- In previous grades, students should have developed an understanding of the properties of integer exponents.
- Students should be able to convert back and forth between radical expressions and expressions with rational exponents.
- Students will utilize the product rule, quotient rule, and power rule to work with expressions with rational exponents.
- Students should be able to convert between radical expressions and expressions with rational exponents to solve equations.
- Students should understand how to use substitution to check answers to radical equations to ensure that solutions are not extraneous.
- Students should have opportunities to use technology and tools to solve radical equations by graphing.
- Students should have opportunities to use technology and tools to explore and solve radical equations to strengthen conceptual understanding.
- Given the volume of a sphere, students could determine the radius of the sphere by writing an equation for the radius, r, and solving for r.
- Students should be able to graph and identify key features of a radical function including: domain, range, and x and y-intercepts; roots, zeros, and solutions; intervals where the function is increasing, decreasing, positive, and/or negative; maximum and minimum values, including endpoint extrema; non-symmetry; end behavior.
- Students should be able to calculate the slope of average rate of change for a given interval, including the estimated rate of change.
- Students should be able to relate the key features of a model (i.e., graph, equation, table) to the real-world situation which the model represents.
- Students should be able to analyze and interpret radical equations presented in mathematical, applicable situations.
- Students should discuss the characteristics of radical functions in context, including domain and range, zeros, intercepts, and other relevant key features.
- Students should be able to solve problems that can be modeled by radical equations.
- Students should have opportunities to use technology and tools to solve radical equations to strengthen conceptual understanding.
- Students should be encouraged to explore multiple solution pathways, which might include graphing with various tools, interpreting key features, and evaluating radical equations.
- Students can create a radical equation using the distance formula, for which the distance and three of the four coordinate values are known, and one is unknown.
- Less time should be devoted to the mechanics of solving radical equations and more time should be devoted to building students’ capacity for interpreting radical functions within context.
- Students can create and interpret problems involving radical equations in which two of the variables are unknown, such as problems involving velocity.
Textbook Connections
Module 6:
Lesson 3- nth Roots and Rational Exponents
Lesson 4- Graphing Radicals
Lesson 5- Operations with Radicals
Lesson 6- Solving Radicals
Module 6:
Lesson 3- nth Roots and Rational Exponents
Lesson 4- Graphing Radicals
Lesson 5- Operations with Radicals
Lesson 6- Solving Radicals