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### 7.RP Ratios and Proportional Relationships

- 7.RP.A Analyze proportional relationships and use them to solve problems.
- 7.RP.A.1 Compute unit rates, including those that involve complex fractions, with like or different units.
- 7.RP.A.2 Recognize and represent proportional relationships between quantities.
- 7.RP.A.2.a Determine when two quantities are in a proportional relationship.
- 7.RP.A.2.b Identify and/or compute the constant of proportionality (unit rate).
- 7.RP.A.2.c Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation.
- 7.RP.A.2.d Recognize that the graph of any proportional relationship will pass through the origin.

- 7.RP.A.3 Solve problems involving ratios, rates, percentages and proportional relationships.

### 7.NS Number Sense and Operations

- 7.NS.A Apply and extend previous understandings of operations to add, subtract, multiply and divide rational numbers.
- 7.NS.A.1 Apply and extend previous understandings of numbers to add and subtract rational numbers.
- 7.NS.A.1.a Add and subtract rational numbers.
- 7.NS.A.1.b Represent addition and subtraction on a horizontal or vertical number line.
- 7.NS.A.1.c Describe situations and show that a number and its opposite have a sum of 0 (additive inverses).
- 7.NS.A.1.d Understand subtraction of rational numbers as adding the additive inverse.
- 7.NS.A.1.e Determine the distance between two rational numbers on the number line is the absolute value of their difference.
- 7.NS.A.1.f Interpret sums and differences of rational numbers.

- 7.NS.A.2 Apply and extend previous understandings of numbers to multiply and divide rational numbers.
- 7.NS.A.2.a Multiply and divide rational numbers.
- 7.NS.A.2.b Determine that a number and its reciprocal have a product of 1 (multiplicative inverse).
- 7.NS.A.2.c Understand that every quotient of integers (with non-zero divisor) is a rational number.
- 7.NS.A.2.d Convert a rational number to a decimal.
- 7.NS.A.2.e Understand that all rational numbers can be written as fractions or decimal numbers that terminate or repeat.
- 7.NS.A.2.f Interpret products and quotients of rational numbers by describing real-world contexts.

- 7.NS.A.3 Solve problems involving the four arithmetic operations with rational numbers.

- 7.NS.A.1 Apply and extend previous understandings of numbers to add and subtract rational numbers.

### 7.EEI Expressions, Equations and Inequalities

- 7.EEI.A Use properties of operations to generate equivalent expressions.
- 7.EEI.A.1 Apply properties of operations to simplify and to factor linear algebraic expressions with rational coefficients.
- 7.EEI.A.2 Understand how to use equivalent expressions to clarify quantities in a problem.

- 7.EEI.B Solve problems using numerical and algebraic expressions and equations.
- 7.EEI.B.3 Solve multi-step problems posed with rational numbers.
- 7.EEI.B.3.a Convert between equivalent forms of the same number.
- 7.EEI.B.3.b Assess the reasonableness of answers using mental computation and estimation strategies.

- 7.EEI.B.4 Write and/or solve linear equations and inequalities in one variable.
- 7.EEI.B.4.a Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers.
- 7.EEI.B.4.b Write and/or solve two-step equations of the form px + q = r and p(x + q) = r, where p, q and r are rational numbers, and interpret the meaning of the solution in the context of the problem.
- 7.EEI.B.4.c Write, solve and/or graph inequalities of the form px + q > r or px + q < r, where p, q and r are rational numbers.

- 7.EEI.B.3 Solve multi-step problems posed with rational numbers.

### 7.GM Geometry and Measurement

- 7.GM.A Draw and describe geometrical figures and describe the relationships between them.
- 7.GM.A.1 Solve problems involving scale drawings of real objects and geometric figures, including computing actual lengths and areas from a scale drawing and reproducing the drawing at a different scale.
- 7.GM.A.2 Use a variety of tools to construct geometric shapes.
- 7.GM.A.2.a Determine if provided constraints will create a unique triangle through construction.
- 7.GM.A.2.b Construct special quadrilaterals given specific parameters.

- 7.GM.A.3 Describe two-dimensional cross sections of pyramids, prisms, cones and cylinders.
- 7.GM.A.4 Understand concepts of circles.
- 7.GM.A.4.a Analyze the relationships among the circumference, the radius, the diameter, the area and Pi in a circle.
- 7.GM.A.4.b Know and apply the formulas for circumference and area of circles to solve problems.

- 7.GM.B Apply and extend previous understanding of angle measure, area and volume.
- 7.GM.B.5 Use angle properties to write and solve equations for an unknown angle.
- 7.GM.B.6 Understand the relationship between area, surface area and volume.
- 7.GM.B.6.a Find the area of triangles, quadrilaterals and other polygons composed of triangles and rectangles.
- 7.GM.B.6.b Find the volume and surface area of prisms, pyramids and cylinders.

### 7.DSP Data Analysis, Statistics and Probability

- 7.DSP.A Use random sampling to draw inferences about a population.
- 7.DSP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population.
- 7.DSP.A.1.a Understand that a sample is a subset of a population.
- 7.DSP.A.1.b Understand that generalizations from a sample are valid only if the sample is representative of the population.
- 7.DSP.A.1.c Understand that random sampling is used to produce representative samples and support valid inferences.

- 7.DSP.A.2 Use data from multiple samples to draw inferences about a population and investigate variability in estimates of the characteristic of interest.

- 7.DSP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population.
- 7.DSP.B Draw informal comparative inferences about two populations.
- 7.DSP.B.3 Analyze different data distributions using statistical measures.
- 7.DSP.B.4 Compare the numerical measures of center, measures of frequency and measures of variability from two random samples to draw inferences about the population.

- 7.DSP.C Develop, use and evaluate probability models.
- 7.DSP.C.5 Investigate the probability of chance events.
- 7.DSP.C.5.a Determine probabilities of simple events.
- 7.DSP.C.5.b Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

- 7.DSP.C.6 Investigate the relationship between theoretical and experimental probabilities for simple events.
- 7.DSP.C.6.a Predict outcomes using theoretical probability.
- 7.DSP.C.6.b Perform experiments that model theoretical probability.
- 7.DSP.C.6.c Compare theoretical and experimental probabilities.

- 7.DSP.C.7 Explain possible discrepancies between a developed probability model and observed frequencies.
- 7.DSP.C.7.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
- 7.DSP.C.7.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

- 7.DSP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams and simulations.
- 7.DSP.C.8.a Represent the sample space of a compound event.
- 7.DSP.C.8.b Design and use a simulation to generate frequencies for compound events.

- 7.DSP.C.5 Investigate the probability of chance events.