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Number and Quantity

 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(51/3) 3=5(1/3) 3to hold, so (51/3) 3must 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 -Units2 -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 i2=-1, and every complex number has the form 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 -i2 -a+bi 2 days N.CN.2 Use the relation i2=-1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 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 Ncn3 Ncn4 Ncn5 Ncn6 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 x2+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 Standard Essential Question Bloom’s Taxonomy Activities Vocabulary Pacing Nvn1 Nvn2 Nvn3 Nvm4 Nvm5 Nvm6 Nvm7 Nvm8 Nvm9 Nvm10 Nvm11 Nvm12