Module 3: Arithmetic and Geometric Sequences

Natural human interest in patterns and algebraic study of function notation are linked in this introductory unit on the properties of sequences. Once presented with a pattern or situation, the class works through how to justify conclusions and predictions mathematically. Scenarios build in complexity as the unit progresses, and learners grow in mathmatical sophistication as they learn to distinguish between and use arithmetic and geometric sequences.

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CCSS: Adaptable
Instructional Ideas

  • Link with a science or biology class to investigate sequences in nature
  • Unit as a whole would make for excellent long-term sub or homebound pupil lesson plans
  • Have the class research famous sequences or fractal extensions to incorporate more writing practice
Classroom Considerations

  • Some of the scenarios (i.e. Breaking the Chain) require more reading than a standard math worksheet; some learners may need additional support
  • Interconnected nature of lessons might necessitate quick remediation for learners with absences
  • Weaknesses in using functional notation will quickly become apparent, might need some reteaching
Pros

  • Real-life situations ground math concepts and provide context
  • Logical and steady increase in difficulty builds mathematical skills gradually
  • Functional notation emphasized, an important skill in higher-level math classes
Cons

  • No whole-unit summative assessment
  • No answer keys provided
  • Evaluating with exponents resource link (pg. 9) and finding equation of a line (pg. 16) are both dead links