El SEGUNDO UNIFIED SCHOOL DISTRICT

EL SEGUNDO HIGH SCHOOL

 

COURSE OF STUDY

 

Course Title:    Basic Pre-Algebra

Department:     Mathematics

Grade Levels:   9-10

 

COURSE DESCRIPTION

 

 

By the end of basic pre-algebra, students are able to manipulate numbers and equations and understand the general principles at work.  Students understand and use factoring of numerators and denominators and properties of exponents.  They know the Pythagorean Theorem and solve problems in which they compute the length of an unknown side.  Students make conversions between different units of measurement.  They know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another.  They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple interest.  They graph linear functions and understand the idea of slope and its relation to ratio.

 

Length:  One or Two Years

Prerequisite for Enrollment:  Individual Education Plan (IEP)

Recommendation for Enrollment:  Entrance exam and successful completion of 6th grade math

Type of  Course:  This course is necessary preparation for Algebra, and meets the math graduation requirement. It is not a college preparatory course.

 

Note:  The highlighted concepts are tested on the California High School Exit Exam

 

Students must master the highlighted concepts to pass Basic Pre-Algebra

 

COURSE OUTLINE AND STANDARDS

California State Standards for 7th Grade Mathematics

 

NUMBER SENSE

 

1.       Students know the properties of and compute with rational numbers expressed in a variety of forms.  (Integration of Core Knowledge)

 

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 the whole number powers. 

 

1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. 

 

1.4 Differentiate between rational and irrational numbers.

 

1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.

 

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. (Integration of Core Knowledge; Critical Thinking/Problem Solving)

 

2.       Students use exponents, powers, and roots and use exponents in working with fractions. (Integration of Core Knowledge)

 

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 fractions 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.

 

ALGEBRA AND FUNCTIONS

 

1.      Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities and graphs. (Integration of Core Knowledge)

 

1.1 Use variables and appropriate operations to write an expression, an equation, an inequality or a system of equations or inequalities that represents a verbal description. 

 

1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2 .

 

1.3  Simplify  numerical expressions by applying properties of rational numbers (identity, inverse, distributive, associative, commutative) and justify the process used. (Critical Thinking/Problem Solving; Effective Communication)

 

1.4  Use algebraic terminology correctly  (e.g., variable, equation, term, coefficient, inequality, expression, constant) 

 

1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in terms of the situation represented by the graph. 

 

2.      Students interpret and evaluate expressions involving integer powers and simple roots. (Integration of Core Knowledge)

 

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.      Students graph and interpret linear and some non-linear functions. (Integration of Core Knowledge)

 

3.1 Graph functions of the form y=nx2 and y=nx3 and use in solving problems

 

3.2  Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths.

 

3.3  Graph linear functions, noting that the vertical change per unit of horizontal change is always the same and know that the ratio is called the slope of a graph

 

3.4  Plot the values of quantities whose ratios are always the same.  Fit a line to the plot and understand that the slope of the line equals the quantities. 

 

4.      Students solve simple linear equations and inequalities over the rational numbers . (Integration of Core Knowledge)

 

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 direct variation. (Critical Thinking/Problem Solving)

 

 

 

MEASUREMENT AND GEOMETRY

 

1.      Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems. (Integration of Core Knowledge)

 

1.1 Compare weights, capacities, geometric measure, times and temperatures within and between measurement systems.  (e.g., miles per hour to feet per second) 

 

1.2 Construct and read scale drawings and models made to scale. 

 

1.3 Use measures expressed as rates and measures expressed as products to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.

 

2.      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: (Integration of Core Knowledge)

 

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, parallelograms, 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 the 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 and to conversions between units, 1 cubic inch is approximately 16.38 cubic centimeters.

 

3.      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.  (Integration of Core Knowledge)

 

3.1  Identify and construct basic elements of geometric figures by using a compass and straightedge.

 

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.

 

3.5  Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.

 

3.6  Identify elements of three-dimensional geometric objects.

 

STATISTICS, DATA ANALYSIS AND PROBABILITY

 

1.       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. (Integration of Core Knowledge)

 

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.

 

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.

 

MATHEMATICAL REASONING

 

1.       Students make decisions about how to approach problems. (Critical Thinking/Problem Solving; Effective Communication)

 

1.1 Analyze problems by identifying relationships, discriminating relevant from

irrelevant information, identifying missing information, sequencing and prioritizing information and observing patterns. 

 

1.2 Formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed. 

 

1.3 Determine when and how to break a problem into simpler parts. 

 

2.       Students use strategies, skills and concepts in finding solutions. (Integration of Core Knowledge)

 

2.1 Use estimation to verify the reasonableness of calculated results.

 

2.2 Apply strategies and results from simpler problems to more complex problems.

 

2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.

 

2.4 Make and test conjectures by using both inductive and deductive reasoning.

 

2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

 

2.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

 

2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

 

2.8  Make precise calculations and check the validity of the results from the context of the problem.

 

3.       Students determine a solution is complete and move beyond a particular problem by generalizing to other situations. (Critical Thinking/Problem Solving; Effective Communication)

 

3.1 Evaluate the reasonableness of the solution in the context of the original situation. 

 

3.2 Note method of deriving the solution and demonstrate conceptual understanding of the derivation by solving similar problems. 

 

3.3  Develop generalizations of the results obtained and the strategies used and apply them to a new problem situations.

 

 

 

 

 

 

 

 

 

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: Pre-Algebra, California Edition by Prentice Hall.

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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3/26/02