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India

Posted:

January 18, 2013

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Resume:

CAHSEE Mathematics Blueprint*

Revised July ****

Number

California Content Standard

of Items

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

1.0 Students compute and analyze statistical measurements for data sets:

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

1.2 Understand how additional data added to data sets may affect these 0

computations of measures of central tendency.

1.3 Understand how the inclusion or exclusion of outliers affects measures

of central tendency.

1.4 Know why a specific measure of central tendency (mean, median, 0

mode) provides the most useful information in a given context.

2.0 Students use data samples of a population and describe the characteristics

and limitations of the samples:

2.1 Compare different samples of a population with the data from the

entire population and identify a situation in which it makes sense to

use a sample.

2.2 Identify different ways of selecting a sample (e.g., convenience

sampling, responses to a survey, random sampling) and which method

makes a sample more representative for a population.

2.3 Analyze data displays and explain why the way in which the question 0

was asked might have influenced the results obtained and why the

way in which the results were displayed might have influenced the

conclusions reached.

2.4 Identify data that represent sampling errors and explain why the

sample (and the display) might be biased.

2.5 Identify claims based on statistical data and, in simple cases, evaluate 1

the validity of the claims.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

3.0 Students determine theoretical and experimental probabilities and use these

to make predictions about events:

3.1 Represent all possible outcomes for compound events in an organized 1

way (e.g., tables, grids, tree diagrams) and express the theoretical

probability of each outcome.

3.2 Use data to estimate the probability of future events (e.g., batting 0

averages or number of accidents per mile driven).

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.

3.4 Understand that the probability of either of two disjoint events

occurring is the sum of the two individual probabilities and that the

probability of one event following another, in independent trials, is the

product of the two probabilities.

3.5 Understand the difference between independent and dependent

events.

Grade 7 Number Sense 14 Items Total

1.0 Students know the properties of, and compute with, rational numbers

expressed in a variety of forms:

1.1 Read, write, and compare rational numbers in scientific notation 1

(positive and negative powers of 10) with approximate numbers using

scientific notation.

1.2 Add, subtract, multiply, and divide rational numbers (integers, 3

fractions, and terminating decimals) and take positive rational numbers

to whole-number powers.

1.3 Convert fractions to decimals and percents and use these 2

representations in estimations, computations, and applications.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

1.4 Differentiate between rational and irrational numbers. 0

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

1.7 Solve problems that involve discounts, markups, commissions, and 2

profit, and compute simple and compound interest.

2.0 Students use exponents, powers, and roots, and use exponents in working

with fractions:

2.1 Understand negative whole-number exponents. Multiply and divide 1

expressions involving exponents with a common base.

2.2 Add and subtract fractions by using factoring to find common 1

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 1

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.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Grade 7 Algebra and Functions 17 Items Total

1.0 Students express quantitative relationships by using algebraic terminology,

expressions, equations, inequalities, and graphs:

1.1 Use variables and appropriate operations to write an expression, an 2

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.

1.3 Simplify numerical expressions by applying properties of rational 0

numbers (e.g., identity, inverse, distributive, associative, commutative)

and justify the process used.

1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient,

inequality, expression, constant) correctly.

1.5 Represent quantitative relationships graphically and interpret the 3

meaning of a specific part of a graph in the situation represented by

the graph.

2.0 Students interpret and evaluate expressions involving integer powers and

simple roots:

2.1 Interpret positive whole-number powers as repeated multiplication and 1

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.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

3.0 Students graph and interpret linear and some nonlinear functions:

3.1 Graph functions of the form y=nx2 and y=nx3 and use in solving 1

problems.

3.2 Plot the values from the volumes of three-dimensional shapes for 0

various values of the edge lengths (e.g., cubes with varying edge

lengths or a triangle prism with a fixed height and an equilateral

triangle base of varying lengths).

3.3 Graph linear functions, noting that the vertical change (change in y- 2

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.

3.4 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.

4.0 Students solve simple linear equations and inequalities over the rational

numbers:

4.1 Solve two-step linear equations and inequalities in one variable over 3

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 multistep problems involving rate, average speed, distance, and 2

time or a direct variation.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

Grade 7 Measurement and Geometry 17 Items Total

1.0 Students choose appropriate units of measure and use ratios to convert within

and between measurement systems to solve problems:

1.1 Compare weights, capacities, geometric measures, times, and 2

temperatures within and between measurement 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

1.3 Use measures expressed as rates (e.g., speed, density) and measures 2

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.

2.0 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:

2.1 Use formulas routinely for finding the perimeter and area of basic two- 3

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 volume is multiplied by the cube of the scale factor.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

2.4 Relate the changes in measurement with a change of scale to the 1

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]).

