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# Mathematics

## 6TH GRADE MATH COURSE DESCRIPTION

**PREREQUISITE:** None

**COURSE DESCRIPTION**

Math 6 coursework reinforces, strengthens, and develops concepts and skills previously taught in order to complete the study of whole numbers, decimals, and fractions. Emphasis is placed on: rational numbers; probability; statistics; the arithmetic of fractions; proportional relationships; multiple representations; functions, patterns and generalizations; discrete mathematics, geometry; logic; real-world applications; and problem-solving strategies.

**TEXTBOOK & MATERIALS**

Course 1: Concepts and Skills (California edition), McDougal-Littell, c. 2001

**COURSE OBJECTIVES**

The student will:

- Compare and order rational numbers on a number line.
- Master the four arithmetic operations (addition, subtraction, multiplication, and division) with whole numbers, positive fractions, positive decimals, and positive and negative integers.
- Demonstrate fluency with the long-division algorithm.
- Add fractions with unlike denominators.
- Convert between percents, decimals, and fractions, esp. for values over 1.0 = 1 = 100%
- Use exponents to show the multiples of a single factor.
- Routinely use ratios, proportions, and decimals to represent and analyze theoretical versus experimental probability and compute probability for independent or dependent events.
- Routinely use addition and multiplication of fractions to calculate the probabilities for compound events.
- Master the concepts of mean, median, and mode of data sets and the process of calculating the range of a data set.
- Analyze data and sampling processes for relevant vs. irrelevant facts, possible bias, and misleading conclusions.
- Understand and apply the concepts of greatest common divisor (GCD), least common multiple, (LCM), ratio, and proportion.
- Understand and apply rate and ratio as context-dependent interpretations of dividing one number by another.
- Accurately compute and solve percentage problems (e.g. discount, tax, tips, interest)
- Know the concept of pi and the formulas for circumference and area of circles.
- Use letters to represent constants or variables in formulas for geometric shapes (square, rhombus, trapezoid, triangle, triangular prism, and cylinder).
- Use letters to represent constants or unknown quantities for parts of expressions, ratios, and proportions.
- Write and solve one-step linear equations.

## PRE-ALGEBRA COURSE DESCRIPTION

**PREREQUISITE**: None for 7th grade students. Placement test for 6th graders.

**COURSE DESCRIPTION**

Pre-Algebra 7 builds a strong foundation of the principles of algebra by integrating topics of geometry, trigonometry, probability, and statistics. Students apply their computational skills to algebraic thinking and conceptual problem solving. Coursework relies heavily on the student’s command of the operations of addition, subtraction, multiplication, and division to extend the study of whole numbers, integers, decimals, and fractions. Attention is given to the relationships between fractions, decimals, and percents. Key content develops a deep understanding of underlying concepts that support algebraic thinking: rational versus irrational numbers, negative fractions and decimals, absolute value, variable, ratio, direct proportion, scale, slope, rate, dimensional analysis, probability, similarity, congruence, and the Pythagorean Theorem.

**TEXTBOOK & MATERIALS**

Course 2: Concepts and Skills (California edition), McDougal-Littell, c. 2001

**COURSE OBJECTIVES**

The students will:

- Manipulate numbers and equations with understanding of the general principles at work.
- Understand and use factoring of numerators and denominators and the properties of exponents.
- Recognize and generate equivalent expressions.
- Solve one- or two-step equations and inequalities in one variable.
- Make conversions between different units of measurement.
- Draw, measure, visualize, compare, transform, and classify geometric objects.
- Know the Pythagorean Theorem and solve problems to compute the length of an unknown side.
- Know how to compute the surface area and volume of basic 3-D objects, and understand how area and volume change with a change in scale.
- Memorize and apply the formulas for the volumes of cylinders and prisms.
- Know and use different representations of fractional numbers (fractions, decimals, and percents), and are proficient at changing from one form to another.
- Have facility with ratio and proportion and apply to rates, percent, similarity, scaling, and slope of linear equations.
- Compute patterns of increase and decrease.
- Compute simple and compound interest.
- Solve and graph linear functions and apply understanding of the idea of slope and its relation to ratio.

