Complexity - It's Simple

By providing a playful introduction to algorithm complexity and measuring complexity, this lesson gets the class up and moving and learning together. The authors expertly balance providing information about how algorithms are developed with pushing discovery learning while supporting all of it with extensive teaching notes. A great lesson to emphasize applications and problem-solving in the math classroom.

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CCSS: Designed
Instructional Ideas

  • Consider using the included extension writing prompts to emphasize math communication and literacy learning
  • Guide individual or class research into more complex sorting algorithms or the application of algorithms in cryptography
  • Use as a cross-curricular unit studying algorithms and programming with a computer science class
Classroom Considerations

  • The fourth and fifth sequences in the Growth of Sequences worksheet are more complex than the others and are given as examples without much analysis required. Closed form of the fourth is n^2 + 1 and could make for an excellent extension. Closed form of the fifth is beyond the scope of high school curriculum, and might cause frustration in perfectionists, with recursive form a[0] = 64; a[n] = a[n-1] + 2^(-n+6)
Pros

  • Wide variety of approaches and activities
  • Clear and approachable explanations for potentially complicated technical ideas
  • Possibilities for extending into deeper investigations noted throughout the activities
  • Possible alignments to some Technology Literacy and Computer Science standards suggested in addition to CCSS
Cons

  • P vs NP problem, Moore's Law, and algorithm analysis links on the top of the second page are dead links
  • London International virtual classroom link at the bottom of page twelve takes the user to a login page, not the resource itself
  • Big-O notation is briefly mentioned, but the underlying structure assumes it is intuitive and does not explain it well
Included Materials - Join to Access

  • Activity
  • Answer Key
  • Lesson Plan