Math 2
Unit 1 Learning Goals
“The Real Number System”
Lesson 1-1: The Real Number System
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I can classify real numbers as rational or irrational according to their definitions and give examples of
each.
I can explain why the sum and product of two rational numbers is rational.
I can explain why the why the sum of a rational and irrational number is irrational.
I can explain why the product of a nonzero rational and irrational number is irrational.
I can apply the definition of an integer to explain why adding, subtracting, or multiplying two integers
always produces an integer.
Lesson 1-2: Exponent Rules: Product and Quotient
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I can solve problems using properties of exponents learned in previous courses, including integer and
variable bases.
Lesson 1-3: Exponent Rules: Power to a Power and Quotient to a Power
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I can solve problems using properties of exponents learned in previous courses, including integer and
variable bases.
Quiz #1
Lesson 1-4: Exponent Rules: Zero and Negative Exponents
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I can solve problems using properties of exponents learned in previous courses, including
integer and variable bases.
Lesson 1-5: Exponent Rules: Rational
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I can apply the definition of an nth root to demonstrate that
 x
n
n
 x for various values of n and
n
explain why this is true.
 1n 
I can apply the properties of exponents to demonstrate that  x   x for various values
 
of n and explain why this is true.
 1n  n
I can apply the properties of exponents and the definition of nth root to explain that  x   x .
 
I can write radical expressions as expressions with rational exponents and vice versa.
Quiz #2
Lesson 1-6: Applications of Rational Exponents
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I can rewrite equations with exponents using the properties of exponents.
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I can interpret the components of an equation with exponents in the context of a problem
(e.g., 𝑦 = 5 ∙ 1.225𝑡/3 ) describes a quantity that was initially 5 and increases 22.5% every three years.)
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I can use the properties of exponents to rewrite an exponential function to emphasize one of its
properties (e.g., 𝑦 = 5 ∙ 1.225𝑡/3 ≈ 5 ∙ 1.07𝑡 , which means that increasing 22.5% in three years is
about the same as increasing 7% per year).