7th Grade Math (Colorado Academic Standards)

Standard 1: Number and Quantity

• MA.7.RP.A Analyze proportional relationships and use them to solve problems.
  • 1. Compute unit rates from ratios of fractions, including lengths, areas and other quantities.
  • 2. Recognize and represent proportional relationships.
  • 2.a. Decide if two quantities are proportional using tables of equivalent ratios or a straight-line graph through the origin.
  • 2.b. Find the constant of proportionality (unit rate) from tables, graphs, equations, diagrams and descriptions.
  • 2.c. Write equations for proportional relationships (e.g. t = pn).
  • 2.d. Explain what a point on a proportional graph means, especially (0, 0) and (1, r).
  • 3. Solve multistep ratio and percent problems such as interest, tax, markups, tips, commissions and percent change or error.
• MA.7.NS.A Extend operations with fractions to rational numbers.
  • 1. Add and subtract rational numbers and show them on a number line.
  • 1.a. Describe situations where opposite quantities combine to make 0.
  • 1.b. Understand p + q as moving |q| from p and that a number plus its opposite is 0.
  • 1.c. Understand subtraction as adding the opposite and distance as the absolute value of a difference.
  • 1.d. Use properties of operations to add and subtract rational numbers.
  • 2. Multiply and divide rational numbers.
  • 2.a. Understand the rules for multiplying signed numbers, such as (−1)(−1) = 1, and interpret products in context.
  • 2.b. Know integers can be divided (non-zero divisor) giving rational numbers, and −(p/q) = (−p)/q = p/(−q).
  • 2.c. Use properties of operations to multiply and divide rational numbers.
  • 2.d. Convert rationals to decimals by long division and know the decimals end or repeat.
  • 3. Solve problems with the four operations on rational numbers.

Standard 2: Algebra and Functions

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

Standard 3: Data, Statistics, and Probability

• MA.7.SP.A Use random samples to make inferences about a population.
  • 1. Know samples can tell us about a population and random sampling gives representative samples.
  • 2. Use random-sample data to make inferences about a population and judge variation across samples.
• MA.7.SP.B Make informal comparisons between two populations.
  • 1. Informally judge the overlap of two distributions with similar spread, expressing the difference in centers as a multiple of spread.
  • 2. Use center and spread from random samples to compare two populations informally.
• MA.7.SP.C Investigate chance and build, use and evaluate probability models.
  • 1. Know probability is a number from 0 to 1, with larger values meaning more likely.
  • 2. Estimate probability from long-run relative frequency in data and predict frequencies.
  • 3. Build probability models, compare their results with observed frequencies and explain differences.
  • 3.a. Build a uniform probability model with equally likely outcomes and use it.
  • 3.b. Build a (possibly non-uniform) model from frequencies observed in a chance process.
  • 4. Find probabilities of compound events with lists, tables, tree diagrams and simulation.
  • 4.a. Know a compound event's probability is the fraction of the sample space where it happens.
  • 4.b. Show sample spaces with lists, tables and tree diagrams and identify the outcomes in an event.
  • 4.c. Design and use a simulation to estimate compound-event probabilities.

Standard 4: Geometry

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