Day 5: Algorithm Design and Testing

Learning Objectives

• AAP-2.A: Express an algorithm that uses sequencing without using a programming language.
• AAP-2.B: Represent a step-by-step algorithmic process using sequential code statements.
• AAP-2.C: Evaluate expressions that use arithmetic operators.

Essential Questions

• How do we design effective algorithms to solve problems?
• Why is testing important in algorithm development?
• How do we ensure our algorithms work correctly for all inputs?

Materials Needed

• Presentation slides on algorithm design and testing
• Algorithm design templates
• Testing strategy worksheet
• Programming environment
• Exit ticket templates

Vocabulary

• Algorithm design
• Testing
• Edge case
• Boundary condition
• Test case
• Input validation
• Debugging
• Verification

Procedure (50 minutes)

Opening (8 minutes)

1. Review and Connection (3 minutes)

   • Review string operations from previous lesson
   • Connect to today's focus on algorithm design and testing

2. Warm-up Activity (5 minutes)

   • Present a simple problem (e.g., finding the maximum of three numbers)
   • Ask students to brainstorm different approaches to solve it
   • Discuss how we might verify that a solution is correct

Main Activities (32 minutes)

3. Lecture: Algorithm Design Principles and Testing Strategies (12 minutes)

   • Explain key principles of algorithm design:
     • Understanding the problem requirements
     • Breaking down complex problems into steps
     • Identifying inputs and outputs
     • Considering different approaches
     • Choosing appropriate operations and structures
   • Introduce testing strategies:
     • Test cases with normal inputs
     • Edge cases and boundary conditions
     • Invalid inputs
     • Comprehensive testing
   • Discuss the importance of testing in algorithm development
   • Explain how testing helps identify errors and edge cases
   • Introduce the concept of algorithm correctness and verification

4. Demo: Testing Algorithms with Different Inputs (8 minutes)

   • Show an algorithm for a specific task (e.g., calculating the average of a list of numbers)
   • Demonstrate how to test the algorithm with different inputs:
     • Normal case (several numbers)
     • Edge case (empty list)
     • Edge case (single number)
     • Edge case (very large numbers)
     • Invalid input (non-numeric values)
   • Show how testing reveals potential issues in the algorithm
   • Demonstrate how to refine the algorithm based on test results

5. Activity: Design, Implement, and Test Algorithms (12 minutes)

   • Students work individually or in pairs
   • Assign mathematical operations for students to implement (e.g., calculating factorial, finding GCD, determining if a number is prime)
   • Students should:
     • Design an algorithm for their assigned operation
     • Implement the algorithm in code
     • Develop a set of test cases, including edge cases
     • Test their algorithm with these cases
     • Refine their algorithm based on test results
   • Circulate to provide guidance and feedback

Closing (10 minutes)

6. Discussion: Importance of Testing Edge Cases (5 minutes)

   • Have students share their algorithms and testing strategies
   • Discuss common issues discovered during testing
   • Emphasize the importance of considering edge cases
   • Highlight how testing improves algorithm quality
   • Discuss real-world consequences of inadequate testing

7. Exit Ticket and Preview (5 minutes)

   • Students design and test an algorithm that solves a specific problem
   • Preview that next class will focus on selection (conditionals)

Assessment

• Formative: Quality of algorithm design and testing strategies
• Exit Ticket: Correctness and thoroughness of algorithm design and testing

Differentiation

For Advanced Students

• Provide more complex problems requiring sophisticated algorithms
• Challenge them to optimize their algorithms for efficiency
• Ask them to develop comprehensive test suites

For Struggling Students

• Offer more structured algorithm design templates
• Provide guidance on identifying test cases
• Focus on simpler problems with clearer steps

Homework/Extension

• Complete the design and testing of an algorithm for a different mathematical operation
• Research testing methodologies used in professional software development
• Create a test plan for a program they've previously written

Teacher Notes

• Emphasize that testing is not an afterthought but an integral part of algorithm development
• Watch for students who test only the "happy path" and miss edge cases
• Make connections to real-world software failures caused by inadequate testing
• Consider discussing test-driven development as an approach
• Remind students that the AP exam will assess their ability to analyze algorithms