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### NR Numerical Reasoning

- Integers, percentages, fractions, decimal numbers
- 7.NR.1 Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).
- 7.NR.1.1 Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.
- 7.NR.1.2 Show and explain
*p*+*q*as the number located a distance |*q*| from*p*, in the positive or negative direction, depending on whether*q*is positive or negative. Interpret sums of rational numbers by describing applicable situations. - 7.NR.1.3 Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems.
- 7.NR.1.4 Show and explain subtraction of rational numbers as adding the additive inverse,
*p*–*q*=*p*+ (-*q*). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in contextual situations. - 7.NR.1.5 Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
- 7.NR.1.6 Make sense of multiplication of rational numbers using realistic applications.
- 7.NR.1.7 Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.
- 7.NR.1.8 Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation.
- 7.NR.1.9 Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
- 7.NR.1.10 Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.
- 7.NR.1.11 Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.

- 7.NR.1 Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).

### PAR Patterning & Algebraic Reasoning

- Linear expressions with rational coefficients, complex unit rates, proportional relationships
- 7.PAR.2 Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant situations.
- 7.PAR.2.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.PAR.2.2 Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in it are related.

- 7.PAR.3 Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.
- 7.PAR.3.1 Construct algebraic equations to solve practical problems leading to equations of the form
*px*+*q*=*r*and*p(x*+*q)*=*r*, where*p*,*q*, and*r*are specific rational numbers. Interpret the solution based on the situation. - 7.PAR.3.2 Construct algebraic inequalities to solve problems, leading to inequalities of the form
*px*±*q*>*r*,*px*±*q*<*r*,*px*±*q*≤*r*, or*px*±*q*≥*r*, where*p*,*q*, and*r*are specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.

- 7.PAR.3.1 Construct algebraic equations to solve practical problems leading to equations of the form
- 7.PAR.4 Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.
- 7.PAR.4.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units presented in realistic problems.
- 7.PAR.4.2 Determine the unit rate (constant of proportionality) in tables, graphs (1,
*r*), equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems. - 7.PAR.4.3 Determine whether two quantities presented in authentic problems are in a proportional relationship.
- 7.PAR.4.4 Identify, represent, and use proportional relationships.
- 7.PAR.4.5 Use context to 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.PAR.4.6 Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
- 7.PAR.4.7 Use similar triangles to explain why the slope,
*m*, is the same between any two distinct points on a nonvertical line in the coordinate plane. - 7.PAR.4.8 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
- 7.PAR.4.9 Use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations.
- 7.PAR.4.10 Predict characteristics of a population by examining the characteristics of a representative sample. Recognize the potential limitations and scope of the sample to the population.
- 7.PAR.4.11 Analyze sampling methods and conclude that random sampling produces and supports valid inferences.
- 7.PAR.4.12 Use data from repeated random samples to evaluate how much a sample mean is expected to vary from a population mean. Simulate multiple samples of the same size.

- 7.PAR.2 Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant situations.

### GSR Geometric & Spatial Reasoning

- Vertical, adjacent, complementary, and supplementary angles, circumference and area of circles, area and surface area, volume of cubes, right prisms, and cylinders
- 7.GSR.5 Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.
- 7.GSR.5.1 Measure angles in whole nonstandard units.
- 7.GSR.5.2 Measure angles in whole number degrees using a protractor.
- 7.GSR.5.3 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.
- 7.GSR.5.4 Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle.
- 7.GSR.5.5 Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.
- 7.GSR.5.6 Solve realistic problems involving surface area of right prisms and cylinders.
- 7.GSR.5.7 Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in the plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.
- 7.GSR.5.8 Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using concrete problems.

- 7.GSR.5 Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.

### PR Probability Reasoning

- Likelihood, theoretical and experimental probability
- 7.PR.6 Using mathematical reasoning, investigate chance processes and develop, evaluate, and use probability models to find probabilities of simple events presented in authentic situations.
- 7.PR.6.1 Represent the probability of a chance event as a number between 0 and 1 that expresses the likelihood of the event occurring. Describe that 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.
- 7.PR.6.2 Approximate the probability of a chance event by collecting data on an event and observing its long-run relative frequency will approach the theoretical probability.
- 7.PR.6.3 Develop a probability model and use it to find probabilities of simple events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.
- 7.PR.6.4 Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.
- 7.PR.6.5 Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
- 7.PR.6.6 Use appropriate graphical displays and numerical summaries from data distributions with categorical or quantitative (numerical) variables as probability models to draw informal inferences about two samples or populations.

- 7.PR.6 Using mathematical reasoning, investigate chance processes and develop, evaluate, and use probability models to find probabilities of simple events presented in authentic situations.