California High School Exit Exam, part 1 (Math)

Hello everyone,

Garfield met today to discuss the California High School Exit Exam and how to help students to pass it (consequently helping our API--if I may paraphrase the classic film "Miracle on 34th Street"). The California Department of Education publishes their blueprint for the CAHSEE, telling exactly which standards will be tested, and how many questions are devoted to each standard.

If I were a math teacher, in middle or high school, and I were trying to help students pass the CAHSEE, I would focus on the standards that have the most questions, or the standards that provide the best foundation for answering the most questions correctly. Some of the standards are never covered on the CAHSEE, and ought not be emphasized unless they provide foundational material.

If I were an English teacher, I would wait until tomorrow when I publish the same blueprint for English.

If I were teaching an elective or a core academic subject (like science) that utilized math extensively, I would focus on the math concepts that my students needed to pass the CAHSEE.

If my students had all passed the CAHSEE, I would focus all my attention on getting them ready for college, which involves much higher skill and content levels than the CAHSEE.

If I were uncertain about what Combe is writing about, or if there were questions I had, I would go to the California Department of Education website and look at the blueprint for the CAHSEE. It's aligned with the California standards. Here is the link:

http://www.cde.ca.gov/ta/tg/hs/documents/bpmath03.pdf

BELOW, YOU WILL FIND THE MATH STANDARDS THAT ARE TESTED ON THE CAHSEE. THE NUMBER IN PARENTHESES IS THE NUMBER OF QUESTIONS FROM EACH GIVEN STANDARD THAT ARE FOUND ON THE TEST. IF WORDS ARE STRICKEN OUT WITH A LINE, THEY ARE NO LONGER TESTED. IF A STANDARD IS NOT LISTED, IT'S NOT TESTED.

Grade 6—Statistics, Data Analysis, and Probability
8 Items Total

1.1 Compute the range, mean, median, and mode of data sets.
(3)

2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
(1)

3.1 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.
(1)

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 Pis the probability of an event, 1-Pis the probability of an event not occurring.
(2)


3.5 Understand the difference between independent and dependent events. (1)

Grade 7—Number Sense
14 Items Total

1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
(1)

1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
(3)

1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
(2)

1.6 Calculate the percentage of increases and decreases of a quantity.
(1)

1.7 Solve problems that involve discounts, markups, commissions, and profit, and compute simple and compound interest.
(2)

2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
(1)

2.2 Add and subtract fractions by using factoring to find common denominators.
(1)

2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
(1)

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.
(1)

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.
(1)

Grade 7—Algebra and Functions
17 Items Total

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 (e.g., three less than a number, half as large as area A).
(2)

1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2 .
(1)

1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
(3)

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.
(1)

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.
(1)

3.1 Graph functions of the form y=nx2 and y=nx3 and use in solving problems.
(1)

3.3 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.
(2)

3.4 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.
(1)

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.
(3)

4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
(2)

Grade 7—Measurement and Geometry
17 Items Total

1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
(2)

1.2 Construct and read drawings and models made to scale.
(1)

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)

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.
(3)

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)

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.
(1)

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 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).
(1)

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.
(2)

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.
(2)

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.
(1)

Grade 7—Statistics, Data Analysis, and Probability
4 Items Total

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.
(2)

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).
(2)

Grade 7—Mathematical Reasoning
8 Item Total
Plus Integrated
into Other Strands

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
(2)

1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
(1)

2.1 Use estimation to verify the reasonableness of calculated results.
(2)

2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
(1)

2.4 Make and test conjectures by using both inductive and deductive reasoning.
(1)

3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
(1)

Algebra I
12 Items Total

2.0
Students understand and use such operations as taking the opposite, finding
the reciprocal, and taking a root, and raising to a fractional power. They
understand and use the rules of exponents.
(1)

3.0
Students solve equations and inequalities involving absolute values.
(1)

4.0
Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
(1)

5.0
Students solve multistep problems, including word problems, involving linear
equations and linear inequalities in one variable and provide justification for
each step.
(1)

6.0
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).
(1 graphing item; 1 computing item)
(2)

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.
(1)

8.0
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.
(1)

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.
(1)

10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
(1)

15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
(1)