Standard | Essential Question | Bloom’s Taxonomy Activities | Vocabulary | Pacing | |

N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notion for radicals in terms of rational exponents. For example, we define(5^{1/3})^{ 3}=5^{(1/3) 3}to hold, so (5^{1/3})^{ 3}must equal 5. | How does primary knowledge of fractions assist with the completion of problems with rational exponents? What is the relationship between radicals and integers with fraction exponents? | -Compare similar appearing rational numbers raised to an exponent to determine the relationship between the properties of integers and real numbers raised to a power | -Rational -Irrational -Integers -Radicals -Rational exponents | 3 days | |

N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. | What is the relationship between radicals and numbers raised to a rational power? What is the relationship to a fractional exponent and the root of a given term? | -Develop a worksheet and answer key containing no less than 6 problems involving radicals and rational exponents, distribute the worksheet to classmates to complete, then correct their work | -Expressions -Properties of exponents | 3 days | |

N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | What is the relationship between multiplication and division in terms of rational numbers? | -Create a poster highlighting: “the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational;” include examples for each statement | -Sum -Product -Difference -Quotient -Irrational number -Rational number | 1 day | |

Standard | Essential Question | Bloom’s Taxonomy Activities | Vocabulary | Pacing | |

N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | How do units guide the process of completing multi-step problems? | -Select the appropriate method to complete a word problem based on the units provided. -Construct a multi-step word problem involving units of measure. | -Units of Measurement -Units ^{2}-UOM for Distance, Volume, and Area | 3 days | |

How are appropriate units determined when solving real-world problems? | -Differentiate the use of units in problems relating to distance, volume, and other forms of measurement. | -Distance -Volume -Area -Perimeter | |||

How does scale relate to the understanding of data on graphs and data displays? | -Design and conduct a small classroom study. -Develop a graph or chart with appropriate scale and units of measure. | -Scale -Data -Graphs | |||

N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. | How do categories in the real number system relate to solving practical problems? | -Determine which type of number will provide the most accurate response to a given problem. -Solve problems relating to models, measures, and statistics. | -Real Number System -Set -Integer -Exponent -Scientific Notation -Whole Number -Rational Number -Irrational Number | 3 days | |

N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | How do limitations assist in determining the accuracy of a response? | -Evaluate a given response based on the limitations of the problem (e.g. distance must be positive). | -Limitation -Accuracy | 3 days | |

Standard | Essential Question | Bloom’s Taxonomy Activities | Vocabulary | Pacing | |

N.CN.1 Know there is a complex number i such that i-1, and every complex number has the form ^{2}=a+bi with a and b real. | What is the role of imaginary numbers in mathematics? What fields of study are imaginary numbers most utilized? | -Using a mirror and a ruler, support the concept of imaginary numbers | -Real number -Complex number -Irrational number - i- i^{2}-a+bi | 2 days | |

N.CN.2 Use the relation i-1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.^{2}= | How are the commutative, associative, and distributive properties open over the complex number system? | -Construct a no less than seven term complex expression which requires the use of the commutative, associative, and distributive properties to solve; solve your creation | -Commutative Property -Associative Property -Distributive Property | 2 days | |

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N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. | In what scenarios would the solution to a quadratic equation be complex? | -Design a visual representing the three possible combinations of solutions for a quadratic equation | -Coefficients -Complex solutions -Discriminate | 1 day | |

N.CN.8 (+) Extend polynomial identities to the complex numbers. For example, rewrite x^{2}+4 as (x+2i)(x-2i). | How could imaginary numbers relate to additional dimensions? | -Create an equation with complex solutions for each polynomial identity | -Complex numbers -Polynomial identities | 1 day | |

N.CN.9 (+) Know the Fundamental Theorem of Algebra, show that it is true for quadratic polynomials. | How could an understanding of the Fundamental Theorem of Algebra help you on your next test? | -Support the Fundamental Theorem of Algebra with 2 real and 2 complex examples | -Fundamental Theorem of Algebra -Roots | 1 day | |

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### Number and Quantity

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