Algebra 1

Algebra 1

Secondary Mathematics Instructional Guide 2008-2009

Los Angeles Unified School District Secondary Mathematics Branch

ALGEBRA 1 AB (Annual Course ? Grade 8 or 9) Prerequisite: Mathematics 7AB

310301 310302

Algebra 1A Algebra 1B

COURSE DESCRIPTION

The purpose of this course is to serve as the vehicle by which students make the transition from arithmetic to symbolic mathematical reasoning. It is an opportunity for students to extend and practice logical reasoning in the context of understanding, writing, solving, and graphing problems involving linear and quadratic equations (including systems of two linear equations in two unknowns).

In this course, students are expected to demonstrate their ability to extend specific problems and conditions to general assertions about mathematical situations. Additionally, they are expected to justify steps in an algebraic procedure and check algebraic arguments for validity.

COURSE SYLLABUS

The following are recurring standards in the course:

Algebra I 24.0 Students use and know simple aspects of a logical argument. Algebra I 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.

Unit 1

Recommended Focus Standards Algebra I 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 I 4.0 Students simplify expressions before solving linear equations and inequalities in one variable. Algebra I 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

Scope and Sequence This unit sets the stage for success in Algebra by providing time to review arithmetic (whole numbers, fractions, decimals, and percents) and proceeds on to cover foundational algebra skills necessary to solve equations. Subsequent to this review, students will proceed to solving equations in one variable (including equations with absolute value).

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Los Angeles Unified School District Secondary Mathematics Branch

Unit 2

Recommended Focus Standards Algebra I 6.0 Students graph a linear equation and compute the x- and y- intercepts. (e.g.,

graph 2 x 6 y 4 ). They are also able to sketch the region defined by linear inequalities (e.g., they sketch the region defined by 2 x 6 y 4 ). Algebra I 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.

Scope and Sequence The focus of this unit is graphing and deriving linear equations using a variety of techniques. The unit also addresses solving inequalities (including absolute value) in one variable.

Unit 3 Recommended Focus Standards

Algebra I 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 I 15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. Algebra I 19.0 Students know the quadratic formula and are familiar with its proof by completing the square. Algebra I 20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. Algebra I 21.0 Students graph quadratic functions and know that their roots are the x-intercepts. Algebra I 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.

Scope and Sequence This unit includes two main foci. Linear relationships are concluded with solving systems of linear equations and inequalities. The students will then learn how to solve quadratic equations and how to interpret the graphs of quadratic functions.

Unit 4

Recommended Focus Standards Algebra I 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve

multistep problems, including word problems, by using these techniques. Algebra I 12.0 Students simplify fractions with polynomials in the numerator and denominator by

factoring both and reducing them to the lowest terms. Algebra I 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 I 14.0 Students solve a quadratic equation by factoring or completing the square.

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Los Angeles Unified School District Secondary Mathematics Branch

Scope and Sequence It is important that students learn how to perform polynomial arithmetic (including factoring) and apply factoring as a technique to solve simple quadratics prior to the CST. After the CST, students will learn the arithmetic of rational expressions and will solve rational equations in one variable.

REPRESENTATIVE PERFORMANCE OUTCOMES AND SKILLS In this course, students will know and be able to:

x Interpret the meaning of variables and variable expressions x Solve linear equations (including proportions) in one variable x Apply the concept of absolute value to simple equations x Graph a linear function by plotting points, using intercepts, and using the slope and y-intercept x Sketch the region defined by a linear inequality x Derive the equation of a line when given a variety of parameters for that line x Solve inequalities in one variable (including those with absolute value) x Solve systems of linear equations by graphing, using substitution, and using elimination x Solve systems of linear inequalities by graphing x Solve quadratic equations by graphing, finding square roots, using the quadratic formula, and

factoring x Simplify and perform arithmetic operations on and with rational expressions x Solve rational equations x Solve application problems using the above techniques

ASSESSMENTS will include: x Teacher designed standards-based quizzes and tests x Projects and group tasks x Teacher designed formative assessments x Periodic Assessments

TEXTS/MATERIALS x LAUSD Secondary Mathematics Instructional Guide x Textbook: District approved materials x Supplemental materials and resources

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U N I T

1

Algebra 1: Unit Concept Organizer

Linear Equations and Functions

Understand the language of algebra

1.0, 1.1, 2.0, 16.0, 17.0, 24.0, 25.1

Understand and solve linear equations 4.0, 5.0

Understand and graph linear equations, functions and patterns

6.0, 7.0, 16.0, 17.0, 18.0

x Understand the meaning of variables and variable expressions

x Evaluate variable expressions x Simplify numerical and variable expressions

using the properties of real numbers including the distributive property x Use properties of numbers to demonstrate whether assertions are true or false x Use properties to formulate counterexamples to claimed assertions x Use operations such as taking the opposite, finding the reciprocal and taking a root

x Translate between verbal sentences and equations

x Solve multi-step linear equations in one variable (involving addition, subtraction, multiplication and division)

x Solve equations for a given variable x Solve problems using proportions x Solve application problems using all of

these techniques

x Identify the domain and range of functions and relations

x Determine whether a relation is a function

x Graph linear equations x Compute the x and y-intercepts of a

linear equation x Verify that a point lies on a line

?KEY Standards - #CST

Questions Other Standards - #CST

Questions * 1 / 2 : 1 question every 2

years

CONCEPT LESSON: TT-Tommy's T-Shirts SP-Surround the Pool SC-Stack of Cups

1.0

1.1

2.0

4.0

5.0

6.0

7.0

16.0

17.0 18.0 24.0 25.0

NA 1/2* ?4 ?3 ?6 ?4 ?4

?*

1

?*

1

1 ?*

TT

SP

SC

SC

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