| Alg1.0 Simplifying Expressions |
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Students … |
| 1AL 1.1 |
EV PDF 8MC
EOT |
Understand and use such operations as finding the opposite and finding the reciprocal. |
| 1AL 1.2 |
EV PDF 16MC
EV PDF 3MC |
Understand determining a root, simplifying a root (e.g. surds) and the meaning of a fractional power (rational exponents) and understand and use the rules of exponents( Index laws). |
| 1AL 1.3 |
EV PDF 8BI
EOT: MC or SA
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Simplify or evaluate linear expressions in one variable with integer, fraction and decimal coefficients. |
| 1AL 1.4 |
EV PDF 16MC
EOT - MC |
Solve equations and inequalities involving absolute value and know how to use both interval and number line notation. |
| Alg2.0 Linear Equations & Inequalities |
| 1AL 2.1 |
EV PDF 4BI
EOT: MC SA
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Graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4) using a table of points, a graph or an equation. |
| 1AL 2.2 |
EV PDF 4MC
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Are able to sketch the region defined by linear inequality (e.g. 2x + 6y < 4). |
| 1AL 2.3 |
EV PDF 16TF |
Can verify that a point lies on a line, given an equation of the line. |
| 1AL 2.4 |
EV PDF 4MC |
Solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. |
| 1AL 2.5 |
slope: EV PDF 8MC
slope-int: EV PDF 8MC
slope from graph: EV PDF 20MC
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Are able to derive linear equations by using the point-slope formula. |
| 1AL 2.6 |
EV PDF 6MC |
Understand the concepts of parallel lines and perpendicular lines and how those slopes are related and are able to find the equation of a line passing through a point and parallel or perpendicular to a given line. |
| 1AL 2.7 |
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Know and apply the formula for the distance between two points and between a point and a line. |
| Alg3.0 Linear Systems |
| 1AL 3.1 |
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Solve a system of two linear equations in two variables graphically. |
| 1AL 3.2 |
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Solve a system of two linear equations in two variables algebraically using the elimination and substitution methods. |
| 1AL 3.3 |
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Understand both algebraically and geometrically the three possible conclusions of a system of two linear equations in two variables (inconsistent, infinite and one solution). |
| 1AL 3.4 |
Work: EV PDF
8MC+3NR
Mixture: EV PDF 2MC
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Solves real-world problems involving the solution of a system of two linear equations in two variables, including rate problems, work problems, and percent mixture problems. |
| Alg4.0 Polynomials |
| 1AL 4.1 |
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Add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques. |
| 1AL 4.2 |
EV PDF 12MC+6NR |
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 (see also 1AL 5.2) |
| 1AL 4.3 |
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Simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. |
| 1AL 4.4 |
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Add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques. |
| Alg5.0 Quadratics |
| 1AL 5.1 |
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Solve a quadratic equation by factoring or completing the square. |
| 1AL 5.2 |
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Know the quadratic formula and are familiar with its proof by completing the square. |
| 1AL 5.3 |
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Use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. |
| 1AL 5.4 |
EV PDF 6MC |
Graph quadratic functions and know that their roots are the x- intercepts (zeros). |
| 1AL 5.5 |
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Determine the axis of symmetry of a quadratic and how the coefficients affect its position on a graph. |
| 1AL 5.6 |
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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. |
| 1AL 5.7 |
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Apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. |
| Alg6.0 Functions |
| 1AL 6.1 |
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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. |
| 1AL 6.2 |
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Determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression. |
| 1AL 6.3 |
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Determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. |
| Alg7.0 Algebraic Logic |
| 1AL 7.1 |
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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. |
| 1AL 7.2 |
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Use and know simple aspects of a logical argument:
- Explain the difference between inductive and deductive reasoning and identify and provide examples of each.
- Identify the hypothesis and conclusion in logical deduction.
- 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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| 1AL 7.3 |
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Use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:
- Use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.
- 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.
- Determine whether the statement is true sometimes, always, or never, given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities.
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