I1. Number Sense and Numerical Operations. Compute with rational numbers fluently and accurately without a calculator.

Evidence of Learning

ADP Benchmarks College Readiness Standards

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I1.1.
Add, subtract, multiply and divide integers, fractions and decimals. [Core]
4.2a
Complete multi-step computations using the order of operations and the properties of operations (associative, commutative, distributive, etc.) in situations involving combinations of real numbers.
4.2b
Recognize and justify the need for an exact answer in a given situation.
4.2c
Select and justify appropriate strategies and tools to compute the answer in a problem.
I1.2.
Calculate and apply ratios, proportions, rates and percentages to solve problems.
4.2a
Complete multi-step computations using the order of operations and the properties of operations (associative, commutative, distributive, etc.) in situations involving combinations of real numbers.
4.2b
Recognize and justify the need for an exact answer in a given situation.
4.2c
Select and justify appropriate strategies and tools to compute the answer in a problem.
5.3b
Apply and justify the applicability of transformations, congruence, similarity, ratios, and proportions in problemsolving situations.
I1.3.
Use the correct order of operations to evaluate arithmetic expressions, including those containing parentheses. [Core]
4.2a
Complete multi-step computations using the order of operations and the properties of operations (associative, commutative, distributive, etc.) in situations involving combinations of real numbers. 
I1.4.
Explain and apply basic number theory concepts such as prime number, factor, divisibility, least common multiple and greatest common divisor.
4.1d
Represent real numbers with rational exponents.
I1.5.
Multiply and divide numbers expressed in scientific notation.
4.1c
Apply the definition for negative integer exponents of real numbers..
4.2a
Complete multi-step computations using the order of operations and the properties of operations (associative, commutative, distributive, etc.) in situations involving combinations of real numbers.
4.2b
Recognize and justify the need for an exact answer in a given situation.
4.2c
Select and justify appropriate strategies and tools to compute the answer in a problem.

I2. Number Sense and Numerical Operations. Recognize and apply magnitude (absolute value) and ordering of real numbers:

Evidence of Learning

ADP Benchmarks College Readiness Standards

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I2.1.
Locate the position of a number on the number line, know that its distance from the origin is its absolute value and know that the distance between two numbers on the number line is the absolute value of their difference.
I2.2
Determine the relative position on the number line of numbers and the relative magnitude of numbers expressed in fractional form, in decimal form, as roots or in scientific notation.
4.1e
Compare and order real numbers without a calculator using relationships between integers, and the effects of radicals and rational exponents on those relationships.

I3. Number Sense and Numerical Operations.Understand that to solve certain problems and equations, number systems need to be extended from whole numbers to the set of all integers (positive, negative and zero), from integers to rational numbers, from rational numbers to real numbers (rational and irrational numbers) and from real numbers to complex numbers; define and give examples of each of these types of numbers.

Evidence of Learning

College Readiness Standards

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4.1a
Explain the meaning of the square root of a number, including why negative numbers have no real square roots.
4.1b
Describe a situation that requires an irrational number and provide an example of an irrational number.
4.1c
Apply the definition for negative integer exponents of real numbers.
4.1d
Represent real numbers with rational exponents.
4.1e
Compare and order real numbers without a calculator using relationships between integers, and the effects of radicals and rational exponents on those relationships.
4.4a
Add, subtract, multiply, and divide complex numbers; express in standard form and explain the properties (i.e., why useful; when used).
4.4b
Describe a situation that requires a complex number (include an algebraic example and a graphical example).

I4. Number Sense and Numerical Operations.Understand the capabilities and the limitations of calculators and computers in solving problems.

Evidence of Learning

ADP Benchmarks College Readiness Standards

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I4.1.
Use calculators appropriately and make estimations without a calculator regularly to detect potential errors. [Core]
4.2c
Select and justify appropriate strategies and tools to compute the answer in a problem.  
4.3a
Recognize and justify the sufficiency of estimating or approximating the result of a calculation involving real numbers.
4.3b
Use estimation to predict or verify the reasonableness of calculated results.
I4.2
Use graphing calculators and computer spreadsheets.
4.2c
Select and justify appropriate strategies and tools to compute the answer in a problem.