Rational+Exponents+and+Radicals+Unit

Rational Exponents and Radicals Unit

__Content Standards:__ N.RN.1 Explain how the definition of the meaning of rational exponents follows form extending the properties of integer exponent to those values, allowing for a notation for radicals in terms of rational exponents. N.RN.2 Rewrite expressions involving radicals exponents using the properties of exponents.

__Learning Cycle:__ Understand numerical placements of rational exponents. Understand how rational exponents can be written in radical form.

Goal: Define rational exponents and where they lie on a number line. The objectives are:
 * 1) Define rational numbers.
 * 2) Understand relationships between rational numbers, rational exponents, and other numbers on number line.
 * 3) Define rational exponents.
 * 4) Understand the relationship between radical form and rational exponents

__Developing Understanding__ __Activity:__ Introduction to Radical Numbers and Rational Exponents

Materials: Number line Worksheet, Radical to Rational Exponents

__Launch/Task #1__ Number line worksheet is handed out as students come in the room. The task is to order numbers in order on a number line. The goal is to have students see the relationship of irrationals to rational numbers.

(Other Option: handout cards/magnets/velcro numbers for students to put on a number line on their desk to make it more hands-on rather than a worksheet.)

__Explore__ Monitor student responses, gather info, questions students, and have several show their number lines.

__Discuss__
 * 1) Rational Exponents have a place on the number line. 2 to the 1 and 2 to the 0 and how they relate to numbers on the number line.
 * 2) Vocabulary: Integers, rational, irrational, whole numbers, counting numbers, natural numbers, sub sets

__Task #2__ Hand out Radical to Rational Exponents worksheet. Goal is to have students discover the equation between radical form and exponential form.

(Other Option: handout cards/magnets/velcro numbers for students to put on the worksheet to show how to rearrange the three numbers of the radical to make the rational exponent.)

__Explore__ Monitor student responses, gather info, questions students, and have several show their responses.

__Discuss__
 * 1) Which number is the index number, the radicand, and how do we know where they go.
 * 2) Talk about grouping numbers and how they are reduced.

__Solidify Understanding__ Materials: Number line with Radicals

__Launch/ Task #1__ Hand out worksheet Number line with Radicals, have students work on it by themselves for 5 minutes and then they can discuss it with their group or partner.

(Other Option: handout cards/magnets/velcro numbers for students to put on a number line on their desk to make it more hands-on rather than a worksheet.)

__Explore__ Monitor student responses, gather info, questions students, and have several show their number lines.

__Discuss__
 * 1) Discuss Vocabulary Radical Form and Exponential Form
 * 2) Equivalent Expressions.
 * 3) Negative Exponents.

__Practice Understanding__ Materials: Roll Three Dice, Grade Worksheet

__Launch/Task #1__ Hand out Roll Three Dice make sure you have dice for every student or group of students. Walk around and make sure students understand the instructions.

__Explore__ Monitor student responses, gather info, questions students, and have several show their responses.

__Discuss__
 * 1) Discuss what the numerator, denominator of the exponents, what is the base, what is the exponent.

__Launch/Task #2__ Hand out Grade Worksheet. Walk around and make sure students understand the instructions.

__Explore__ Monitor student responses, gather info, questions students, and have several show their responses.

__Discuss__
 * 1) Discuss the mistakes in the worksheet. Discuss how some the problems are simplified or written in a different way.