Technologies · Year 9

Active learning ideas

Comparing Algorithm Efficiency

Active learning helps students grasp algorithm efficiency because abstract concepts like time complexity become visible through hands-on trials. When students physically count steps or time code runs, they connect mathematical patterns to real-world performance in ways that lectures alone cannot achieve.

• ACARA Content Descriptions
• AC9DT10K01

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inquiry Circle
• 35 min · Small Groups

Card Simulation: Linear vs Binary Search

Provide shuffled numbered cards as lists. Groups perform linear search by checking sequentially and binary search by halving sorted piles, recording steps for lists of 10, 20, and 40 items. Discuss patterns in step counts as sizes increase.

Compare how a linear search finds an item versus a simpler search method.

Facilitation Tip

During Card Simulation: Linear vs Binary Search, have students record every comparison on scrap paper to make the hidden work of algorithms visible.

What to look for

Provide students with a small, unsorted list of numbers and a target number. Ask them to manually count the number of comparisons needed to find the target using a linear search. Then, ask them to predict how many comparisons would be needed if the list doubled in size.

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

Activity 02

• Inquiry Circle
• 45 min · Pairs

Coding Duel: Search Timings

Pairs write simple linear and binary search functions in Python or pseudocode. Test on lists of growing sizes, measure execution steps or approximate times using loops. Graph results to compare scalability visually.

Predict which algorithm might be 'faster' for a very large list of items.

Facilitation Tip

In Coding Duel: Search Timings, assign roles so one student writes code while the other times and records results, ensuring both students engage with the data.

What to look for

Pose this scenario: 'Imagine you have a digital library with 10 books versus a library with 10,000 books. Would the best way to find a specific book be the same for both libraries? Explain why or why not, considering how you might search.'

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

Activity 03

• Inquiry Circle
• 30 min · Whole Class

Prediction Walkthrough: Step Counts

Individuals predict steps for sample algorithms on paper inputs of varying sizes. Share predictions in whole class walkthroughs, then verify by tracing actual paths. Adjust predictions based on class evidence.

Justify why one way of solving a problem might be better than another for a computer.

Facilitation Tip

For Prediction Walkthrough: Step Counts, pause after each prediction to ask students to explain their reasoning before revealing outcomes.

What to look for

Students are given two pseudocode snippets for searching a list: one representing a linear search and another a more efficient method (e.g., assuming a sorted list). Ask them to write one sentence explaining which algorithm is likely faster for a very large list and why, focusing on the number of steps.

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

Activity 04

• Inquiry Circle
• 40 min · Small Groups

Relay Race: Algorithm Actors

Divide class into teams acting as algorithms. One student per team represents data elements; others search linearly or by dividing. Time races for different team sizes and tally operations to reveal efficiency.

Compare how a linear search finds an item versus a simpler search method.

Facilitation Tip

In Relay Race: Algorithm Actors, use a visible timer projected on the board so the class sees how small delays compound across steps.

What to look for

Provide students with a small, unsorted list of numbers and a target number. Ask them to manually count the number of comparisons needed to find the target using a linear search. Then, ask them to predict how many comparisons would be needed if the list doubled in size.

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

A few notes on teaching this unit

Teachers should connect efficiency to real decisions, like choosing between searching a bookshelf by scanning each book versus using a card catalog. Avoid overemphasizing code syntax during these lessons; focus instead on the relationship between input size and operation counts. Research shows students grasp Big O best when they first experience inefficiency physically before formalizing it mathematically.

Students will clearly articulate why linear search slows as lists grow while binary search remains efficient. They will use operation counts and timing data to justify choices between algorithms, showing confidence in predicting scalability.

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Watch Out for These Misconceptions

• During Card Simulation: Linear vs Binary Search, watch for students who assume binary search works on unsorted lists because they see cards in hand.

  In Card Simulation: Linear vs Binary Search, have students shuffle the cards first to demonstrate that binary search requires a sorted list, then ask them to explain why order matters for halving the search space.

• During Coding Duel: Search Timings, watch for students who equate faster code execution with more efficient code.

  In Coding Duel: Search Timings, guide students to compare total operation counts alongside timings, prompting them to notice that code structure affects steps differently than raw speed.

• During Relay Race: Algorithm Actors, watch for students who focus only on speed and ignore the number of operations or memory use.

  In Relay Race: Algorithm Actors, have teams present both their step counts and timing results, requiring them to justify efficiency based on multiple metrics during the discussion.

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Methods used in this brief

• Inquiry Circle