• N.ME.07.01 Understand derived quantities such as density, velocity, and weighted averages.
• N.FL.07.02 Solve problems involving derived quantities.

Understand and solve problems involving rates, ratios, and proportions

• N.FL.07.03 Calculate rates of change including speed.
• N.MR.07.04 Convert ratio quantities between different systems of units such as feet per second to miles per hour.
• N.FL.07.05 Solve simple proportion problems using such methods as unit rate, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables.

Recognize irrational numbers

• N.MR.07.06 Understand the concept of square root and cube root, and estimate using calculators.

Compute with rational numbers

• N.FL.07.07 Solve problems involving operations with integers.
• N.FL.07.08 Add, subtract, multiply and divide negative rational numbers.
• N.FL.07.09 Estimate results of computations with rational numbers.

ALGEBRA Understand and apply directly proportional relationships and relate to linear relationships

• A.PA.07.01 Recognize when information given in a table, graph, or formula suggests a proportional or linear relationship.
• A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations.
• A.PA.07.03 Given a directly proportional or linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = kx for specific x values, given k, e.g., weight vs. volume of water, base cost plus cost per unit.
• A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container with uniform cross-section, height of water in a tank being filled at a constant rate, degrees Celsius and degrees Fahrenheit, distance and time under constant speed.
• A.PA.07.05 Understand and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional relationship between two quantities one quantity is a constant multiple of the other quantity.

Understand and represent linear functions

• A.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of “rise/run” for a pair of points on the graph, and express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change.
• A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept.
• A.FO.07.08 Know that the solution to a linear equation corresponds to the point at which its graph crosses the x-axis.

Understand and solve problems about inversely proportional relationships

• A.PA.07.09 Recognize inversely proportional relationships in contextual situations; know that quantities are inversely proportional if their product is constant, e.g., the length and width of a rectangle with fixed area, and that an inversely proportional relationship is of the form y = k/x where k is some non-zero number.
• A.RP.07.10 Know that the graph of y = k/x is not a line; know its shape; and know that it crosses neither the x nor the y-axis.

Apply basic properties of real numbers in algebraic contexts

• A.PA.07.11 Understand and use basic properties of real numbers: additive and multiplicative identities, additive and multiplicative inverses, commutativity, associativity, and the distributive property of multiplication over addition.

Combine algebraic expressions and solve equations

• A.FO.07.12 Add, subtract, and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) – 5x + y, or – 2x (5x – 4), and justify using properties of real numbers.
• A.FO.07.13 From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions.

GEOMETRY Draw and construct geometric objects

• G.SR.07.01 Use a ruler and other tools to draw squares, rectangles, triangles and parallelograms with specified dimensions.
• G.SR.07.02 Use compass and straightedge to perform basic geometric constructions: the perpendicular bisector of a segment, an equilateral triangle, and the bisector of an angle; understand informal justifications.

Understand the concept of similar polygons, and solve related problems

• G.TR.07.03 Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor.
• G.TR.07.04 Solve problems about similar figures and scale drawings.
• G.TR.07.05 Show that two triangles are similar using the criteria: corresponding angles are congruent (AAA similarity); the ratios of two pairs of corresponding sides are equal and the included angles are congruent (SAS similarity); ratios of all pairs of corresponding sides are equal (SSS similarity); use these criteria to solve problems and to justify arguments.
• G.TR.07.06 Understand and use the fact that when two triangles are similar with scale factor of r, their areas are related by a factor of r 2 .

Data and Probability Represent data and interpret

• D.RE.07.01 Represent and interpret data using circle graphs, stem and leaf plots, histograms, and box-and-whisker plots, and select appropriate representation to address specific questions.
• D.AN.07.02 Create and interpret scatter plots and find line of best fit and use an estimated line of best fit to answer questions about the data.

Compute statistics about datasets

• D.AN.07.03 Calculate and interpret relative frequencies and cumulative frequencies for given data sets.
• D.AN.07.04 Find and interpret the median, quartiles, and interquartile range of a given set of data.