Summary
In this lesson, students will use their knowledge of domain and range to match pictures of graphs of rational functions with their corresponding domains and ranges. Students will learn about asymptotes, including what they are and how to find vertical and horizontal asymptotes of rational functions. Students will finish the lesson with a Card Matching activity to compare graphs, domains, ranges, asymptotes, equations, tables, and intercepts. This is the first lesson of two in the "Can't Touch This" lesson series.
Essential Question(s)
What can cause asymptotes?
Snapshot
Engage
Students recall domain and range to match graphs of rational functions with their corresponding domains and ranges in a Card Matching activity.
Explore
Students get a brief introduction to asymptotes and add cards with asymptotes to the Card Matching activity.
Explain
Students complete guided notes with the class and formalize their understanding of graphing rational functions.
Extend
Students apply what they have learned to graph rational functions.
Evaluate
Students add cards with equations, tables, and intercepts to complete the Card Matching activity.
Instructional Formats
The term "Multimodality" refers to the ability of a lesson to be offered in more than one modality (i.e. face-to-face, online, blended). This lesson has been designed to be offered in multiple formats, while still meeting the same standards and learning objectives. Though fundamentally the same lesson, you will notice that the different modalities may require the lesson to be approached differently. Select the modality that you are interested in to be taken to the section of the course designed for that form of instruction.
Materials
Lesson Slides (attached)
Card Matching document (attached; one set per pair of students; printed front only)
Card Matching Results handout (attached; one per pair of students; printed front only)
Guided Notes handout (attached; one per student; printed front/back)
Graphing With Asymptotes handout (attached; one per student; printed front/back)
Pencils
Scientific calculators
Engage
5 Minute(s)
Introduce the lesson using the attached Lesson Slides. Display slide 3 to show the lesson’s essential question: What can cause asymptotes? Slide 4 identifies the lesson’s learning objectives. Review each of these with your class to the extent you feel necessary.
Ask students to find a partner or assign partners yourself. Remind students to be kind and careful with the printed cards, then pass out a set of cards to each pair of students. Display slide 5 and pass out the attached Card Matching Results handout to each pair of students. Have students find the graph and domain/range cards, these are the cards they will be working with first. Students should set aside the remaining cards. Share the instructional strategy Card Matching with the class, and have students use this strategy to match the graph and domain/range cards.
As students complete their Card Matching activity, direct them to write the label of each domain/range card in the second column of the Card Matching Results table, corresponding to the label of the matching graph cards. The label of the domain/range cards is a number found in the top-left corner of each card.
Once students have finished, show slide 6. Give students time to discuss, check their work, ask questions, and correct their thinking. Use student responses to determine if students need a quick refresh on domain and/or range.
Before moving on, let students know that they or their partners should hold on to their Card Matching Results handouts. They will add to it throughout the lesson and use it as a way to check their results.
Explore
10 Minute(s)
Go to slide 7. Show students the video on the slide, "What are Vertical Asymptotes?," from the beginning to the 1:25 timestamp. The video gives a very brief overview of an asymptote, particularly that it is a line that the curve approaches but does not touch or cross. Students may need a more detailed explanation of asymptotes during the Explain phase of the lesson.
Show slide 8 and instruct students to locate and add the asymptotes cards to their existing Card Matching activity. As students work with a partner to match the asymptotes cards with the graphs and domain/range cards from earlier, remind them to record their matches in the table on their Card Matching Results handout. As before, the letter label on each asymptote card is located on the top-left corner.
Show slide 9. Give students time to discuss, check their work, ask questions, and correct their thinking.
Instruct students to set aside their cards and Card Matching Results handout to resume later.
Explain
25 Minute(s)
Go to slide 10. Give each student a copy of the attached Guided Notes handout. Distribute a scientific calculator to each student. Complete the handout as a class. Students should use the table feature of their scientific calculators to save time when calculating y-values.
Once finished, have students add this to their math notebook if that is a classroom norm.
Extend
25 Minute(s)
Have each pair of students find another pair and partner up to create groups of four students. Pass out a copy of the attached Graphing With Asymptotes handout to each student and display slide 11. Instruct students to work with their group to graph the first rational function.
As groups finish question 1, transition through slides 12–13 so students can check their work. Instruct students to now work with only one person from their group of four to complete question 2.
As students work through and complete question 2, transition through slides 14–15 so students can check their work. Direct students to work with a different person from their group to complete question 3.
As students work through and finish question 3, transition through slides 16–17 so students can check their work. Challenge students to now work independently to complete question 4. Remind students that this is a great opportunity to reflect on what they know and what questions they may have.
As students complete question 4, transition through slides 18–19 so students can check their work. Give students an opportunity to ask questions and correct misunderstandings.
Evaluate
15 Minute(s)
Direct students to find their original partner and get out their Card Matching cards and Card Matching Results handout. Tell students they now need all of the cards on their desks. Show slide 20 and have students complete their matching activity. Remind students to record their matches on their Card Matching Results handout.
Guide a brief whole-group discussion by asking for volunteers to look over their cards one more time and explain their thinking. Use student responses to see which misconceptions persist before moving on to the next lesson: "Can’t Touch This, Part 2."
Remember to collect students’ cards and prepare each set for the next class if necessary.
Resources
K20 Center. (n.d.). Card Matching. Strategies. https://learn.k20center.ou.edu/strategy/1837
K20 Center. (n.d.). Desmos Classroom. Tech tools. https://learn.k20center.ou.edu/tech-tool/1081
King, K. [KristaKingMath]. (2017, February 20). What are vertical asymptotes? [Video]. YouTube. https://www.youtube.com/watch?v=xz7fNEaQh3U
