NUMBER SENSE 
NUMBER SENSE 1.0: Students understand the place value of whole numbers:

NUMBER SENSE 1.0: Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems
involving fractions, ratios, proportions, and percentages:

Number Sense 1.1  Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

Number Sense 1.2  Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using
appropriate notations (a/b, a to b, a:b).

Number Sense 1.3  Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a
known polygon). Use crossmultiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative
inverse. 
Number Sense 1.4  Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.



NUMBER SENSE 2.0: Students calculate and solve problems involving addition, subtraction, multiplication, and division:

Number Sense 2.1  Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation
was used for a given situation.

Number Sense 2.2  Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5/8 รท 15/16 = 5/8 x 16/15 =
2/3).

Number Sense 2.3  Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and
negative integers and combinations of these operations.

Number Sense 2.4  Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions
(e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).



ALGEBRA AND FUNCTIONS 
ALGEBRA AND FUNCTIONS 1.0: Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate
algebraic expressions, solve simple linear equations, and graph and interpret their results:

Algebra and Functions 1.1  Write and solve onestep linear equations in one variable.

Algebra and Functions 1.2  Write and evaluate an algebraic expression for a given situation, using up to three variables.

Algebra and Functions 1.3  Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and
justify each step in the process.

Algebra and Functions 1.4  Solve problems manually by using the correct order of operations or by using a scientific calculator.



ALGEBRA AND FUNCTIONS 2.0: Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:

Algebra and Functions 2.1  Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

Algebra and Functions 2.2  Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.
Rates

Algebra and Functions 2.3  Solve problems involving rates, average speed, distance, and time.



ALGEBRA AND FUNCTIONS 3.0: Students investigate geometric patterns and describe them algebraically:

Algebra and Functions 3.1  Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = pd  the formulas for the
perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).

Algebra and Functions 3.2  Express in symbolic form simple relationships arising from geometry.



MEASUREMENT AND GEOMETRY 
MEASUREMENT AND GEOMETRY 1.0: Students deepen their understanding of the measurement of plane and solid shapes and use this
understanding to solve problems:

Measurement and Geometry 1.1  Understand the concept of a constant such as pi; know the formulas for the circumference and area of a circle.

Measurement and Geometry 1.2  Know common estimates of pi (3.14; 22/7) and use these values to estimate and calculate the circumference and the
area of circles; compare with actual measurements.

Measurement and Geometry 1.3  Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these
formulas and explain the similarity between them and the formula for the volume of a rectangular solid.


MEASUREMENT AND GEOMETRY 2.0: Students identify and describe the properties of twodimensional figures:

Measurement and Geometry 2.1  Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

Measurement and Geometry 2.2  Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems
involving an unknown angle.

Measurement and Geometry 2.3  Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right
angles, a right isosceles triangle).



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 1.2  Understand how additional data added to data sets may affect these computations of measures of central
tendency.

Statistics, Data Analysis, and Probability 1.3  Understand how the inclusion or exclusion of outliers affects measures of central tendency.

Statistics, Data Analysis, and Probability 1.4  Know why a specific measure of central tendency (mean, median, mode) provides the most useful
information in a given context.


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 2.1  Compare different samples of a population with the data from the entire population and identify a situation in
which it makes sense to use a sample.

Sampling Analysis

Statistics, Data Analysis, and Probability 2.2  Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random
sampling) and which method makes a sample more representative for a population.

Statistics, Data Analysis, and Probability 2.3  Analyze data displays and explain why the way in which the question was asked might have influenced the
results obtained and why the way in which the results were displayed might have influenced the conclusions reached.

Statistics, Data Analysis, and Probability 2.4  Identify data that represent sampling errors and explain why the sample (and the display) might be biased.

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 3.2  Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile
driven).

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 3.4  Understand that the probability of either of two disjoint events occurring is the sum of the two individual
probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.

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



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.



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

Mathematical Reasoning 2.5  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 2.6  Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of
accuracy.

Mathematical Reasoning 2.7  Make precise calculations and check the validity of the results from the context of the problem.



MATHEMATICAL REASONING 3.0: Students 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 in new problem situations.

