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Connecting Multiple Representations (Topic 1.9)

Unit 1 - Day 8

​Learning Objectives​
  • Identify a re-expression of mathematical information presented in a given representation.

​Success Criteria
  • I can match graphical, verbal, and analytical representations of limits.

  • I can communicate my reasoning to my peers.

Quick Lesson Plan
Activity: Limits Card Sort


Lesson Handout

Answer Key


This lesson does not feature new content objectives but allows students to make connections between various representations of limits: graphical, analytical, verbal, etc. Students should work in pairs or small groups to match up graphs, equations, and limit statements. The cards used in this card sort can be reused in many upcoming lessons. You will not need the function description cards (a-l) in this lesson, but these can be added back in after the lessons on continuity.

Flex time can be used by teachers to go over homework questions, do a journal entry, finish up a previous lesson, work on a warm-up problem, or make quiz corrections.

Teaching Tips

There are many ways to differentiate this activity. The standard approach is to match all 12 graphs will all 12 equations with all 12 limit descriptions (We like to print each representation on different colored card stock). For struggling students, you can remove the equation cards and just match graphs to limit descriptions. Similarly, you could reduce the number of cards being matched, or have students pre-sort the cards into categories (piece-wise vs. non piece-wise, for example). To challenge students, consider removing one card from each trio and having students make their own blank card with the graphical, analytical, or verbal representation that is missing. You could also have students add a fourth card to each trio by adding a tabular representation.

We recommend having students record their answers on an answer sheet and sharing the correct answers at the end of the activity. If you have extra time, you could have each group present a few of the matchings.

Student Misconceptions

Students tend to have the hardest time matching the equations to the graphs, because they usually don’t have all their parent function graphs committed to memory (or don’t recognize the parent function in the equation). This activity is a great way to review some of those graphs that students should know from previous courses!

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