7th Grade Math (South Dakota Content Standards)

Ratios and Proportional Relationships (RP)

• 7.RP.1 Find unit rates for ratios of fractions, including lengths and areas.
• 7.RP.2 Recognize and represent proportional relationships.
  • 7.RP.2a Decide whether two quantities are proportional using tables or graphs.
  • 7.RP.2b Find the constant of proportionality in tables, graphs, equations, diagrams and words.
  • 7.RP.2c Show proportional relationships with equations.
  • 7.RP.2d Explain what points on a proportional graph mean, especially (0, 0) and (1, r).
• 7.RP.3 Solve multistep ratio and percent problems such as interest, tax, markups and discounts.

The Number System (NS)

• 7.NS.1 Add and subtract rational numbers, including on number lines.
  • 7.NS.1a Describe situations where opposite quantities combine to make zero.
  • 7.NS.1b Understand p + q as a distance from p and show a number plus its opposite is zero.
  • 7.NS.1c Understand subtraction as adding the opposite and distance as the absolute value of a difference.
  • 7.NS.1d Use properties of operations to add and subtract rational numbers.
• 7.NS.2 Multiply and divide rational numbers.
  • 7.NS.2a Extend multiplication to rational numbers, e.g. (−1)(−1) = 1, and interpret products in context.
  • 7.NS.2b Know integers can be divided (nonzero divisor) and interpret quotients in context.
  • 7.NS.2c Use properties of operations to multiply and divide rational numbers.
  • 7.NS.2d Convert rational numbers to decimals by long division, knowing they end or repeat.
• 7.NS.3 Solve real problems with all four operations on rational numbers.

Expressions and Equations (EE)

• 7.EE.1 Combine, factor and expand linear expressions that have rational coefficients.
• 7.EE.2 Understand how rewriting an expression in other forms helps interpret a problem.
• 7.EE.3 Solve multistep problems with rational numbers in any form, using tools strategically.
  • 7.EE.3a Convert between fractions, decimals and percents when calculating.
  • 7.EE.3b Check answers are reasonable with mental math and estimation.
• 7.EE.4 Use variables to write and solve equations and inequalities.
  • 7.EE.4a Solve two-step equations shaped like px + q = r or p(x + q) = r, comparing algebra and arithmetic methods.
  • 7.EE.4b Solve inequalities of these forms, graph the solutions and interpret them in context.

Geometry (G)

• 7.G.1 Solve problems with scale drawings, including real lengths and areas and changing the scale.
• 7.G.2 Draw shapes from given conditions and decide when one, many or no triangles fit.
• 7.G.3 Describe 2D cross-sections made by slicing prisms and pyramids.
• 7.G.4 Know and use the area and circumference formulas for a circle.
• 7.G.5 Use supplementary, complementary, vertical and adjacent angles to find unknown angles.
• 7.G.6 Solve problems about area, surface area and volume of 2D and 3D objects.

Statistics and Probability (SP)

• 7.SP.1 Understand that a sample must represent the population for valid inferences.
• 7.SP.2 Use random samples to make inferences about a population and judge variation in estimates.
• 7.SP.3 Compare informally how much two data distributions overlap, using center and variability.
• 7.SP.4 Use measures of center and variability from random samples to compare two populations.
• 7.SP.5 Understand probability as a number from 0 to 1 showing how likely an event is.
• 7.SP.6 Estimate probability from long-run relative frequency.
• 7.SP.7 Develop probability models and use them to find probabilities.
  • 7.SP.7a Use a uniform model in which all outcomes are equally likely.
  • 7.SP.7b Develop a non-uniform model from observed frequencies in chance data.
• 7.SP.8 Work out the probability of a compound event using organized lists, tables, tree diagrams or a simulation.
  • 7.SP.8a Know that a compound event's probability is the share of sample-space outcomes in which the event happens.
  • 7.SP.8b Show the sample space of a compound event as a list, table or tree diagram and pick out the outcomes that make up the event.
  • 7.SP.8c Design and run a simulation that produces frequencies for a compound event.