7th Grade Math (West Virginia CCR Standards)

Ratios and Proportional Relationships – Analyze proportional relationships

• M.7.1 Compute unit rates from ratios of fractions, including lengths, areas and other quantities in like or unlike units.
• M.7.2 Recognize and represent proportional relationships between quantities.
  • a. Decide whether quantities are proportional using tables or a straight-line graph through the origin.
  • b. Find the constant of proportionality in tables, graphs, equations, diagrams and descriptions.
  • c. Write equations for proportional relationships.
  • d. Explain what a point on the graph means in context, especially (0, 0) and (1, r).
• M.7.3 Use proportional reasoning for multistep ratio and percent problems such as interest, tax and markups.

The Number System – Operations with rational numbers

• M.7.4 Add and subtract rational numbers and show it on number lines.
  • a. Describe situations where opposite quantities combine to make 0.
  • b. Understand adding as moving along a number line 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.
• M.7.5 Multiply and divide rational numbers.
  • a. Understand multiplying rational numbers and the sign rules, such as (–1)(–1) = 1.
  • b. Understand dividing integers, that the quotient is rational, and the sign rules.
  • c. Use properties of operations to multiply and divide rational numbers.
  • d. Convert rational numbers to decimals and know the decimals terminate or repeat.
• M.7.6 Solve real-world problems with the four operations on rational numbers, including complex fractions.

Expressions and Equations – Generate equivalent expressions

• M.7.7 Use properties of operations to add, subtract, factor and expand linear expressions with rational coefficients.
• M.7.8 See that rewriting an expression can show how quantities relate (e.g. a 5% increase is multiplying by 1.05).

Expressions and Equations – Solve problems with expressions and equations

• M.7.9 Solve multistep problems with positive and negative rational numbers in any form, checking with estimation.
• M.7.10 Write and solve equations and inequalities to model word problems.
  • a. Solve equations of the forms px + q = r and p(x + q) = r and compare algebraic and arithmetic methods.
  • b. Solve inequalities of the form px + q > r or px + q < r, graph the solutions and interpret them.

Geometry – Draw, construct and describe figures

• M.7.11 Solve scale drawing problems, including actual lengths and areas and redrawing at a different scale.
• M.7.12 Draw shapes with given conditions, focusing on triangles from three angle or side measures.
  • a. Recognize conditions that give exactly one triangle (e.g. sides meeting the triangle inequality).
  • b. Recognize conditions that give more than one triangle (e.g. three angles summing to 180°).
  • c. Recognize conditions that give no triangle.
• M.7.13 Describe the plane shapes made by slicing right rectangular prisms and pyramids at different angles.

Geometry – Angle measure, area, surface area and volume

• M.7.14 Use the formulas for a circle's area and circumference and explain informally how they relate.
• M.7.15 Use supplementary, complementary, vertical and adjacent angles to write and solve equations in multistep problems.
• M.7.16 Solve area, volume and surface area problems for composite figures made of polygons, cubes and right prisms.

Statistics and Probability – Random sampling and inference

• M.7.17 Understand that a sample supports conclusions about a population only if it is representative, and random sampling tends to give that.
• M.7.18 Use random sample data to infer unknown population features, using several simulated samples to see variation.

Statistics and Probability – Compare two populations informally

• M.7.19 Identify measures of center and measures of variation in two data displays.
• M.7.20 Compare two numerical data sets in context.
  • a. Report the number of observations.
  • b. Describe the attribute, how it was measured and its units.
  • c. Give and describe measures of center (median and/or mean) and the overall pattern.
  • d. Give measures of variability (IQR, range and/or mean absolute deviation) and note striking deviations.
  • e. Link the choice of center and spread measures to the shape of the data and the context.
• M.7.21 Judge informally how much two distributions with similar spread overlap, giving the gap between centers as a multiple of spread.
• M.7.22 Use center and variability from random samples to compare two populations informally.

Statistics and Probability – Chance processes and probability models

• M.7.23 Understand probability as a number from 0 to 1 showing how likely an event is.
• M.7.24 Estimate probabilities from long-run relative frequency and predict frequencies from probabilities.
• M.7.25 Develop probability models, use them and compare them with observed results.
  • a. Build a uniform model with equally likely outcomes and find event probabilities.
  • b. Build a non-uniform model from observed frequencies, such as a spinning penny.
• M.7.26 Find probabilities of compound events with lists, tables, tree diagrams and simulation.
  • a. Understand that a compound event's probability is the fraction of sample-space outcomes in it.
  • b. Represent sample spaces and identify the outcomes that make up an event.
  • c. Design and run a simulation to estimate how often compound events happen.