EL SEGUNDO UNIFIED
EL SEGUNDO HIGH SCHOOL
COURSE OF STUDY
Course Title: Algebra 1AB
Department: Mathematics
Grade Levels: 7-12
COURSE DESCRIPTION
ALGEBRA 1
Symbolic reasoning and calculations with symbols are central in Algebra, and in the understanding of Algebra, a student develops an understanding of the symbolic language of mathematics. In addition, algebraic skills and concepts are developed and used in a wide variety of problem solving situations. By the end of Algebra, students understand, use, and connect a variety of techniques for solving linear equations, inequalities and systems of equations in applied contexts. They understand the meaning of variables, expressions, equations, and inequalities, and their use as models for situations. Students evaluate, graph, and interpret the graphs of a wide variety of functions, and connect the behavior of the graphs to their corresponding representations as tables, equations, and situations. Students apply proportional reasoning to connect geometric situations involving similarity to algebraic and numerical situations involving direct variation.
Length: One Year
Prerequisite for Enrollment: High School: 80 % or better in high school pre-algebra; Score 75% or better on placement exam. Middle School : 75% or better in 8th grade Honors math; 90% or better in 7th grade math; Score 80% or better on placement exam.
Recommendation for Enrollment: Math placement test and Teacher Recommendation.
Type of Course: College preparatory (UC/CSU), meets high school Algebra requirement
COURSE OUTLINE AND STANDARDS
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:
1.1: Students use properties of numbers to
demonstrate whether assertions are true or false.
(Effective Communication)
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. (Meaningful Integration of Core Knowledge)
3.0: Students solve equations and inequalities
involving absolute values. (Meaningful
Integration of Core Knowledge)
4.0: Students simplify expressions before solving
linear equations and inequalities in one variable, such as 3(2x-5)+4(x-2)=12. (Meaningful Integration of Core Knowledge)
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.
(Critical Thinking/Problem Solving; Meaningful Integration of Core Knowledge; Effective Communication)
6.0: Students graph a linear equation and compute
the x- and y-intercepts. They are also
able to sketch the region defined by linear inequality. (Meaningful Integration of Core Knowledge)
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. (Critical Thinking/Problem Solving; Meaningful
Integration of Core Knowledge)
8.0: Students understand the concepts of parallel
lines and perpendicular lines and how their slopes are related. Students are able to find the equation of a
line perpendicular to a given line that passes through a given point. (Meaningful Integration of Core Knowledge)
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. (Meaningful Integration of Core
Knowledge; Critical Thinking; Effective Communication)
10.0: Students add, subtract, multiply, and divide
monomials and polynomials. Students
solve multi-step problems, including word problems, by using these techniques. (Critical Thinking/Problem Solving; Meaningful
Integration of Core Knowledge; Effective
Communication)
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. (Meaningful Integration of Core Knowledge; Critical Thinking; Effective Communication)
12.0: Students simplify fractions with polynomials
in the numerator and denominator by factoring both and reducing them to the
lowest terms. (Meaningful Integration of Core
Knowledge)
13.0: Students add, subtract, multiply, and divide
rational expressions and functions.
Students solve both computationally and conceptually challenging
problems by using these techniques. (Critical
Thinking/Problem Solving; Meaningful Integration of Core Knowledge; Effective
Communication)
14.0: Students solve a quadratic equation by factoring or completing the square. (Meaningful Integration of Core Knowledge)
15.0: Students apply algebraic techniques to solve
rate problems, work problem, and percent mixture problems. (Critical Thinking/Problem Solving; Meaningful
Integration of Core Knowledge; Effective Communication)
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. (Critical Thinking/Problem Solving; Meaningful Integration of Core Knowledge; Effective Communication)
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. (Meaningful Integration of Core Knowledge)
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. (Critical Thinking/Problem Solving; Meaningful Integration of Core Knowledge; Effective Communication)
19.0: Students know the quadratic formula and are familiar with its proof by completing the square. (Critical Thinking/Problem Solving; Meaningful Integration of Core Knowledge; Effective Communication)
20.0: Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. (Meaningful Integration of Core Knowledge)
21.0: Students graph quadratic functions and know that their roots are the x-intercepts. (Meaningful Integration of Core Knowledge)
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. (Meaningful Integration of Core Knowledge/ Critical
Thinking)
23.0: Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. (Critical Thinking/Problem Solving; Meaningful Integration of Core Knowledge; Effective Communication)
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
(Critical Thinking/Problem Solving; Meaningful Integration of Core Knowledge; Effective Communication)
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 correctly applied 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.
(Critical Thinking/Problem Solving; Meaningful Integration of Core Knowledge; Effective Communication)
INSTRUCTIONAL METHODS
A. Lecture and Guided Practice
B. Investigations (Personal/Social Development)
C. Manipulatives
D. Classwork and Homework
E. Individual work
F. Group Work (Personal/Social Development)
G. Short term projects (Personal/Social Development)
EVALUATION/GRADING OF STUDENT WORK
A. Quizzes and Chapter tests (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
B. Semester exam (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
C. Comprehensive final exam (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
D. Homework and classroom participation (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)
E. Projects (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)
F. Written Essays (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)
INSTRUCTIONAL MATERIALS
A.
Text: Algebra 1,
B. Scientific Calculator
1. Students will learn when it is appropriate to use the calculator as a valuable tool.
2. Calculators are not to be used for skills; however are necessary for certain types of problem solving.