Limits and Continuity

For learners who are used to smooth lines and curves on graphs, confronting gaps and corners in their functions is often quite disconcerting. These notes, presentation, and worksheet set do an excellent job of breaking down how and when a function is discontinuous as well as providing practice in identifying these discontinuities. Problems throughout the set build from simple arithmetic through to class-creation of new functions to fit given criteria. A great supplement to an existing unit on limits and continuity, or exercises for remediation and reteaching.

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CCSS: Adaptable
Instructional Ideas

  • Consider having learners work together on the additional worksheet, particularly on problems where they need to come up with their own functions to given criteria
  • Instruct learners to create their own dot-to-dot style picture with discontinuous piecewise functions
  • Link with a physics or physical science unit on distance vs. time and velocity vs. time graphs with potential discontinuities
Classroom Considerations

  • Notes and follow-up worksheets to main resource presentation are attached in additional resources
  • Main presentation would make a great interactive whiteboard lesson by revealing steps as problems are worked by the class
  • Break up additional worksheet problems as a follow-up bell ringer or homework problems to sprinkle into later lessons

  • Summary of instructions for each section in the notes
  • Presentation follows note sheet, solving each problem step-by-step
  • Problems scaffold in difficulty without depending on correct answers from previous work

  • The included Continuity and Piecewise Functions Worksheet does not have answers
  • The student notes and presentation do not have accompanying teaching notes / methods