Unit: 2

The Powers The Powers That BeThat Be

Unit Essential Question:•How can rational and irrational numbers be expressed by exponents, square roots and scientific notation?

Standard(s): M8N1•Students will understand different representations of numbers including square roots, exponents, and scientific notation

Standard(s): M8G2:

•Students will understand and use the Pythagorean theorem.

Concept 1:

Exponent Notation

Lesson Essential Questions:

•1. How do we write numbers using exponents?•2. How do we use

exponents within the order of operations?

Vocabulary 1:

Exponent Base

PowerSquared

Cubed

Concept 2:

Multiplication and Division of

Exponents

Lesson Essential Questions:• 1. How do I multiply powers with

the same base?• 2. How do I divide powers with the

same base?• 3. How do I simplify a power to a

power?• 4. How do I simplify expressions

with negative and zero exponents?

Vocabulary 2:

Power to a Power

Concept 3:

Scientific Notation

Lesson Essential Questions:

• 1. How do I write numbers in scientific notation?• 2. How do I calculate with

scientific notation?• 3. When would I use scientific

notation?

Vocabulary 3:

Scientific NotationExponential Notation

Concept 4:

Rational/Irrational Numbers

Lesson Essential Questions:

•1. How do I identify and classify numbers in the real number system?

Vocabulary 4:Rational NumbersIrrational Numbers

Real NumbersWhole Numbers

IntegersNatural NumbersAdditive InverseSignificant Digits

Concept 5:

Square Roots

Lesson Essential Questions:

•1. How do I find the square root of perfect squares?•2. How do I estimate the

square root of a positive number?

Vocabulary 5:

Square RootRadical SymbolPerfect Square

Concept 6:

Operations with Radicals

Lesson Essential Questions:

•1. How do I simplify radical expressions? •2. How do I add, subtract, multiply and divide radicals?

Concept 7:

Pythagorean Theorem

Lesson Essential Questions:

•1. What is the Pythagorean theorem?•2. How do I solve problems using the Pythagorean theorem?

Vocabulary 7:Hypotenuse

Right TriangleLegs

Pythagorean theoremConverse

Pythagorean triple