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College Algebra Unit 0 – Algebra of Calculus Scoring Criteria U1.PI 1 Interpret rational and irrational numbers and use properties of rational and irrational numbers. “1” – Emerging I have demonstrated the most basic knowledge/skills relevant to this standard. CCSS Domain(s): Number and Quantity ; Algebra “2” – Developing I have demonstrated relevant knowledge/skills, but have not yet demonstrated convincing evidence of fully meeting the standard. “3” – Achieving I have demonstrated that I have the knowledge/skills defined in the standard. Level 1 I can identify rational numbers and I know that numbers that are not rational are irrational. L2: Level 1, plus… I can perform basic Algebraic operations involving rational and irrational numbers. L3: Level 2, plus… I can explain informally that every number has a decimal expansion ; for rational numbers show that decimal expansion repeats eventually into a rational number. I can apply basic properties of integer exponents to generate equivalent numerical expressions. I can use radical symbols to represent solutions to power equations. I can explain the properties of rational exponents and apply these properties to simplify polynomial expressions. “4” – Excelling I have demonstrated the knowledge/skills defined by the standard with a high level of understanding/ability as defined by the discipline. L4: Level 3, plus… I can use rational approximation of irrational number to compare the size of irrational numbers without the use of a calculator. Performance Indicators CCSS: N-RN 3 U1.PI 2 Extend the properties of exponents to rational exponents I can apply the properties of rational exponents to rewrite more complex rational expressions in their simplified equivalent form. CCSS: N-RN 1, N-RN 2 U1.PI 3 Interpret Structure of Expressions and use the structure of an expression to rewrite it. I can interpret parts of an expression, such as terms, factors, and coefficients. I can use the structure of an expression to identify ways to re-write it. For example, I recognize that the difference of the squares can be use to rewrite I can rewrite a simple rational expression involving polynomials in different forms and add, subtract, multiply, and divide rational expressions. x 4 y 4 ( x 2 )2 ( y 2 )2 CCSS: A-SSE 2, A-APR 6, A-APR 7 I can explain that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression. ( x 2 y 2 )( x 2 y 2 ) U1.PI 4 Perform Arithmetic Operations with Complex Numbers. CCSS: N-CN1, N-CN 2, N-CN 3 I can identify a complex number i such that i²=-1, and I know that every complex number has the form a+bi with a and b real. I can convert complex numbers from their radical form into standard a+bi form. I can use the relationship i²=-1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. I can find a conjugate of a complex number; and use complex conjugates to find products and quotients of complex numbers.