Grade 6 Computation Grade 6 Measurement & Analysis & Probability Grade 6 Problem Solving Grade 7 Computation Grade 7 Measurement Grade 7 Problem Solving Grade 8 Computation Grade 8 Data Analysis and Probability Grade 8 Problem Solving

6.2.1 Add and subtract positive and negative integers.
6.2.2 Multiply and divide positive and negative integers.
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.
Algebra and Functions
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.

Grade 6 Analysis and Probability

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.
6.6.3 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.

Grade 6 Problem Solving

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.
Algebra and Functions
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.
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.

Grade 7 Problem Solving

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.
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.
8.3.2 Solve systems of two linear equations using the substitution method and identify approximate solutions graphically.
8.3.4 Use the correct order of operations to find the values of algebraic expressions involving powers.
8.3.8 Demonstrate an understanding of the relationships among tables, equations, verbal expressions, and graphs of linear functions.
8.3.9 Represent simple quadratic functions using verbal descriptions, tables, graphs, and formulas and translate among these representations.

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.
8.6.3 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.
8.6.5 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.
8.6.7 Find the number of possible arrangements of several objects by using the Basic Counting Principle.

Grade 8 Problem Solving

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.

 Grade 6 Computation Grade 6 Measurement & Analysis & Probability Grade 6 Problem Solving Grade 7 Computation Grade 7 Measurement Grade 7 Problem Solving Grade 8 Computation Grade 8 Data Analysis and Probability Grade 8 Problem Solving