7th Grade Math (Massachusetts Curriculum Frameworks)

Ratios and Proportional Relationships (7.RP)

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

The Number System (7.NS)

• 7.NS.A.1 Add and subtract rational numbers and show addition and subtraction on a number line.
  • a. Describe situations where opposite quantities combine to make 0.
  • b. Understand p + q as the point at distance (absolute value of q) from p, in the direction set by q's sign; opposites add to 0.
  • c. Understand subtraction as adding the additive inverse; distance is the absolute value of the difference.
  • d. Apply properties of operations when adding and subtracting rational numbers.
• 7.NS.A.2 Multiply and divide rational numbers.
  • a. Extend multiplication to rational numbers keeping the properties of operations, giving rules like (−1)(−1) = 1.
  • b. Know integers can be divided (non-zero divisor) giving a rational number; interpret quotients in context.
  • c. Apply properties of operations when multiplying and dividing rational numbers.
  • d. Convert a rational number to a decimal by long division; the decimal ends in 0s or repeats.
• 7.NS.A.3 Solve real-world and math problems with all four operations on integers and other rational numbers.

Expressions and Equations (7.EE)

• 7.EE.A.1 Use properties of operations to add, subtract, expand and factor linear expressions that have rational coefficients.
• 7.EE.A.2 Rewrite an expression in another form to show how quantities are related, e.g. a + 0.05a = 1.05a.
• 7.EE.B.3 Solve multistep real-world problems with rational numbers in any form (whole, fraction, decimal) and check by estimating.
• 7.EE.B.4 Use variables for quantities and build simple equations and inequalities to solve problems.
  • a. Solve word problems leading to px + q = r and p(x + q) = r; compare algebraic and arithmetic methods.
  • b. Solve word problems leading to px + q > r or px + q < r; graph and interpret the solutions.
  • c. Explore arithmetic and geometric sequences with expressions and tables.

Geometry (7.G)

• 7.G.A.1 Solve scale drawing problems, find actual lengths and areas and redraw at another scale.
• 7.G.A.2 Draw shapes with given conditions; build triangles from three angles or sides and see when one, many or no triangles exist.
• 7.G.A.3 Describe the 2D cross-sections made by slicing right rectangular prisms and pyramids.
• 7.G.B.4 Circles and measurement.
  • a. Know a circle is the flat shape made of all points the same distance from a center point.
  • b. Describe how a circle's radius, diameter and circumference are related.
  • c. Describe how a circle's radius, diameter and area are related.
  • d. Know and apply the formulas for a circle's area and circumference.
  • e. Explain informally how a circle's circumference and area are linked.
• 7.G.B.5 Use supplementary, complementary, vertical and adjacent angle facts to write and solve equations for unknown angles.
• 7.G.B.6 Solve real problems on area, volume and surface area of shapes and solids built from polygons, cubes and right prisms.

Statistics and Probability (7.SP)

• 7.SP.A.1 Know a sample tells about a population only if it is representative; random sampling tends to give representative samples.
• 7.SP.A.2 Use random-sample data to infer about a population and simulate several samples to see how estimates vary.
• 7.SP.B.3 Judge how much two distributions with similar spread overlap, giving the difference in centers as a multiple of variability.
• 7.SP.B.4 Compare two populations informally using centers and variability of random samples.
• 7.SP.C.5 Understand probability as a number from 0 to 1, with values near 0 unlikely and near 1 likely.
• 7.SP.C.6 Estimate probability from long-run relative frequency and predict frequency from a known probability.
• 7.SP.C.7 Build probability models, compare them with observed frequencies and explain differences.
  • a. Build a uniform model with equal probability for all outcomes and find event probabilities.
  • b. Build a (possibly non-uniform) model from observed frequencies of a chance process.
• 7.SP.C.8 Find probabilities of compound events with lists, tables, tree diagrams and simulations.
  • a. A compound event's probability equals the share of sample-space outcomes in which it happens.
  • b. Show sample spaces with lists, tables and tree diagrams and identify outcomes making up an event.
  • c. Design and use a simulation to estimate probabilities of compound events.