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# A2-N-1-4

last edited by 5 years, 1 month ago

A2.N.1.4 Understand and apply the relationship of rational exponents to integer exponents and radicals to solve problems.

In a Nutshell

Students will understand the relationship between rational exponents and radicals and apply this understanding to solve problems.

## Teacher Actions

• Students will develop accurate and appropriate procedural fluency as they understand the relationship between rational exponents and radicals. Students will be able to write and verbally explain how to express a radical in rational exponent form and vice versa.

• Students will extend properties of integer exponents to include rational exponents.

• Students will develop a deep understanding of the relationship between radicals and rational exponents

• Students can use, discuss and make connections about the relationship between radical and rational expressions.

• Students will develop strategies to decide which form, rational exponent or radical, will be most efficient to solve problems.

• Build procedural fluency from conceptual understanding by allowing students to discover the connection between properties of integer exponents and the definition of radical exponents.

• Provide students with opportunities to become fluent in converting between rational exponents and radicals and applying properties of exponents. (ex. Give students problems that have been worked and ask for the mistakes to be identified and then classified as procedural or conceptual misunderstandings. Students would also provide corrected response with justification.)

• Support productive struggle by providing time and situations for students to discuss and make connections about the relationship between radical and rational expressions through various methods (ie graphing calculator, desmos, )

• Pose purposeful questions that advance student understanding of the relationship between radicals and rational exponents by asking questions that build, but do not take over or funnel, student thinking.

• Facilitate meaningful mathematical discourse by choosing tasks for students to explore and defend which form, rational exponent or radical, is most efficient to solve problems.

• Elicit and use evidence of student thinking by providing questions or activities for students to discuss, explain and justify their choices of forms to solve mathematical and real world problems.

## Misconceptions

Procedural

• Fluently apply the properties of exponents to rational exponents.

• Convert between rational exponents and radical form.

Conceptual

• Choose the most efficient form, radical or rational exponent to solve mathematical and real-world problems.

• Explain and defend how to use properties of exponents correctly.

• Students do not recognize that rational exponents are radicals in a different form and vice versa.

• When multiplying or dividing rational exponents, students will not add or subtract the exponents correctly.

• Students will place the root in the numerator when converting from a radical to a rational exponent.

• Students mistake a number raised to power and then taken a root as different than a number taken to a root and then raised to a power (ex. is equivalent to
• When one side of an equation is raised with a rational exponent, students mistakenly only apply the exponent to the closest base, not the entire side.

OKMath Framework Introduction