algorithms (e.g., finding the largest number in a list of 5 items using two different methods). Ask them to count the operations for each and write down which is more efficient and why.

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

A few notes on teaching this unit

Teachers should focus on guiding students to notice patterns in operation counts rather than memorizing algorithms. Avoid rushing to conclusions; instead, let students discover efficiency through repeated trials and group discussions. Research shows that students learn best when they articulate their own reasoning aloud and compare it with peers.

Students will confidently compare algorithms by counting steps and explaining which is more efficient for small datasets. They will justify their choices with data from trials and recognize that efficiency depends on context.

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Watch Out for These Misconceptions

• During Sorting Race, watch for students assuming Bubble Sort is always better because it feels more intuitive.

  Use the card-swapping activity to have students count swaps in Bubble Sort and compare them to the fixed steps of Selection Sort, highlighting cases where fewer swaps occur in Selection Sort.

• During Search Challenge, watch for students believing Linear Search is never efficient.

  Use sticky notes to label items and have students physically walk through both searches, counting comparisons to show Linear Search can be efficient for very small or unsorted lists.

• During Maze Path Competition, watch for students assuming DFS always finds the solution faster.

  Have students mark each step on the whiteboard and tally totals, then discuss how BFS may require fewer steps for shorter paths, correcting the assumption that depth guarantees speed.

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Methods used in this brief

• Think-Pair-Share