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Math and The Mind’s Eye Common Core State Standards Correlation Charts Unit 12 Modeling Real and Complex Numbers Math and The Mind’s Eye 1 © The Math Learning Center Unit 12 Modeling Real and Complex Numbers 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Activity 6 Complex Numbers Activity 5 Squares and Square Roots Activity 4 Fraction Products and Quotients Activity 3 Fractions Sums and Differences Activity 2 Decimals and Fractions Standard Activity 1 Heximals and Fractions This unit of instruction provides students with an opportunity to solidify their understanding of rational number and integer exponents. In addition it provides students with a concrete model of non-real number operation. Comments Activity 1 uses base six numbers to look at exponents and place value. The activity lays the foundation for an understanding of repeating and terminating decimals. 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. It is not uncommon for secondary students to still struggle with rational number concepts and operations. This unit gives them a different vehicle to try to understand and become more efficient with some of these critical concepts without it being "more of the same". A-SSE.3a Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. A-SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V IR to highlight resistance R. Math and The Mind’s Eye 2 © The Math Learning Center Activity 6 Complex Numbers Activity 5 Squares and Square Roots Activity 4 Fraction Products and Quotients Activity 3 Fractions Sums and Differences Activity 2 Decimals and Fractions Standard Activity 1 Heximals and Fractions Unit 12 Modeling Real and Complex Numbers continued Comments 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 notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. N.RN.2 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. 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. Models for complex numbers follow naturally from students' prior work with algebraic models and models for arithmetic operations. N-CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. N-CN.7 Solve quadratic equations with real coefficients that have complex solutions. Math and The Mind’s Eye 3 © The Math Learning Center