Clarke/MISIC 9-12 Math Standards/Benchmarks 12/2009
Clarke Community Schools
Math 9 – 12
Standards and Benchmarks
Standard 1: Acquire and use powerful, flexible and widely applicable skills in
all areas of mathematics.
Standard 2: Understand and apply basic and advanced properties of the
concepts of numbers.
Standard 3: Use basic and advanced procedures while performing in the
processes of computation.
Standard 4: Understand and apply basic and advanced properties of the
concepts of measurement.
Standard 5: Understand and apply basic and advanced properties of the
concepts of geometry.
Standard 6: Understand and apply basic and advanced concepts of statistics
and data analysis.
Standard 7: Understand and apply basic and advanced concepts of
probability.
Standard 8: Understand and apply basic and advanced properties of
functions and algebra.
Clarke/MISIC 9-12 Math Standards/Benchmarks 12/2009
MISIC MATH 9-12 STANDARDS/BENCHMARKS
Standard 1: Acquire and use powerful, flexible and widely applicable
skills in all areas of mathematics.
M.09-12.01.01
Understand, use and construct a mathematical proof.
M.09-12.01.02
Apply the process of math modeling to open-ended real world
problem situations (i.e. problem formation, math modeling,
solve, interpret, and justify use of technology when
appropriate.)
M.09-12.01.03
Construct logical arguments to test conjectures and to justify
solutions to problems.
M.09-12.01.04a
Construct equations for simple problems.
M.09-12.01.04b
Construct equations for multi-step problems.
M.09-12.01.05
Understand and use the mathematical concepts and methods
needed to make decisions in a democratic society, as related to
voting.
Standard 2: Understand and apply basic and advanced properties of the concepts of
numbers.
M.09-12.02.01
Use discrete structures (finite graphs, tables and finite
differences, matrices, sequences) to represent and to solve
problems.
M.09-12.02.02
Understand the properties of the real number system and its
subsystems (irrational numbers, natural numbers, integers,
rational numbers)
M.09-12.02.03
Understand the properties and basic theorems of roots and
exponents.
M.09-12.02.04
Understand appropriate use and corresponding notation of
ratios, proportions, decimals, and percents.
M.09-12.02.05
Analyze, interpret, generate, and describe the different
representations of recursion and iteration (now-next, subscript,
function)
M.09-12.02.06
Understands basic issues of information processing on the
internet to be informed consumers.
M.09-12.02.07
Understand and apply elementary set theory, logic, and basic
number theory.
Clarke/MISIC 9-12 Math Standards/Benchmarks 12/2009
Standard 3: Use basic and advanced procedures while performing in the processes of
computation.
M.09-12.03.01
Add, subtract, multiply, and divide rational expressions.
M.09-12.03.02
Use a variety of operations on expressions containing real
numbers (e. g., adding, subtracting, multiplying, dividing,
finding a reciprocal, raising to a power, taking a root, taking
opposites and reciprocals, determining absolute value).
M.09-12.03.03
Solve problems using proportional reasoning (e.g., Finding
percent and percents of a number, finding percent
increase/decrease, using data from tables and graphs, use of
scale).
M.09-12.03.04
Add, subtract, multiply, divide, and simplify radical
expressions containing positive rational numbers.
M.09-12.03.05
Use a variety of approximation and estimation strategies to
solve and to check reasonableness and results of a variety of
problems.
M.09-12.03. 06
Selects and uses appropriate computational methods (e.g.,
mental, paper and pencil, calculator, computer) for a given
situation.
Standard 4: Understand and apply basic and advanced properties of the concepts of
measurement.
M.09-12.04.01
Solve real world problems involving 2- and 3-dimensional
measures (e.g. area, volume, and perimeter).
M.09-12.04.02
Solve problems involving rate as a measure (e.g., velocity).
M.09-12.04.03
Determine precision and accuracy of measurement.
M.09-12.04.04
Use the appropriate tools or units to determine measurement.
M.09-12.04.05
Converts units by means of dimensional analysis.
Clarke/MISIC 9-12 Math Standards/Benchmarks 12/2009
Standard 5: Understand and apply basic and advanced properties of the concepts of
geometry.
M.09-12.05.01
Understand and use inductive and deductive reasoning to
make observations about and to verify properties of and
relationships among figures (e.g., the relationship among
interior angles of parallel lines cut by a transversal, the
relationship of angles and sides in polygons).
M.09-12.05.02a
Know and use the Pythagorean Theorem and its converse to
solve mathematical and real-world problems.
M.09-12.05.02b
Know and use the properties of special right triangles (e.g., 30
– 60 – 90 degree right triangles) to solve mathematical and
real-world problems.
M.09-12.05.03
Use properties of circles to solve mathematical and real-world
problems.
M.09-12.05.04
Use geometric constructions (e.g., the parallel to a line
through a given point not on the line, line segment congruent
to a given line segment) to complete simple proofs, to model,
and to solve mathematical and real-world problems.
M.09-12.05.05
Understand the properties of linear models algebraically and
geometrically.
M.09-12.05.06
Understand and use geometric transformations and their
properties to solve problems.
