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### 7.RP Ratios and Proportional Relationships

- 7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems.
- 7.RP.A.1 Compute unit rates, including those involving complex fractions, with like or different units.
- 7.RP.A.2 Recognize and represent proportional relationships between quantities.
- 7.RP.A.2A Decide whether two quantities in a table or graph are in a proportional relationship.
- 7.RP.A.2B Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- 7.RP.A.2C Represent proportional relationships with equations.
- 7.RP.A.2D 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.

- 7.RP.A.3 Solve multistep real world and mathematical problems involving ratios and percentages.

### 7.NS The Number System

- 7.NS.B Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
- 7.NS.B.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.
- 7.NS.B.1A Describe situations in which opposite quantities combine to make zero (the additive identity).
- 7.NS.B.1B Understand that
*p*+*q*represents the distance |*q*| from*p*whose placement is determined by the sign of*q*. Interpret sums of rational numbers by describing real-world contexts. - 7.NS.B.1C Show that a number and its opposite have a sum of 0 (are additive inverses).
- 7.NS.B.1D Understand subtraction of rational numbers as adding the additive inverse,
*p*–*q*=*p*+ (–*q*). Apply this principal in real-world contexts. - 7.NS.B.1E Apply properties of addition as strategies to add and subtract rational numbers.

- 7.NS.B.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
- 7.NS.B.2A.1 Understand that the multiplicative inverse of a number is its reciprocal and their product is equal to one (the multiplicative identity).
- 7.NS.B.2A.2 Understand positive and negative sign rules for multiplying rational numbers. Interpret products of rational numbers by describing real-world contexts.
- 7.NS.B.2B Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers is a rational number. Recognize that if
*p*and*q*are integers then –(*p*/*q*) = (–*p*)/*q*=*p*/(–*q*). Interpret quotients of rational numbers by describing real-world contexts. - 7.NS.B.2C Apply properties of multiplication (commutative, associative, distributive, or properties of identity and inverse elements) to multiply and divide rational numbers.
- 7.NS.B.2D Convert a rational number to a decimal. Recognize that rational numbers can be written as fractions or decimal numbers that terminate or repeat.

- 7.NS.B.3 Solve real-world and mathematical problems involving the four arithmetic operations with rational numbers.

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

### 7.EE Expressions and Equations

- 7.EE.C Use properties of operations to generate equivalent expressions.
- 7.EE.C.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.EE.C.2 Recognize that algebraic expressions may have a variety of equivalent forms that reveal different information, and determine an appropriate form for a given real-world situation.

- 7.EE.D Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
- 7.EE.D.3 Solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol.
- 7.EE.D.4 Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations.
- 7.EE.D.4A Write and fluently solve linear equations of the form
*a**x*+ b =*c*and*a*(*x*+ b) =*c*where*a*, b, and*c*are rational numbers. - 7.EE.D.4B Write and solve multi-step linear equations that include the use of the distributive property and combining like terms. Exclude equations that contain variables on both sides.
- 7.EE.D.4C Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning.
- 7.EE.D.4D Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.

- 7.EE.D.4A Write and fluently solve linear equations of the form

### 7.G Geometry

- 7.G.E Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.E.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing.
- 7.G.E.2 Draw geometric shapes with given conditions using a variety of tools (e.g., ruler and protractor, or technology). Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
- 7.G.E.3 Describe the two-dimensional figures that result from slicing three-dimensional figures parallel to the base, as in plane sections of right rectangular prisms and right rectangular pyramids.

- 7.G.F Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- 7.G.F.4 Investigate the concept of circles.
- 7.G.F.4A Demonstrate an understanding of the proportional relationships between diameter, radius, and circumference of a circle.
- 7.G.F.4B Understand that pi is defined by the constant of proportionality between the circumference and diameter.
- 7.G.F.4C Given the formulas for circumference and area of circles, solve real-world and mathematical problems.

- 7.G.F.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
- 7.G.F.6 Solve real-world and mathematical problems involving:
- 7.G.F.6A area and surface area of objects composed of triangles and quadrilaterals;
- 7.G.F.6B volume of objects composed only of right prisms having triangular or quadrilateral bases.

- 7.G.F.4 Investigate the concept of circles.

### 7.SP Statistics and Probability

- 7.SP.G Use random sampling to draw inferences about a population.
- 7.SP.G.1 Solve real-world and mathematical problems involving:
- 7.SP.G.1A Understand that a sample is a subset of a population.
- 7.SP.G.1B Differentiate between random and non-random sampling.
- 7.SP.G.1C Understand that generalizations from a sample are valid only if the sample is representative of the population.
- 7.SP.G.1D Understand that random sampling is used to gather a representative sample and tends to support valid inferences about the population.

- 7.SP.G.2 Draw inferences about a population by collecting multiple random samples of the same size to investigate variability in estimates of the characteristic of interest.

- 7.SP.G.1 Solve real-world and mathematical problems involving:
- 7.SP.H Draw informal comparative inferences about two populations.
- 7.SP.H.3 Visually compare the centers, spreads, and overlap of two displays of data (e.g., back-to-back stem and leaf plots, dot plots, histograms, box plots) that are graphed on the same scale and draw inferences about this data.
- 7.SP.H.4 Given measures of center and variability (mean, median and/or mode; range, interquartile range, and/or standard deviation), for numerical data from random samples, draw appropriate informal comparative inferences about two populations.

- 7.SP.I Investigate chance processes and develop, use, and evaluate probability models.
- 7.SP.I.5 Find and interpret the probability of a random event. Understand that the probability of a random event is a number between, and including, 0 and 1 that expresses the likelihood of the event occurring.
- 7.SP.I.6 Collect multiple samples to compare the relationship between theoretical and experimental probabilities for simple events.
- 7.SP.I.7 Apply the concepts of theoretical and experimental probabilities for simple events.
- 7.SP.I.7A Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
- 7.SP.I.7B Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
- 7.SP.I.7C Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancies.

- 7.SP.I.8 Find probabilities of compound events using organized lists, tables, and tree diagrams.
- 7.SP.I.8A Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
- 7.SP.I.8B Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.