| 1.0 |
| Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable: |
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| 1.1 |
Students use properties of numbers to demonstrate whether assertions are true or false. |
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| 2.0 |
| Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. |
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| 3.0 |
| Students solve equations and inequalities involving absolute values. |
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| 4.0 |
| Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12. |
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| 5.0 |
| Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. |
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| 6.0 |
| Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). |
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| 7.0 |
| Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. |
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| 8.0 |
| Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. |
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| 9.0 |
| Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. |
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| 10.0 |
| Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques. |
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| 11.0 |
| Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. |
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| 12.0 |
| Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. |
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| 13.0 |
| Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques. |
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| 14.0 |
| Students solve a quadratic equation by factoring or completing the square. |
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| 15.0 |
| Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. |
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| 16.0 |
| Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. |
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| 17.0 |
| Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pair, or a symbolic expression. |
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| 18.0 |
| Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. |
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| 19.0 |
| Students know the quadratic formula and are familiar with it proof by completing the square. |
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| 20.0 |
| Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. |
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| 21.0 |
| Students graph quadratic functions and know that their roots are the x-intercepts. |
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| 22.0 |
| Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points. |
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| 23.0 |
| Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. |
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| 24.0 |
| Students use and know simple aspects of a logical argument: |
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| 24.1 |
Students explain the difference between inductive and deductive reasoning and identify and provide examples of each. |
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| 24.2 |
Students identify the hypothesis and conclusion in logical deduction. |
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| 24.3 |
Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion. |
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| 25.0 |
| Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion. |
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| 25.1 |
Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. |
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| 25.2 |
Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step. |
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| 25.3 |
Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, student determine whether the statement is true sometimes, always, or never. |
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