Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.
California Standards for Algebra l | Omega Math's Alignment to California Standards |
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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: | Algebra l - e1.1 |
1.1 Students use properties of numbers to demonstrate whether assertions are true or false. | Algebra l - e1.1, e1.5, e1.7, e3.1, e3.2, e4.1, e5.5, e6.5, e7.2, e7.3, e7.4, e8.5, e10.3 |
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. | Algebra l - e1.4, chapter 8, e2.1, e2.2, e6.4 |
3.0 Students solve equations and inequalities involving absolute values. | Algebra l - Chapter 3, e1.7, e6.5 |
4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12. | Algebra l - e3.2 |
5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. | Algebra l - Chapter 10, e3.5 |
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). | Algebra l - e6.2, e6.3, e6.5 |
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. | Algebra l - e6.4 |
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. | Algebra l - e6.2, e6.4 |
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. | Algebra 1 - e7.4 |
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. | Algebra l - e2.4, e2.5, e2.7, e3.5, e4.6, e6.4, e7.3, e8.6, e10.1, e10.2, e10.3 |
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. | Algebra l - Chapter 4 |
12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. | Algebra l - e5.4 |
13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques. | Algebra l - Chapter 5 |
14.0 Students solve a quadratic equation by factoring or completing the square. | Algebra l - e4.6, e9.2 |
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. | Algebra l - Chapter 10 |
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. | Algebra ll - Chapter 10 |
17.0 Students 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. | Algebra ll - i10.2 |
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. | Algebra ll - i10.1 |
19.0 Students know the quadratic formula and are familiar with its proof by completing the square. | Algebra l - e9.3 |
20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. | Algebra l - e9.3 |
21.0 Students graph quadratic functions and know that their roots are the x-intercepts. | Algebra ll - i8.5 |
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. | Algebra l-e9.3 |
23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. | Algebra l - e4.6 |
24.0 Students use and know simple aspects of a logical argument. | Geometry - g2.1 |
24.1 Students explain the difference between inductive and deductive reasoning and identify and provide examples of each. | N/A |
24.2 Students identify the hypothesis and conclusion in logical deduction. 24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion. | Geometry - g2.1 |
25.0 Students 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: | Algebra l - e1.1 |
25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. | Geometry - g2.1, g2.2, g2.3 |
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. | Algebra l - e1.1, e1.5, e1.6, e1.7, e3.1, e3.2, e3.4, e5.5, e6.5, e7.2, e7.3, e7.4, e8.2, e8.5, e10.3 |
25.3 Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never. | Algebra 1 - e3.2 |