Evaluating Statements about Radicals
This lesson unit is intended to help you assess how well students are able to:
- Use the properties of exponents, including rational exponents and manipulate algebraic statements involving radicals.
- Discriminate between equations and identities.
In this lesson there is also the (optional) opportunity to consider the role of the imaginary number .
The unit is structured in the following way:
- Before the lesson, students work alone on an assessment task designed to reveal their current understanding. You review their work, creating questions to help students improve their solutions.
- During the lesson, students first work in small groups on a collaborative discussion task. After sharing their solutions with another group, students extend and generalize the math.
- An optional collaborative task focuses on imaginary numbers.
- During a whole-class discussion, students review the main mathematical concepts of the lesson.
- In a follow-up lesson, students review their initial solutions and then use what they have learned to revise the same introductory assessment task and complete a second, similar task.
- Each student will need a copy of Operations with Radicals and Operations with Radicals (revisited), a mini-whiteboard, pen, and eraser.
- Each small group of students will need the Card Set: Always, Sometimes, or Never True?, scissors, glue, and a large sheet of poster paper. To begin with, cut Cards G and H off the sheet, but do not cut up the rest of the cards.
- There is a projector resource to support whole-class discussions. You may also want to copy the cards onto transparencies to be used on an overhead projector to support discussions.
15 minutes before the lesson, a 95-minute lesson (or two 50-minute lessons) (more if introducing imaginary numbers), and 20 minutes in a follow-up lesson. Exact timings will depend on the class.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
Mathematical Content Standards
This lesson asks students to select and apply mathematical content from across the grades, including the content standards:
- H.A-REI: Understand solving equations as a process of reasoning and explain the reasoning
- H.N-CN: Perform arithmetic operations with complex numbers.
- H.N-RN: Extend the properties of exponents to rational exponents