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.

Checkpoint opportunity

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.

Checkpoint opportunity

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.

Checkpoint opportunity

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.

Checkpoint opportunity

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.

Checkpoint opportunity

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.