# Math 7 Grade

1.0 | NUMBERS AND OPERATIONS | ||

A | Understand Derived Quantities | ||

N.MR.07.02 | Solve problems involving derived quantities such as density, velocity, and weighted averages.* | ||

B | 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 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.* | ||

C | Recognize Irrational Numbers | ||

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

D | Compute with Rational Numbers | ||

N.FL.07.07 | Solve problems involving operations with integers. | ||

N.FL.07.08 | Add, subtract, multiply, and divide positive and negative rational numbers fluently.* | ||

N.FL.07.09 | Estimate results of computations with rational numbers. | ||

2.0 | ALGEBRA | ||

E | 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 directly 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 other linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = mx + b for specific x values, 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 | Recognize 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.* | ||

F | 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 | Find and interpret the x and/or y intercepts of a linear equation or function. Know that the solution to a linear equation of the form ax+b=0 corresponds to the point at which the graph of y=ax+b crosses the x axis.* | ||

G | 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. | ||

H | 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. | ||

I | 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 x(x+2) 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. | ||

3.0 | GEOMETRY | ||

J | 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. | ||

K | 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 r2. | ||

4.0 | DATA AND PROBABILITY | ||

L | Represent and Interpret Data | ||

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; use an estimated line of best fit to answer questions about the data. | ||

M | Compute Statistics About Data Sets | ||

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. |