M.09-12.05.07
Understand the basic concepts of right triangle trigonometry
(e.g., basic trig ratios, such a sine, cosine, and tangent) and
use trigonometric ratio methods and the unit circle to solve
mathematical and real-world problems.
M.09-12.05.08
Use geometric means to solve mathematical and real-world
problems (e.g., congruent and similar polygons, parallel and
perpendicular lines).
M.09-12.05.09
Understand the characteristics and uses of vectors (e.g.,
representations of velocity and force) and basic operations on
vectors (e.g., vector addition, scalar multiplication).
M.09-12.05.10
Compare, describe, and analyze two-and three-dimensional
figures and their intersections with a plane.
M.09-12.05.11
Use coordinates and algebraic techniques to analyze, interpret,
represent and verify geometric relationships.
Clarke/MISIC 9-12 Math Standards/Benchmarks 12/2009
M.09-12.05.12
M.09-12.05.13
M.09-12.05.14
M.09-12.05.15
M.09-12.05.16
M.09-12.05.17
Identify and distinguish among geometric representations of
parabolas, circles, ellipses, and hyperbolas.
Identify, create, describe, and justify transformations using
multiple representations.
Represent, analyze, and apply vertex-edge graphs to model
and solve problems in real world, involving relationships
among a finite number of elements, and abstract-settings.
Analyze, compare, and contrast vertex-edge graphs.
Represent and analyze vertex-edge graphs using adjacency
matrices.
Represent three-dimensional figures using rectangular
coordinates.
Standard 6: Understand and apply basic and advanced concepts of statistics and data
analysis.
M.09-12.06.01a
Understands and applies basic concepts of data collection,
data analysis, and distribution.
M.09-12.06.01b
Understands and applies advanced concepts of data collection,
data analysis, and distribution.
M.09-12.06.02
Understands appropriate methods for using data to make
predictions (trends, surveys, samples).
M.09-12.06.03
Selects and uses the best method of representing and
describing a set of data (e.g., scatter plot, line graph, two-way
table).
M.09-12.06.04
Understands measures of central tendency and variability
(e.g., standard deviation, range, quartile deviation) and their
applications to specific situations.
M.09-12.06.05
Formulate questions and problems and gather and interpret
data to answer those questions.
Standard 7: Understand and apply basic and advanced concepts of probability.
M.09-12.07.01
Understands the basic concepts of probability and applies
them to real-world situations.
M.09-12.07.02
Understands the differences between experimental and
theoretical probability techniques and uses the appropriate
method to determine probabilities.
M.09-12.07.03
Determines the probability and understands the concepts of
independent and dependent events.
Clarke/MISIC 9-12 Math Standards/Benchmarks 12/2009
Standard 8: Understand and apply basic and advanced properties of functions and
algebra.
M.09-12.08.01a
Understand properties of linear graphs and the relationships
between a graph and its corresponding expression arising from
real-world and non real-world contexts. (e.g., maximum and
minimum points, slopes, intercepts).
M.09-12.08.01b
Understand properties of linear and nonlinear graphs and the
relationships between a graph and its corresponding
expression (e.g., maximum and minimum points, slopes,
intercepts).
M.09-12.08.02
Understand the general properties and characteristics of many
types of basic functions and their corresponding graph, table,
and function notation (e.g., notation and terminology, domain
and range, global behavior of linear, quadratic, step, absolute
value).
M.09-12.08.03
Understand the general properties and characteristics of many
types of trigonometric functions and their corresponding
graphs (e.g., sine, cosine).
M.09-12.08.04
Understand the general properties and characteristics of many
types of advanced functions and their corresponding graphs
(e.g., exponential, logarithmic).
M.09-12.08.05a
Use a variety of methods (e.g. with graphs, algebraic methods,
and matrices) to solve linear and quadratic equations
M.09-12.08.05b
Use a variety of methods (e.g. with graphs, algebraic methods,
and matrices) to solve linear inequalities.
M.09-12.08.05c
Use a variety of methods (e.g. with graphs, algebraic methods,
numerically (e.g., tables) and matrices) to solve systems of
equations and inequalities.
M.09-12.08.05d
Represent and interpret functions using graphs, tables, words
and symbols (explicit and recursive)
M.09-12.08.05e
Apply formulas and equations using and defining variables
appropriately for various situations.
M.09-12.08.06
Understand the basic concept of complex numbers (e.g.
conjugate)
Clarke/MISIC 9-12 Math Standards/Benchmarks 12/2009
M.09-12.08.07
Understand various applications (compound interest) of
formal notation (e.g., sigma notation, factorial representation)
of the Binomial Theorem.
M.09-12.08.08
Use a variety of methods to manipulate functions: e.g.,
compare and contrast properties of different types (families)
of functions, analyze the transformations of functions, and
determine the composition and inverses of functions.
Represent and interpret algebraic expressions contextually
using graphs, tables, words and symbols.
Use trigonometry to solve problems involving fundamental
trigonometric relationships.
Represent relationships arising from various contexts using
symbolic expressions, including explicit and recursive forms.
M.09-12.08.09
M.09-12.08.10
M.09-12.08.11