Continuity (Lesson 8.3 Day 2)

Unit 8 - Day 9

​Learning Objectives​
  • Justify whether a function is continuous at a particular x-value using the definition of continuity

  • Determine when and how discontinuous functions can be made continuous

Quick Lesson Plan
Activity: Continuity Card Sort and Task Cards



Lesson Handout

Answer Key


Recording Sheet

Experience First

Today we’ll be revisiting the card sort we started on day 2 of this unit. Students will now match the continuity descriptions and the equations (if they have not done so already) with the graphs and limit statements they previously matched. For materials and instructions, check out our blog from Day 2


The final half of the class period will be spent on a set of continuity task cards. Print the task cards on cardstock and cut up into the ten problems. You may wish to laminate these so they last longer. Have students work in pairs on the problems, keeping track of their work in the recording sheet. The order in which the cards are completed is not important. You can have students pass the cards from group to group or post all the cards around the room and have the pairs travel to each card.

Formalize Later

Our students struggled with card “B” the most, since they couldn’t simply plug in 0 into the top function. This was a great opportunity to discuss the difference between evaluating functions and evaluating limits, and how we can use limit notation to justify an answer.