## ALGEBRA I COURSE DESCRIPTION

**PREREQUISITE:** 7th grade pre-Algebra.

**COURSE DESCRIPTION**

Algebra students learn to reason and calculate with symbols over a wide variety of problem-solving situations. Algebra emphasizes concepts and skills that support successful abstract thinking. Attention is given to proportional relationships, multiple representations, patterns and generalizations, error analysis, and estimation. Students learn to recognize and apply familiar operations, procedures, and mathematical patterns to real-world problems involving unknown variables. Key content involves understanding, writing, solving, and graphing linear and quadratic equations, including systems of linear equations in two unknowns and systems of linear inequalities in two unknowns. Students may earn High School graduation credits by taking and passing the District Algebra HE exit exam.

**TEXTBOOK & MATERIALS**

Algebra One: Concepts and Skills (California edition), McDougal-Littell, c. 2001

**COURSE OBJECTIVES**

The student will:

- Learn to reason using algebraic symbols and algebraic procedures.
- Understand, write, solve, and graph linear equations and linear inequalities with one variable.
- Use a graph or the point-slope formula to compute the x- and y-intercepts and derive linear equations.
- Understand, write, solve, and graph systems of two linear equations in two variables, and two linear inequalities in two variables.
- Understand, write, solve, and graph quadratic equations.
- Solve, quadratic equations by factoring, completing the square, using graphs, or applying the formula.
- Be adept with operations on monomial and polynomial expressions.
- Justify steps in an algebraic procedure.
- Check algebraic arguments for validity.

## ALGEBRA I HE COURSE DESCRIPTION

**PREREQUISITE:** Pre-Algebra and placement test.

**COURSE DESCRIPTION**

Algebra HE is a rigorous high school level course. Algebra students learn to reason and calculate with symbols over a wide variety of problem-solving situations. This course introduces students to equations, inequalities, and polynomials. Students will explore the rectangular coordinate plane, systems of equations in two variables, rational expressions, radicals, and quadratic equations. As students gain understanding of subject matter, they will develop skills in critical thinking and problem solving. This course meets all California state requirements for Algebra 1. Students may earn High School graduation credits by taking and passing the District Algebra HE exit exam.

**TEXTBOOK & MATERIALS**

Algebra I:; Larson, Boswell, Kanold, & Stiff (H.S. Edition), McDougal Litell, 2001

**COURSE OBJRCTIVES**

The students will:

- Understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power and they understand and use the rules of exponents.
- Understand how to solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
- Understand how to communicate a mathematical relationship with a graph.
- Understand the concepts of graphing linear relationships and linear inequalities using a variety of algebraic techniques.
- Understand and solve a system of two linear equations in two variables algebraically and interpret the answer graphically.
- Apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
- 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.
- Understand and use 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.
- Understand the use of quadratic equations to model real-world phenomena.

## GEOMETRY COURSE DESCRIPTION

**PREREQUISITE**: Algebra HE and pass Algebra HE Exam.

**COURSE DESCRIPTION**

This course introduces students to properties of angles, triangles and other polygons, circles, space figures, coordinate geometry, and transformations. Course content emphasizes the use of logic, valid arguments, and construction of proofs. This course meets all California state requirements for Geometry. Students may earn high school graduation credits by taking and passing the District Geometry exit exam.

**TEXTBOOK & MATERIALS**

Geometry (California edition), McDougal-Littell, c. 2004

**COURSE OBJECTIVES**

The student will:

- Employ inductive and deductive reasoning to formulate logical arguments and justify conclusions using a library of definitions, axioms, theorems, and postulates.
- Use counterexamples to disprove statements when conclusions cannot be drawn.
- Be able to differentiate between one-, two-, and three-dimensional objects.
- Use the appropriate quantity to measure the span, coverage, or capacity of an object.
- Select and apply the proper formula to determine the area and volume of a geometric figure.
- Be able to compare the perimeter, area, and volume of an object with that of a similar object that has undergone a size change.
- Recognize under what conditions use of the Pythagorean Theorem is appropriate, find the missing length of a right triangle given the lengths of the remaining sides using the Pythagorean Theorem, and apply the Pythagorean Theorem to a variety of two- and three-dimensional situations.
- Use the trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
- Use trigonometric functions in a variety of pure and applied contexts.
- Draw on the special right triangles to find missing sides.
- Identify what is invariant under rotations, translations, and reflections.
- Extend the concepts of rotations, translations, and reflections to develop the idea of congruence.

• Link to California Mathematics Content Standards