6.2.1 Add and subtract positive and negative integers.
6.2.2 Multiply and divide positive and negative integers.
6.2.3 Multiply and divide decimals.
6.2.5 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
6.2.6 Interpret and use ratios to show the relative sizes of two quantities. Use the notations: a/b, a to b, a:b.
6.2.7 Understand proportions and use them to solve problems.
6.2.9 Use estimation to decide whether answers are reasonable in decimal problems.
6.2.10 Use mental arithmetic to add or subtract simple fractions and decimals.

6.3.1 Write and solve one-step linear equations and inequalities in one variable and check the answers.
6.3.2 Write and use formulas with up to three variables to solve problems.
6.3.3 Interpret and evaluate mathematical expressions that use grouping symbols such as parentheses.
6.3.4 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.
6.3.6 Apply the correct order of operations and the properties of real numbers (e.g., identity, inverse, commutative, associative, and distributive properties) to evaluate numerical expressions. Justify each step in the process.
6.3.9 Investigate how a change in one variable relates to a change in a second variable.

6.5.1 Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.
6.5.6 Understand the concept of significant figures and round answers to an appropriate number of significant figures.
6.5.10 Add, subtract, multiply, and divide with money in decimal notation.

6.6.1 Organize and display single-variable data in appropriate graphs and stem-and-leaf plots, and explain which types of graphs are appropriate for various data sets.
6.6.2 Make frequency tables for numerical data, grouping the data in different ways to investigate how different groupings describe the data. Understand and find relative and cumulative frequency for a data set. Use histograms of the data and of the relative frequency distribution, and a broken line graph for cumulative frequency, to interpret the data.
6.6.3 Compare the mean, median, and mode for a set of data and explain which measure is most appropriate in a given context.
6.6.4 Show all possible outcomes for compound events in an organized way and find the theoretical probability of each outcome.
6.6.5 Use data to estimate the probability of future events.
6.6.6 Understand and represent probabilities as ratios, measures of relative frequency, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable.

6.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
6.7.2 Make and justify mathematical conjectures based on a general description of a mathematical question or problem.
6.7.3 Decide when and how to break a problem into simpler parts.
6.7.4 Apply strategies and results from simpler problems to solve more complex problems.
6.7.5 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
6.7.6 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
6.7.7 Select and apply appropriate methods for estimating results of rational-number computations.
6.7.8 Use graphing to estimate solutions and check the estimates with analytic approaches.
6.7.9 Make precise calculations and check the validity of the results in the context of the problem.
6.7.10 Decide whether a solution is reasonable in the context of the original situation.
6.7.11 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.

7.2.1 Solve addition, subtraction, multiplication, and division problems that use integers, fractions, decimals, and combinations of the four operations.
7.2.2 Calculate the percentage increase and decrease of a quantity.
7.2.4 Use estimation to decide whether answers are reasonable in problems involving fractions and decimals.
7.2.5 Use mental arithmetic to compute with simple fractions, decimals, and powers.

7.3.1 Use variables and appropriate operations to write an expression, a formula, an equation, or an inequality that represents a verbal description.
7.3.2 Write and solve two-step linear equations and inequalities in one variable and check the answers.
7.3.3 Use correct algebraic terminology, such as variable, equation, term, coefficient, inequality, expression, and constant.
7.3.4 Evaluate numerical expressions and simplify algebraic expressions by applying the correct order of operations and the properties of rational numbers (e.g., identity, inverse, commutative, associative, distributive). Justify each step in the process.
7.3.5 Solve an equation or formula with two variables for a particular variable.

7.5.1 Compare lengths, areas, volumes, weights, capacities, times, and temperatures within measurement systems.
7.5.2 Use experimentation and modeling to visualize similarity problems. Solve problems using similarity.

Grade 7 Data Analysis and Probability
7.6.1 Analyze, interpret, and display data in appropriate bar, line, and circle graphs and stem-and-leaf plots and justify the choice of display.
7.6.2 Make predictions from statistical data.
7.6.3 Describe how additional data, particularly outliers, added to a data set may affect the mean, median, and mode.
7.6.4 Analyze data displays, including ways that they can be misleading. Analyze ways in which the wording of questions can influence survey results.
7.6.7 Find the number of possible arrangements of several objects using a tree diagram.

7.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
7.7.2 Make and justify mathematical conjectures based on a general description of a mathematical question or problem.
7.7.3 Decide when and how to divide a problem into simpler parts.
7.7.4 Apply strategies and results from simpler problems to solve more complex problems.
7.7.5 Make and test conjectures by using inductive reasoning.
7.7.6 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
7.7.7 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
7.7.8 Select and apply appropriate methods for estimating results of rational-number computations.
7.7.9 Use graphing to estimate solutions and check the estimates with analytic approaches.
7.7.10 Make precise calculations and check the validity of the results in the context of the problem.
7.7.11 Decide whether a solution is reasonable in the context of the original situation.
7.7.12 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.

8.2.1 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) in multi-step problems.
8.2.3 Use estimation techniques to decide whether answers to computations on a calculator are reasonable.
8.2.4 Use mental arithmetic to compute with common fractions, decimals, powers, and percents.
Algebra and Functions
8.3.1 Write and solve linear equations and inequalities in one variable, interpret the solution or solutions in their context, and verify the reasonableness of the results.
8.3.7 Demonstrate an understanding of rate as a measure of one quantity with respect to another quantity.
8.3.8 Demonstrate an understanding of the relationships among tables, equations, verbal expressions, and graphs of linear functions.

8.5.1 Convert common measurements for length, area, volume, weight, capacity, and time to equivalent measurements within the same system.
8.5.2 Solve simple problems involving rates and derived measurements for attributes such as velocity and density.

Grade 8 Data Analysis and Probability

8.6.1 Identify claims based on statistical data and, in simple cases, evaluate the reasonableness of the claims. Design a study to investigate the claim.
8.6.2 Identify different methods of selecting samples, analyzing the strengths and weaknesses of each method, and the possible bias in a sample or display.
8.6.3 Understand the meaning of, and be able to identify or compute the minimum value, the lower quartile, the median, the upper quartile, the interquartile range, and the maximum value of a data set.
8.6.4 Analyze, interpret, and display single- and two-variable data in appropriate bar, line, and circle graphs; stem-and-leaf plots; and box-and-whisker plots and explain which types of display are appropriate for various data sets.
8.6.5 Represent two-variable data with a scatterplot on the coordinate plane and describe how the data points are distributed. If the pattern appears to be linear, draw a line that appears to best fit the data and write the equation of that line.
8.6.6 Understand and recognize equally likely events.
8.6.7 Find the number of possible arrangements of several objects by using the Basic Counting Principle.

8.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
8.7.2 Make and justify mathematical conjectures based on a general description of a mathematical question or problem.
8.7.3 Decide when and how to divide a problem into simpler parts.
8.7.4 Apply strategies and results from simpler problems to solve more complex problems.
8.7.5 Make and test conjectures using inductive reasoning.
8.7.6 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
8.7.7 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
8.7.8 Select and apply appropriate methods for estimating results of rational-number computations.
8.7.9 Use graphing to estimate solutions and check the estimates with analytic approaches.
8.7.10 Make precise calculations and check the validity of the results in the context of the problem.
8.7.11 Decide whether a solution is reasonable in the context of the original situation.
8.7.12 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.