7th Grade Math (Arizona Mathematics Standards)

Ratios and Proportional Relationships (RP)

• 7.RP.A.1 Compute unit rates from ratios of fractions, including lengths, areas and other quantities.
• 7.RP.A.2 Recognize and represent proportional relationships.
  • a. Decide if two quantities are proportional using tables of equivalent ratios or a straight-line graph through the origin.
  • b. Find the constant of proportionality (unit rate) from tables, graphs, equations, diagrams and descriptions.
  • c. Write equations for proportional relationships (e.g. t = pn).
  • d. Explain what a point on a proportional graph means, especially (0, 0) and (1, r).
• 7.RP.A.3 Solve multistep ratio and percent problems such as interest, tax, markups, tips, commissions and percent change or error.

The Number System (NS)

• 7.NS.A.1 Add and subtract rational numbers and show them on a number line.
  • a. Describe situations where opposite quantities combine to make 0.
  • b. Understand p + q as moving |q| from p and that a number plus its opposite is 0.
  • c. Understand subtraction as adding the opposite and distance as the absolute value of a difference.
  • d. Use properties of operations to add and subtract rational numbers.
• 7.NS.A.2 Multiply and divide rational numbers.
  • a. Understand the rules for multiplying signed numbers, such as (−1)(−1) = 1, and interpret products in context.
  • b. Know integers can be divided (non-zero divisor) giving rational numbers, and −(p/q) = (−p)/q = p/(−q).
  • c. Use properties of operations to multiply and divide rational numbers.
  • d. Convert rationals to decimals by long division and know the decimals end or repeat.
• 7.NS.A.3 Solve problems with the four operations on rational numbers, extending fraction rules to complex fractions.

Expressions and Equations (EE)

• 7.EE.A.1 Use properties of operations to expand, factor and combine linear expressions that have rational coefficients.
• 7.EE.A.2 Rewrite expressions in different forms to show how quantities in a problem relate.
• 7.EE.B.3 Solve multistep problems with rational numbers in any form, converting between forms and checking with estimation.
• 7.EE.B.4 Use variables and build simple equations and inequalities to solve problems.
  • a. Solve word problems leading to equations like px + q = r or p(x + q) = r, fluently, and compare with arithmetic methods.
  • b. Solve word problems with inequalities px + q > r or < r, graph the solution set and interpret it.

Geometry (G)

• 7.G.A.1 Solve problems with scale drawings, including real lengths and areas, and redraw at a new scale.
• 7.G.A.2 Draw or construct triangles from three given angle or side measures and note whether one, many or no triangles result.
• 7.G.A.3 Describe the 2-D cross-sections formed by slicing right rectangular prisms and pyramids.
• 7.G.B.4 Know and use circle area and circumference formulas and explain informally how they are related.
• 7.G.B.5 Write and solve simple equations for unknown angles using supplementary, complementary, vertical and adjacent angle facts.
• 7.G.B.6 Solve problems on area, volume and surface area of composite 2-D and 3-D shapes, including prisms.

Statistics and Probability (SP)

• 7.SP.A.1 Know samples can tell us about a population and random sampling gives representative samples.
• 7.SP.A.2 Use random-sample data to make inferences about a population and judge variation across samples.
• 7.SP.B.3 Informally judge the overlap of two distributions with similar spread, expressing the difference in centers as a multiple of spread.
• 7.SP.B.4 Use center and spread from random samples to compare two populations informally.
• 7.SP.C.5 Know probability is a number from 0 to 1, with larger values meaning more likely.
• 7.SP.C.6 Estimate probability from long-run relative frequency in data and predict frequencies.
• 7.SP.C.7 Build probability models, compare their results with observed frequencies and explain differences.
  • a. Build a uniform probability model with equally likely outcomes and use it.
  • b. Build a (possibly non-uniform) model from frequencies observed in a chance process.