Course Description:
In this two-semester course, students will study the topics from the four
mathematical
standards of Number Sense and Operations, Algebra and Functions , Geometry and
Measurement, Data, Statistics and Probability and Mathematical Reasoning.
Students will
explore the mathematics and their application to the real world. Students will
be required to
demonstrate proficiency in the content to pass the course.
The standards for this course are the California Exit Exam Mathematics Standards
as
approved by the California Board of Education. The curriculum for this course
prepares
students for both the annual state testing and for High School Exit Exam.
Content Standards:
Grade 6—Statistics, Data Analysis, and Probability
1.0 Students compute and analyze statistical measurements for data sets:
1.1 Compute the range, mean, median, and mode of data sets.
1.2 Understand how additional data added to data sets may affect these
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, 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 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 the
validity of the claims.
3.0 Students de termine theoretical and experimental probabilities and use
these to make
predictions about events:
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.
3.2 Use data to estimate the probability of future events (e.g., batting
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 fol lowing
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
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
(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
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.
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
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.
Grade 7—Algebra and Functions
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
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(2 x +5)2.
1.3 Simplify numerical expressions by applying properties of rational numbers
(e.g., identity,
inverse, and distributive , associative, commutative) and justify the process
used.
1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient ,
inequality, and expression,
constant) correctly.
1.5 Represent quantitative relationships graphically and interpret the 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
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.
3.0 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
problems.
3.2 Plot the values from the volumes of three-dimensional shapes for 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 yvalue)
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
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 time
or a direct variation.
Grade 7—Measurement and Geometry
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 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.
1.3 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.
2.0 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-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 threedimensional
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 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., 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, 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 (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).
