Summary
In this lesson, students will recall solving equations with rational exponents and radicals. Using graphs, students will recall evaluating and solving equations with function notation. Students then will learn how to address extraneous solutions and why they exist. Students will apply this new knowledge to mathematical problems.
Essential Question(s)
How do we know if a solution is extraneous?
Snapshot
Engage
Students recall solving equations using rational exponents and/or radicals.
Explore
Students use graphs to evaluate expressions and solve equations with function notation.
Explain
Students complete guided notes with the class and formalize their understanding of extraneous solutions.
Extend
Students apply what they have learned to solve mathematical problems.
Evaluate
Students reflect on their learning and decide what they found easiest and what they found most confusing about solving equations using rational exponents and/or radicals.
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)
Exploring Functions handout (attached; one per pair; printed front only)
Guided Notes handout (attached; one per student; printed front only)
Guided Notes (Teacher Guide and Model Notes) (attached; for teacher use)
Pencils
Looking for Extraneous Solutions handout (optional; attached; one per student; printed front only)
Engage
5 Minute(s)
As students enter the classroom, display slide 3 from the attached Lesson Slides. To begin the lesson, ask students to answer the Bell Ringer questions on a piece of notebook paper or elsewhere if you have a classroom norm for bell work.
After giving students time to answer these questions, transition through slides 4–5 so students can check their work. Use this time to address any misconceptions that remain from the previous lesson(s): "Radical Yet Rational, Part 2" and/or "Radical Yet Rational, Part 1."
Go to slide 6 to share the lesson’s essential question with students. Go to slide 7 to identify the lesson’s learning objectives. Review each of these with students to the extent you feel necessary.
Explore
5 Minute(s)
Ask students to find partners or assign student pairs. Display slide 8 and pass out the attached Exploring Functions handout to each pair of students.
Have students work with their partners to evaluate expressions and solve equations by using the provided graph. As students complete the handout, go to slide 9 so students can check their work.
Explain
30 Minute(s)
Display slide 10 and pass out the attached Guided Notes handout to each student. Complete the handout as a class. Have students add it to their math notebooks if that is a classroom norm.
Transition through slides 11–13 to provide students with a graphical explanation of where extraneous solutions come from.
Extend
20 Minute(s)
Inform students it is time for them to apply what they have learned. Display slide 14 and have students work with their partners to solve the given equations with radicals and rational exponents and check for extraneous solutions.
Evaluate
5 Minute(s)
Display slide 24 and introduce the Muddiest Point strategy to help students reflect on the lesson and their overall understanding of the content. Use this strategy to determine students’ confidence in solving equations with radicals and/or rational exponents.
After collecting students’ responses, use their feedback to determine if remediation is needed or if students are ready for the next topic. If the class is split, consider remediation by grouping students who found something to be crystal clear with students who found that same thing to be most confusing.
Resources
ElisaRiva. (February 13, 2017). Brain [Illustration]. Pixabay.https://pixabay.com/illustrations/brain-mind-psychology-idea-drawing-2062057/
K20 Center. (n.d.). Bell Ringers and Exit Tickets. Strategies. https://learn.k20center.ou.edu/strategy/125
K20 Center. (n.d.). Muddiest Point. Strategies. https://learn.k20center.ou.edu/strategy/109
K20 Center. (n.d.). Desmos Classroom. Tech tools. https://learn.k20center.ou.edu/tech-tool/1081
