NUMBER SENSE 
NUMBER SENSE 1.0: Students know the properties of, and compute with,
rational numbers expressed in a variety of forms:

Number Sense 1.1  Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.

Number Sense 1.2  Add, subtract, multiply, and divide rational numbers (integers,
fractions, and terminating decimals) and take positive rational numbers to wholenumber powers.

Number Sense 1.3  Convert fractions to decimals and percents and use these
representations in estimations, computations, and applications.

Number Sense 1.5  Know that every rational number is either a terminating or repeating
decimal

Number Sense 1.6  Calculate the percentage of increases and decreases of a quantity.

Number Sense 1.7  Solve problems that involve discounts, markups, commissions, and
profit and compute simple and compound interest.

NUMBER SENSE 2.0: Students use exponents, powers, and roots and use
exponents in working with fractions:

Number Sense 2.1  Understand negative wholenumber exponents. Multiply and divide
expressions involving exponents with a common base.

Number Sense 2.2  Add and subtract fractions by using factoring to find common
denominators.

Number Sense 2.3  Multiply, divide, and simplify rational numbers by using exponent
rules.

Number Sense 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.

Number Sense 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.



ALGEBRA AND FUNCTIONS 
ALGEBRA AND FUNCTIONS 1.0: Students express quantitative
relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:

Algebra and Functions 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).

Algebra and Functions 1.2  Use the correct order of operations to evaluate algebraic
expressions such as 3(2x + 5)2.

Algebra and Functions 1.3  Simplify numerical expressions by applying properties of
rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the
process used.

Algebra and Functions 1.5  Represent quantitative relationships graphically and interpret
the meaningof a specific part of a graph in the situation represented by the graph.



ALGEBRA AND FUNCTIONS 2.0: Students interpret and evaluate expressions
involving integer powers and simple roots:

Algebra and Functions 2.1  Interpret positive wholenumber powers as repeated
multiplication and negative wholenumber powers as repeated division or multiplication by the
multiplicative inverse. Simplify and evaluate expressions that include exponents.

Algebra and Functions 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.

ALGEBRA AND FUNCTIONS 3.0: Students graph and interpret linear and
some nonlinear functions:

Algebra and Functions 3.1  Graph functions of the form y = nx2 and y = nx3 and use in
solving problems.

Algebra and Functions 3.3  Graph linear functions, noting that the vertical change
(change in yvalue) per unit of horizontal change (change in xvalue) is always the same and know
that the ratio ("rise over run") is called the slope of a graph.

Algebra and Functions 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 the line equals the quantities.

ALGEBRA AND FUNCTIONS 4.0: Students solve simple linear equations
and inequalities over the rational numbers:

Algebra and Functions 4.1  Solve twostep 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.

Algebra and Functions 4.2  Solve multistep problems involving rate, average speed,
distance, and time or a direct variation.



MEASUREMENT AND GEOMETRY 
MEASUREMENT AND GEOMETRY 1.0: Students choose appropriate units
of measure and use ratios to convert within and between measurement systems to solve problems:

Measurement and Geometry 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).

Measurement and Geometry 1.2  Construct and read drawings and models made to
scale.

Measurement and Geometry 1.3  Use measures expressed as rates (e.g., speed,
density) and measures expressed as products (e.g., persondays) to solve problems; check the
units of the solutions; and use dimensional analysis to check the reasonableness of the answer.

MEASUREMENT AND GEOMETRY 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:

Measurement and Geometry 2.1  Use formulas routinely for finding the perimeter and
area of basic twodimensional figures and the surface area and volume of basic threedimensional
figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and
cylinders.

Measurement and Geometry 2.2  Estimate and compute the area of more complex or
irregular twoand threedimensional figures by breaking the figures down into more basic
geometric objects.

Measurement and Geometry 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 the volume is multiplied by the cube of the scale
factor.

Measurement and Geometry 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 (1 square
foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic
centimeters or [1 in3] = [16.38 cm3]).

MEASUREMENT AND GEOMETRY 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:

Measurement and Geometry 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.

Measurement and Geometry 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.



STATISTICS, DATA ANALYSIS, AND
PROBABILITY 
STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.0: Students
compute and analyze statistical measurements for data sets:

Statistics, Data Analysis, and Probability 1.1  Compute the range, mean, median, and
mode of data sets.

STATISTICS, DATA ANALYSIS, AND PROBABILITY 2.0: Students use
data samples of a population and describe the characteristics and limitations of the samples:

Statistics, Data Analysis, and Probability 2.5  Identify claims based on statistical data
and, in simple cases, evaluate the validity of the claims.

STATISTICS, DATA ANALYSIS, AND PROBABILITY 3.0: Students
determine theoretical and experimental probabilities and use these to make predictions about
events:

Statistics, Data Analysis, and Probability 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.

Statistics, Data Analysis, and Probability 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, 1P is the
probability of an event not occurring.

Statistics, Data Analysis, and Probability 3.5  Understand the difference between
independent and dependent events.

STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.0 (7): 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:

Statistics, Data Analysis, and Probability 1.1  Know various forms of display for data
sets, including a stemandleaf plot or boxandwhisker plot; use the forms to display a single set
of data or to compare two sets of data.

Statistics, Data Analysis, and Probability 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).

Statistics, Data Analysis, and Probability 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.



MATHEMATICAL REASONING 
MATHEMATICAL REASONING 1.0: Students make decisions about how to
approach problems:

Mathematical Reasoning 1.1  Analyze problems by identifying relationships,
distinguishing relevant from irrelevant information, identifying missing information, sequencing and
prioritizing information, and observing patterns.

Mathematical Reasoning 1.2  Formulate and justify mathematical conjectures based on
a general description of the mathematical question or problem posed.

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

Mathematical Reasoning 2.1  Use estimation to verify the reasonableness of calculated
results.

Mathematical Reasoning 2.3  Estimate unknown quantities graphically and solve for
them by using logical reasoning and arithmetic and algebraic techniques.

Mathematical Reasoning 2.4  Make and test conjectures by using both inductive and
deductive reasoning.

MATHEMATICAL REASONING 3.0: Students determine a solution is
complete and move beyond a particular problem by generalizing to other situations:

Mathematical Reasoning 3.1  Evaluate the reasonableness of the solution in the context
of the original situation.

Mathematical Reasoning 3.3  Develop generalizations of the results obtained and the
strategies used and apply them to new problem situations.