3.0 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:

3.1 Identify and construct basic elements of geometric figures (e.g., 0

altitudes, mid-points, diagonals, angle bisectors, and perpendicular

bisectors; central angles, radii, diameters, and chords of circles) by

using a compass and straightedge.

3.2 Understand and use coordinate graphs to plot simple figures, 2

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 2

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 (e.g.,

diagonals of rectangular solids) and describe how two or more

objects are related in space (e.g., skew lines, the possible ways three

planes might intersect).

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

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

1.0 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:

1.1 Know various forms of display for data sets, including a stem-and-leaf 2

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.

8 Items Total

Grade 7 Mathematical Reasoning Plus Integrated

into Other Strands

1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant 2

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.

1.3 Determine when and how to break a problem into simpler parts. 0

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

2.0 Students use strategies, skills, and concepts in finding solutions:

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

2.2 Apply strategies and results from simpler problems to more complex 0

problems.

2.3 Estimate unknown quantities graphically and solve for them by using 1

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, 0

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 0

context of the problem.

3.0 Students determine a solution is complete and move beyond a particular

problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the

original situation.

3.2 Note the method of deriving the solution and demonstrate a 0

conceptual understanding of the derivation by solving similar

problems.

3.3 Develop generalizations of the results obtained and the strategies 1

used and apply them to new problem situations.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

Algebra I 12 Items Total

1.0 Students identify and use the arithmetic properties of subsets of integers and

rational, irrational, and real numbers, including closure properties for the

four basic arithmetic operations where applicable:

1.1 Students use properties of numbers to demonstrate whether assertions 0

are true or false.

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.

3.0 Students solve equations and inequalities involving absolute values. 1

4.0 Students simplify expressions before solving linear equations and 2

inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.

5.0 Students solve multistep 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). They are also able to sketch the region defined by

(1 graphing item;

linear inequality (e.g., they sketch the region defined by 2x + 6y

1 computing item)

7.0 Students verify that a point lies on a line, given an equation of the line. 1

Students are able to derive linear equations. by using the point-slope

formula.

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.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

9.0 Students solve a system of two linear equations in two variables 1

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 multistep problems, including word problems, by using these

techniques.

11.0 Students apply basic factoring techniques to second- and simple third-

degree polynomials. These techniques include finding a common factor for

all terms in a polynomial, recognizing the difference of two squares, and

recognizing perfect squares of binomials.

12.0 Students simplify fractions with polynomials in the numerator and 0

denominator by factoring both and reducing them to the lowest terms.

13.0 Students add, subtract, multiply, and divide rational expressions and 0

functions. Students solve both computationally and conceptually challenging

problems by using these techniques.

14.0 Students solve a quadratic equation by factoring or completing the square. 0

15.0 Students apply algebraic techniques to solve rate problems, work problems, 1

and percent mixture problems.

16.0 Students understand the concepts of a relation and a function, determine 0

whether a given relation defines a function, and give pertinent information

about given relations and functions.

17.0 Students determine the domain of independent variables and the range of 0

dependent variables defined by a graph, a set of ordered pairs, or a

symbolic expression.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

18.0 Students determine whether a relation defined by a graph, a set of ordered 0

pairs, or a symbolic expression is a function and justify the conclusion.

19.0 Students know the quadratic formula and are familiar with its proof by

completing the square.

20.0 Students use the quadratic formula to find the roots of a second-degree 0

polynomial and to solve quadratic equations.

21.0 Students graph quadratic functions and know that their roots are the x- 0

intercepts.

22.0 Students use the 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.

23.0 Students apply quadratic equations to physical problems, such as the

motion of an object under the force of gravity.

24.0 Students use and know simple aspects of a logical argument:

24.1 Students explain the difference between inductive and deductive 0

reasoning and identify and provide examples of each.

24.2 Students identify the hypothesis and conclusion in logical deduction. 0

24.3 Students use counterexamples to show that an assertion is false and 0

recognize that a single counterexample is sufficient to refute an

assertion.

25.0 Students use properties of the number system to judge the validity of results,

to justify each step of a procedure, and to prove or disprove statements:

25.1 Students use properties of numbers to construct simple, valid 0

arguments (direct and indirect) for, or formulate counterexamples to,

claimed assertions.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

CAHSEE Mathematics Blueprint*

Revised July 2003

Number

California Content Standard

of Items

25.2 Students judge the validity of an argument according to whether the 0

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 0

absolute value expressions or equations or inequalities, students

determine whether the statement is true sometimes, always, or never.

*Blueprint approved by the State Board of Education on July 9, 2003.

Note: Strikethroughs within a standard indicate that this particular part of the standard is not to be assessed on the CAHSEE but is still part

of the original standard.

California Department of Education

Standards and Assessment Division

Contact this candidate