Unit: 2 The Powers That Be. Unit Essential Question: How can rational and irrational numbers be expressed by exponents, square roots and scientific notation?

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Presentation transcript:

Unit: 2 The Powers That 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 Power Squared 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 Notation Exponential 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 Numbers Irrational Numbers Real Numbers Whole Numbers Integers Natural Numbers Additive Inverse Significant 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 Root Radical Symbol Perfect 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 Triangle Legs Pythagorean theorem Converse Pythagorean triple