ALGEBRA 1AB (Annual Course-Grade 8-12)
Prerequisite: none
August 18, 1997

31-03-01/02 Algebra 1AB

COURSE DESCRIPTION

In Algebra, students learn to reason symbolically, and the complexity and types of equations and problems that they are able to solve increase dramatically as a consequence.  The key content for the course, Algebra I, involves understanding, writing, solving, and graphing linear and quadratic equations, including systems of two linear equations in two unknowns.  Quadratic equations may be solved by factoring, completing the square, using graphs or applying the quadratic formula.

Students should also become comfortable with operations on monomial and polynomial expressions.  They learn to solve problems employing all of these techniques, and they extend their mathematical reasoning in many and important ways, including justifying steps in an algebraic procedure and checking algebraic arguments for validity.

CALIFORNIA BENCHMARK ALGEBRA I STANDARDS

Upon graduation from LAUSD, students will be able to: 

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.

3.0 Students solve equations and inequalities involving absolute values.

4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12. (Anchor on 5.0 and 6.0)

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.

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).

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.

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.

10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques.

12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

13.0 Students add, subtract, multiply, and divide rational expressions and functions.   Students solve both computationally and conceptually challenging problems by using these techniques.

14.0 Students solve a quadratic equation by factoring or completing the square.

15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.

19.0 Students know the quadratic formula and are familiar with its proof
by completing the square.

20.0 Students use the quadratic formula to find the roots of a second-degree
polynomial and to solve quadratic equations.

21.0 Students graph quadratic functions and know that their roots are the
x-intercepts.

23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.

24.0 Students use and know simple aspects of a logical argument:

24.1 Students explain the difference between inductive and deductive reasoning and identify and provide examples of each.

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.

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:

25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

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.

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.