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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