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 1.4  Differentiate between rational and irrational numbers.

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 1.4  Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.

Algebra and Functions 1.5  Represent quantitative relationships graphically and interpret the meaning of 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 3.2  Plot the values from the volumes of threedimensional 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).

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.



EASUREMENT 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 3.1  Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and
perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.

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.

Measurement and Geometry 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.

Measurement and Geometry 3.5  Construct twodimensional patterns for threedimensional models, such as cylinders, prisms, and cones.

Measurement and Geometry 3.6  Identify elements of threedimensional 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).



STATISTICS, DATA ANALYSIS, AND PROBABILITY 
STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.0: 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 1.3  Determine when and how to break a problem into simpler parts.

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 2.2  Apply strategies and results from simpler problems to more complex problems.

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 2.5  Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain
mathematical reasoning.

Mathematical Reasoning 2.6  Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language;
support solutions with evidence in both verbal and symbolic work.

Mathematical Reasoning 2.7  Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of
accuracy.

Mathematical Reasoning 2.8  Make precise calculations and check the validity of the results from the context of the problem.

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 3.2  Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar
problems.

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