### M07.A-N: The Number System

#### M07.A-N.1: Apply and extend previous understandings of operations to add, subtract, multiply, and divide rational numbers.

M07.A-N.1.1: Solve real-world and mathematical problems involving the four operations with rational numbers.

M07.A-N.1.1.1: Apply properties of operations to add and subtract rational numbers, including real-world contexts.

M07.A-N.1.1.2: Represent addition and subtraction on a horizontal or vertical number line.

M07.A-N.1.1.3: Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

### M07.A-R: Ratios and Proportional Relationships

#### M07.A-R.1: Demonstrate an understanding of proportional relationships.

M07.A-R.1.1: Analyze, recognize, and represent proportional relationships and use them to solve real-world and mathematical problems.

M07.A-R.1.1.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

M07.A-R.1.1.2: Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

M07.A-R.1.1.3: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

M07.A-R.1.1.4: Represent proportional relationships by equations.

M07.A-R.1.1.5: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.

M07.A-R.1.1.6: Use proportional relationships to solve multi-step ratio and percent problems.

### M07.B-E: Expressions and Equations

#### M07.B-E.1: Represent expressions in equivalent forms.

M07.B-E.1.1: Use properties of operations to generate equivalent expressions.

M07.B-E.1.1.1: Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.

#### M07.B-E.2: Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

M07.B-E.2.1: Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers.

M07.B-E.2.1.1: Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.

M07.B-E.2.2: Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems.

M07.B-E.2.2.1: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.

M07.B-E.2.2.2: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality.

### M07.C-G: Geometry

#### M07.C-G.1: Demonstrate an understanding of geometric figures and their properties.

M07.C-G.1.1: Describe and apply properties of geometric figures.

M07.C-G.1.1.1: Solve problems involving scale drawings of geometric figures, including finding length and area.

M07.C-G.1.1.2: Identify or describe the properties of all types of triangles based on angle and side measures.

M07.C-G.1.1.3: Use and apply the triangle inequality theorem.

#### M07.C-G.2: Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume.

M07.C-G.2.1: Identify, use, and describe properties of angles and their measures.

M07.C-G.2.1.1: Identify and use properties of supplementary, complementary, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

M07.C-G.2.1.2: Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).

M07.C-G.2.2: Determine circumference, area, surface area, and volume.

M07.C-G.2.2.1: Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided.

M07.C-G.2.2.2: Solve real-world and mathematical problems involving area, volume, and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.

### M07.D-S: Statistics and Probability

#### M07.D-S.1: Use random sampling to draw inferences about a population.

M07.D-S.1.1: Use random samples.

M07.D-S.1.1.1: Determine whether a sample is a random sample given a real-world situation.

M07.D-S.1.1.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

#### M07.D-S.2: Draw comparative inferences about populations.

M07.D-S.2.1: Use statistical measures to compare two numerical data distributions.

M07.D-S.2.1.1: Compare two numerical data distributions using measures of center and variability.

#### M07.D-S.3: Investigate chance processes and develop, use, and evaluate probability models.

M07.D-S.3.1: Predict or determine the likelihood of outcomes.

M07.D-S.3.1.1: Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event).

M07.D-S.3.2: Use probability to predict outcomes.

M07.D-S.3.2.1: Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability.

M07.D-S.3.2.2: Find the probability of a simple event, including the probability of a simple event not occurring.

M07.D-S.3.2.3: Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation.

Correlation last revised: 9/15/2020

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