EL SEGUNDO UNIFIED
EL SEGUNDO HIGH SCHOOL
COURSE OF STUDY
Course Title: Algebra 1A and Algebra 1B
Department: Mathematics
Grade Levels: 10-12
COURSE DESCRIPTION
Algebra 1A: This course focuses on the mathematical concepts tested on the California High School Exit Exam. Students will develop an understanding of the symbolic language of mathematics. Students will understand the meaning of variables, expressions, equations, and inequalities. Students will evaluate, graph, and interpret the graphs of linear equations.
Algebra 1B: Symbolic reasoning and calculations with symbols are central in Algebra, and in the understanding of Algebra. In addition to the symbolic language required, algebraic skills and concepts are developed and used in a wide variety of problem solving situations. By the end of Algebra 1B, students understand, use, and connect a variety of techniques for solving linear equations, inequalities and systems of equations in applied contexts. 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: Two year Algebra 1AB program
Prerequisite for Enrollment: Algebra 1A: 79% or below in High School Pre-Algebra;
Score 69% or below on Entrance Exam
Algebra 1B: 60% or better in Algebra 1A
Recommendation for Enrollment: Teacher Recommendation.
Type of Course: Completion of Algebra 1B satisfies the Algebra requirement for High School. Satisfactory for admission to Community College (Both courses are not UC/CSU approved).
COURSE OUTLINE AND STANDARDS
California
State Standards tested on the California High School Exit Exam
ALGEBRA
1A:
I. STATISTICS, DATA ANALYSIS, and PROBABILITY (Integration of Core Knowledge)
Sixth Grade Standards:
1.1 Compute the mean, median, and mode of data sets
2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims
3.0 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1-P is the probability of an event not occurring.
3.5 Understand the difference between independent and dependent events.
Seventh Grade:
1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box and whisker plot; use the forms to display a single set of data or to compare two sets of data.
1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level)
1.3 Understand the meaning of, and be able to compute the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.
II. NUMBER SENSE (Integration of Core Knowledge)
Seventh Grade:
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
1.3 Convert fractions to decimals and percents and use these representations in estimation, computations, and applications.
1.6 Calculate the percentage of increases and decreases of a quantity.
1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
2.2 Add and subtract fractions by using factoring to find common denominators.
2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
III. ALGEBRA and FUNCTIONS (Integration of Core Knowledge)
Seventh Grade
1.1 Use variable and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A)
1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)^2.
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
3.1 Graph functions of the form y=nx^2 and y=nx^3 and use in solving problems.
3.2 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.
3.3 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of a line equals the quantities.
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
4.2 Solve multi-step problems involving rate, average speed, distance, and time or a direct variation.
IV. MEASUREMENT and GEOMETRY (Integration of Core Knowledge)
Seventh Grade
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurements systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters)/
1.2 Construct and read drawings and models made to scale.
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelogram, trapezoids, squares, triangles, circles, prisms and cylinders
2.2 Estimate and compute the area of more complex or irregular two-and three-dimensional figures by breaking the figures down into more basic geometric objects.
2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and volume is multiplied by the cube of the scale factor.
2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1square foot = 144 square inches or 1 ft^2 = 144 in^2)
3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations empirically verify the Pythagorean theorem by direct measurement.
3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
V. MATHEMATICAL REASONING (Integration of Core Knowledge; Critical Thinking/Problem Solving)
Seventh Grade
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
2.1 Use estimation to verify the reasonableness of calculated results.
2.3Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4Make and test conjectures by using both inductive and deductive reasoning.
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situation.
VI ALGEBRA 1
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, and taking a root. They understand and use the rules of exponents. (Integration of Core Knowledge)
3.0 Students solve equations and inequalities involving absolute value. (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 (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. (Integration of Core Knowledge; Critical Thinking/Problem Solving)
6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g. graph 2x + 6y = 4) (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. (Integration of Core Knowledge)
8.0 Students understand the concepts of parallel lines and how their slopes are related. (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. (Integration of Core Knowledge)
10.0Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques. (Integration of Core Knowledge; Critical Thinking/Problem Solving)
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. (Integration of Core Knowledge; Critical Thinking/Problem Solving)
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
function. (Integration
of Core Knowledge)
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. (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. (Integration of Core Knowledge)
21.0 Students graph quadratic functions and know that their roots are the x-intercepts (Integration of Core Knowledge)
23.0Students apply quadratic equations
to physical problems, such as the motion of an object under the force of
gravity. (Integration
of Core Knowledge; Critical Thinking/Problem Solving)
24.2 Students identify the hypothesis and conclusion in logical deduction. (Integration of Core Knowledge; Critical Thinking/Problem Solving)
24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion. (Integration of Core Knowledge; Critical Thinking/Problem Solving)
25.1 Students use properties of
numbers to construct simple, valid arguments (direct and indirect) for, or
formulate counterexamples to, claimed assertions. (Integration of Core Knowledge; Critical
Thinking/Problem Solving; Effective Communication)
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. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
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 sometime, always, or never. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)
Algebra 1B:
Review the Algebra 1 standards covered in Algebra 1A and include the following 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: (Integration of Core
Knowledge)
1.1: Students use properties of numbers to
demonstrate whether assertions are true or false. (Integration of Core Knowledge; Critical Thinking/Problem Solving)
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. (Integration
of Core Knowledge)
12.0
Students simplify fractions with polynomials in the numerator and
denominator by factoring both and reducing them to the lowest terms. (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. (Integration of Core Knowledge)
14.0: Students
solve a quadratic equation by factoring or completing the square (Integration of Core Knowledge)
19.0: Students know
the quadratic formula and are familiar with its proof by completing the square (Integration of Core
Knowledge; Critical Thinking/Problem Solving)
20.0: Students use
the quadratic formula to find the roots of a second-degree polynomial and to
solve quadratic equations. (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. (Integration Of Core
Knowledge)
24.0 Students use and know simple aspects of a logical argument
24.1: Students explain the difference between inductive and deductive reasoning
(Integration
of Core Knowledge; Critical Thinking/Problem Solving; 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. (Integration of Core Knowledge; Critical Thinking/Problem Solving; 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. Computer Program: Accelerated Math
C. College Prep Math (CPM)
D. 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.