The high school standards are set at a level of performance approximately
equivalent to the end of the tenth grade. It is expected that some students
might achieve this level earlier and others later than this grade. (See
"Deciding what constitutes a
standardsetting performance.")
M 
Mathematics 

Number and Operation
Concepts
a 
Use addition, subtraction, multiplication, division, exponentiation,
and rootextraction. 
b 
Understand and use opposite, reciprocal, raising to a power,
taking a root, and taking a logarithm. 
c 
Have facility with the mechanics of operations as well as
understanding of their typical meaning and uses in applications. 
d 
Understand and use number systems. 
e 
Represent numbers in various forms and graph them. 
f 
Compare numbers using order relations, differences, ratios,
proportions, percents, and proportional change. 
g 
Carry out proportional reasoning. 
h 
Understand dimensionless numbers as well as numbers with specific
units of measure. 
i 
Carry out counting procedures such as those involving sets
and arrangements. 
j 
Use concepts in solving problems involving integers. 
k 
Use a scientific calculator effectively and efficiently. 
l 
Recognize and represent basic number patterns. 


Geometry and Measurement
Concepts
a 
Model situations geometrically to formulate and solve problems. 
b 
Work with two and three dimensional figures and their properties. 
c 
Use congruence and similarity in describing relationships
between figures. 
d 
Visualize objects, paths, and regions in space and describe
these using geometric language. 
e 
Know, use, and derive formulas for perimeter, circumference,
area, surface area, and volume. 
f 
Use the Pythagorean Theorem in many types of situations. 
g 
Work with similar triangles and use the three basic trigonometric
functions. 
h 
Analyze figures in terms of their symmetries. 
i 
Compare slope and angle. 
j 
Investigate geometric patterns. 
k 
Work with geometric and nongeometric measures. 
l 
Use quotient measures and product measures. 
m 
Understand the structure of standard measurement systems. 
n 
Solve problems involving scale. 
o 
Represent geometric curves and graphs of functions in standard
coordinate systems. 
p 
Analyze geometric figures and prove simple things about them
using deductive methods. 
q 
Explore geometry using computer programs. 


Function and Algebra
Concepts
a 
Model given situations with formulas and functions, and interpret
given formulas and functions in terms of situations. 
b 
Describe, generalize, and use basic types of functions. 
c 
Utilize the concepts of slope, evaluation, and inverse. 
d 
Work with rates, expressed numerically, symbolically, and
graphically. 
e 
Represent constant rates and interpret slope. 
f 
Understand and use linear functions as a mathematical representation
of proportional relationships. 
g 
Use arithmetic sequences and geometric sequences and their
sums. 
h 
Define, use, and manipulate expressions. 
i 
Represent functional relationships. 
j 
Solve equations symbolically, graphically, and numerically
and know how to use the quadratic formula. 
k 
Make predictions by interpolating or extrapolating. 
l 
Understand the basic algebraic structure of number systems. 
m 
Use equations to represent curves. 
n 
Use technology to represent and analyze functions and their
graphs. 
o 
Use functions to analyze patterns and represent their structure. 


Statistics and Probability
Concepts
a 
Organize, analyze, and display singlevariable data appropriately. 
b 
Organize, analyze, and display twovariable data appropriately. 
c 
Use sampling techniques to draw inferences. 
d 
Understand that inferencing from a sample involves uncertainty
and that the role of statistics is to estimate the size of that
uncertainty. 
e 
Formulate hypotheses to answer a question and use data to
test hypotheses. 
f 
Interpret representations of data, compare distributions of
data, and critique conclusions. 
g 
Explore questions of experimental design, control groups,
and reliability. 
h 
Create and use models of probability and understand the role
of assumptions. 
i 
Use concepts in analyzing situations involving chance. 
j 
Construct appropriate sample spaces and apply the addition
and multiplication principles for probabilities. 
k 
Use the concept of a probability distribution. 
l 
Choose and use an appropriate probability model. 
m 
Use relative frequencies based on empirical data to arrive
at an experimental probability for a chance event. 
n 
Design simulations to estimate probabilities. 
o 
Work with the normal distribution. 


Problem Solving and Reasoning
a 
Formulation. 
b 
Implementation. 
c 
Conclusion. 
d 
Mathematical reasoning. 


Mathematical Skills and
Tools
a 
Carry out numerical calculations and symbol manipulations
effectively. 
b 
Use a variety of methods to estimate the values, in appropriate
units, to an appropriate degree of accuracy. 
c 
Evaluate and analyze formulas and functions using both pencil
and paper and more advanced technology. 
d 
Use basic geometric terminology accurately, and deduce information
about basic geometric figures in solving problems. 
e 
Make and use rough sketches, schematic diagrams, or precise
scale diagrams. 
f 
Use the number line and Cartesian coordinates in the plane
and in space. 
g 
Create and interpret graphs of many kinds. 
h 
Set up and solve equations symbolically and graphically. 
i 
Know how to use algorithms in mathematics. 
j 
Use technology to create graphs or spreadsheets. 
k 
Write a simple computer program to carry out a computation
or simulation. 
l 
Use tools in solving problems. 
m 
Know standard methods to solve basic problems and use these
methods in approaching more complex problems. 


Mathematical Communication
a 
Be familiar with basic mathematical terminology, standard
notation and use of symbols, common conventions for graphing,
and general features of effective mathematical communication
styles. 
b 
Use mathematical representations with appropriate accuracy. 
c 
Organize work and present mathematical procedures and results
correctly. 
d 
Communicate logical arguments clearly, showing sensibility
and validity. 
e 
Present mathematical ideas effectively. 
f 
Explain mathematical concepts clearly enough to be of assistance
to those who may be having difficulty with them. 
g 
Write narrative accounts of the history and process of work
on a mathematical problem or extended project. 
h 
Write succinct accounts of the mathematical results obtained
in a mathematical problem or extended project. 
i 
Keep narrative accounts of process separate from succinct
accounts of results, and realize that doing so can enhance the
effectiveness of each. 
j 
Read writings about mathematics with understanding. 


Putting Mathematics to
Work
a 
Data study. 
b 
Mathematical model. 
c 
Design a physical structure. 
d 
Management and planning. 
e 
Pure mathematics investigation. 
f 
Pure mathematics investigation. 
g 
History of a mathematical idea. 

