The Binomial Theorem

Investigate patterns in the binomial theorem. Pupils begin by reviewing the coefficients from Pascal's triangle. They look at the individual terms, the sums of the coefficients on a row, and the alternating sum of each row. Individuals then use the Binomial Theorem to calculate rates of changes for the volume of a sphere and the area of a circle when changing the radius. 

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CCSS: Designed
Additional Tags
Instructional Ideas
  • Investigate whether similar patterns occur with finding average rate of change of the volume of a cube and a cylinder
Classroom Considerations
  • Assumes exposure to Pascal's triangle
  • Requires knowledge of the powers of i
  • Fifth of 23 consecutive Precalculus lessons
  • Shows all the steps in determining the coefficients
  • Provides scaffolding suggestions for struggling learners
  • None
Common Core