The middle school standards are set at a level of performance approximately
equivalent to the end of the eighth grade. It is expected that some student
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 
Consistently and accurately add, subtract, multiply, and divide
rational numbers. 
b 
Use and understand the inverse relationships between multiplication
and division, and exponentiation and rootextraction. 
c 
Apply and convert the different kinds and forms of rational
numbers. 
d 
Be familiar with characteristics of numbers. 
e 
Interpret percent as part of 100. 
f 
Reason proportionally to solve problems involving equivalent
fractions, equal ratios, or constant rates. 
g 
Order numbers with the > and < relationships; estimate
and compare rational numbers using sense of the magnitudes and
relative magnitudes of numbers. 


Geometry and Measurement
Concepts
a 
Be familiar with assorted two and threedimensional objects. 
b 
Identify similar and congruent shapes and use transformations
in the coordinate plane. 
c 
Identify three dimensional shapes from two dimensional perspectives;
draw two dimensional sketches of three dimensional objects. 
d 
Determine and understand length, area, and volume. 
e 
Recognize similarity and rotational and bilateral symmetry
in two and threedimensional figures. 
f 
Analyze and generalize geometric patterns. 
g 
Measure angles, weights, capacities, times, and temperatures
using appropriate units. 
h 
Choose appropriate units of measure and convert with ease
between like units. 
i 
Reason proportionally in situations with similar figures. 
j 
Reason proportionally with measurements. 
k 
Model situations geometrically to formulate and solve problems. 


Function and Algebra
Concepts
a 
Discover, describe, and generalize patterns, and represent
them with variables and expressions. 
b 
Represent relationships. 
c 
Analyze tables to determine functional relationships. 
d 
Find solutions for unknown quantities in linear equations. 


Statistics and Probability
Concepts
a 
Organize and display data. 
b 
Analyze data with respect to frequency and distribution. 
c 
Analyze central tendencies of data. 
d 
Make conclusions and recommendations based on data analysis. 
e 
Critiques the conclusions and recommendations of others’
statistics. 
f 
Considers the effects of missing or incorrect information. 
g 
Formulates hypotheses to answer a question and uses data to
test hypotheses. 
h 
Represent and determine probability, recognize equally likely
outcomes, and construct sample spaces. 
i 
Make predictions based on experimental or theoretical probabilities. 
j 
Predict the result of a series of trials once the probability
for one trial is known. 


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


Mathematical Skills and
Tools
a 
Compute accurately with arithmetic operations on rational
numbers. 
b 
Know and use the correct order of operations for arithmetic
computations. 
c 
Estimate numerically. 
d 
Measure accurately. 
e 
Refer to geometric shapes and terms correctly. 
f 
Use equations, formulas, and simple algebraic notation appropriately. 
g 
Read and organize data on charts and graphs. 
h 
Use calculators, as appropriate, to achieve solutions. 


Mathematical Communication
a 
Use mathematical language and representations with appropriate
accuracy. 
b 
Organize work, explain a solution orally and in writing, and
use other techniques to
make meaning clear to the audience. 
c 
Use mathematical language to make complex situations easier
to understand. 
d 
Exhibit developing reasoning abilities by justifying statements
and defending work. 
e 
Show understanding of concepts by explaining ideas to others. 


Putting Mathematics to
Work
a 
Data study. 
b 
Mathematical model. 
c 
Design a physical structure. 
d 
Management and planning. 
e 
Pure mathematics investigation. 

