Portable Assisted Study Sequence (PASS) Program

Course Description

This course is aligned with the California State Mathematics Standards and Frameworks and the five strands adopted by the State Board of Education: Statistics and Data Analysis, Number Sense, Algebra and Functions, Mathematical Reasoning and Measurement, and Geometry. Proficiency in the California Mathematics Standards covered in the course will help students acquire rudimentary math skills and sharpen critical thinking skills. It will prepare students to be successful on the Mathematics portion of the California High School Exit Exam (CAHSEE) and it can also be used as an intervention methodology for students who do not pass the math portion of the CAHSEE.

Credits: 5
Languages: English and Spanish

State Standards

High School Exit Exam

Course Content

Unit 1 - Number Sense and Mathematical Reasoning

California Mathematics Curriculum Standards

Students understand the place value of whole numbers (Grade 3: Number Sense 1.0)

Students know how to factor small whole numbers (Grade 4: Number Sense 4.0, 4.2)

Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers. (Grade 5: Number Sense 1.3, 1.4, 1.5)

Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages: (Grade 6: Number Sense 1.3)

Students calculate and solve problems involving addition, subtraction, multiplication, and division (Grade 6: Number Sense 2.4)

Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions. (Grade 6: Algebra and Functions 2.0)

Students know the properties of, and compute with, rational numbers expressed in a variety of forms. (Grade 7: Number Sense 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7)

Students use exponents, powers, and roots and use exponents in working with fractions. (Grade 7: Number Sense 2.1, 2.2, 2.3, 2.4, 2.5)

Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs. (Grade 7: Algebra and Functions 1.2, 1.3)

Students interpret and evaluate expressions involving integer powers and simple roots. (Grade 7: Algebra and Functions 2.1, 2.2)

Students make decisions about how to approach problems. (Grade 7: Mathematical Reasoning 1.1, 1.2, 1.3)

Students use strategies, skills, and concepts in finding solutions. (Grade 7: Mathematical Reasoning 2.1, 2.3, 2.4)

Students determine a solution is complete and move beyond a particular problem by generalizing to other situations. (Grade 7: Mathematical Reasoning 3.3)

Unit Objectives

Upon completion of this Unit, students will:

Understand the number system.
Understand properties and rules of operations.
Work with factors, multiples, primes, exponents, and square roots.
Understand algorithms.
Solve word problems involving ratios and proportions, percentage increase and decrease, the markups and discounts in the sale of goods, commissions and profit, and simple and compound interest.

Unit 2 - Algebra I and Mathematical Reasoning

California Mathematics Curriculum Standards

Students make decisions about how to approach problems. (Grade 7: Mathematical Reasoning 1.1, 1.2, 1.3)

Students use strategies, skills, and concepts in finding solutions. (Grade 7: Mathematical Reasoning 2.1, 2.3, 2.4)

Students determine a solution is complete and move beyond a particular problem by generalizing to other situations. (Grade 7: Mathematical Reasoning 3.3)

Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a power. They understand and use the rules of exponents. (Algebra I 2.0)

Students solve equations and inequalities involving absolute values. (Algebra I 3.0)

Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x –5) + 4(x–2) = 12. (Algebra I 4.0)

Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. (Algebra I 5.0)

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 6.0)

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 7.0)

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. (Algebra 8.0)

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 9.0)

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

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

Unit Objectives

Upon completion of this Unit, students will:

Understand operations with real numbers.
Solve algebraic expressions.
Solve linear equations in both one and two variables.
Solve linear inequalities in one variable.
Understand word problem applications dealing with rates, work, and mixtures.

Unit 3 - Algebra & Functions and Mathematical Reasoning

California Mathematics Curriculum Standards

Students make decisions about how to approach problems. (Grade 7: Mathematical Reasoning 1.1, 1.2, 1.3)

Students use strategies, skills, and concepts in finding solutions. (Grade 7: Mathematical Reasoning 2.1, 2.3, 2.4)

Students determine a solution is complete and move beyond a particular problem by generalizing to other situations. (Grade 7: Mathematical Reasoning 3.3)

Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs. (Grade 7: Algebra and Functions 1.1, 1.2, 1.5)

Students interpret and evaluate expressions involving integer powers and simple roots. (Grade 7: Algebra and Functions 2.1, 2.2)

Students graph and interpret linear and some nonlinear functions. (Grade 7: Algebra and Functions 3.1, 3.3, 3.4)

Students solve simple linear equations and inequalities over the rational numbers. (Grade 7: Algebra and Functions 4.1, 4.2)

Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x –5) + 4(x–2) = 12. (Algebra I 4.0)
Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. (Algebra I 5.0)

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 7.0)

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

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 I 16.0)

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 I 18.0)

Unit Objectives

Upon completion of this Unit, students will:

Simplify and evaluate algebraic expressions.
Solve equations and inequalities.
Solve linear functions.
Solve graphs and nonlinear functions.
Understand word problem applications dealing with rates, motion, and direct variation.

Unit 4 - Measurement & Geometry and Mathematical Reasoning

California Mathematics Curriculum Standards

Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems. (Grade 4: Measurements and Geometry 3.1, 3.5, 3.7)

Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures. (Grade 5: Measurements and Geometry 2.1)

Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions. (Grade 6: Algebra and Functions 2.1, 2.2)

Students identify and describe the properties of two-dimensional figures. (Grade 6: Measurements and Geometry 2.1, 2.2, 2.3)

Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems. (Grade 7: Measurements and Geometry 1.1, 1.2, 1.3)

Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale. (Grade 7: Measurements and Geometry 2.1, 2.2, 2.3, 2.4)

Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures. (Grade 7: Measurements and Geometry 3.2, 3.3, 3.4)

Students make decisions about how to approach problems. (Grade 7: Mathematical Reasoning 1.1, 1.2, 1.3)

Students use strategies, skills, and concepts in finding solutions. (Grade 7: Mathematical Reasoning 2.1, 2.3, 2.4)

Students determine a solution is complete and move beyond a particular problem by generalizing to other situations. (Grade 7: Mathematical Reasoning 3.3)

Unit Objectives

Upon completion of this Unit, students will:

Solve ratios and proportions.
Understand measurements and conversions.
Understand basic elements of geometry.
Solver perimeter and area problems.
Solve surface area and volume problems.
Understand coordinate graphs and geometry.

Unit 5 - Data Analysis and Intermediate Algebra

California Mathematics Curriculum Standards

Students compute and analyze statistical measurements for data sets. (Grade 6: Statistics, Data Analysis, and Probability 1.1)

Students use data samples of a population and describe the characteristics and limitations of the samples. (Grade 6: Statistics, Data Analysis, and Probability 2.5)

Students determine theoretical and experimental probabilities and use these to make predictions about events. (Grade 6: Statistics, Data Analysis, and Probability 3.1, 3.3, 3.5)

Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program. (Grade 7: Statistics, Data Analysis, and Probability 1.1, 1.2)

Students know the properties of, and compute with, rational numbers expressed in a variety of forms. (Grade 7: Number Sense 1.1, 1.2, 1.3, 1.6, 1.7)