EL SEGUNDO UNIFIED
EL SEGUNDO HIGH SCHOOL
Department: Mathematics
Grade
Levels: 11-12
Students who are enrolled in this course will work solely on the concepts being tested on the math sections of the High School Exit Exam. Another component of this course will be testing strategies and how to approach math multiple choice questions.
Length: One year
Prerequisite for Enrollment: Failed the math section of the CAHSEE
Type of Course: Math elective
COURSE OUTLINE AND STANDARDS
Based on the California State
Standards tested on the CAHSEE
I. STATISTICS, DATA ANALYSIS, and PROBABILITY
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
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
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.
1.5Represent 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
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
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.
3.0 Students solve equations and inequalities involving absolute value.
4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2)=12
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.
6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g. graph 2x + 6y = 4)
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations.
8.0 Students understand the concepts of parallel lines and how their slopes are related.
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.
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques.
15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
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.
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.
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.
21.0 Students graph quadratic functions and know that their roots are the x-intercepts
23.0Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.
24.2 Students identify the hypothesis and conclusion in logical deduction.
24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.
25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.
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.
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.
INSTRUCTIONAL METHODS
1. Students will be individually assessed using the STAR math computer program.
2. Based on the results of the assessment, students will be placed in the Accelerated Math Program according to their skill level in relation to the California Math Content Standards & HSEE math content.
3. The teacher will use a combination of direct instruction, pair share, and group work to meet the needs of each individual student.
4. Following the administration of the High School Exit Exam in May, the focus of the class will shift to helping students successfully complete their math course.
EVALUATION/GRADING OF STUDENT WORK
1. Students will be required to keep a notebook with the worksheets completed during class; class notes; and a daily written conclusion stating what mathematics has been learned and what problems still remain.
2. Students earn pass or no pass credit.
3. Teachers will work closely with the student’s math instructor to identify and support weaknesses and validate strengths.
INSTRUCTIONAL MATERIALS
1. Accelerated & STAR Math computer program
2. Pre-Algebra and Algebra 1 textbooks by Prentice Hall
3-26-02