7th Grade Math (Maryland MCCRS)

Number and Operation Sense – 7.NOS.A: Reason with rational numbers

• 7.NOS.A.1 Add and subtract rational numbers with a range of strategies and number line models.
  • a. Describe real situations where opposite quantities combine to make 0.
  • b. Show addition as movement on a number line and that a number plus its opposite is 0.
  • c. Rewrite subtraction as adding the opposite and use absolute value for distance between numbers.
  • d. Model and solve multistep addition and subtraction word problems efficiently.
• 7.NOS.A.2 Multiply and divide rational numbers with a range of strategies and representations.
  • a. Use number lines, arrays or area models to justify the sign rules for multiplication.
  • b. Interpret quotients of signed numbers in context, with a nonzero divisor.
  • c. Apply properties of operations to multiply and divide flexibly.
  • d. Write quotients as decimals to show that rational numbers terminate or repeat.
  • e. Model and solve multistep multiplication and division word problems efficiently.
• 7.NOS.A.3 Solve multistep problems with positive and negative fractions, decimals and percents using all four operations.
  • a. Use properties and convert between forms to compute efficiently.
  • b. Check answers for reasonableness with estimation, mental math and the context.

Algebraic Thinking – 7.AT.A: Proportional relationships

• 7.AT.A.1 Compute unit rates from ratios of fractions, including lengths, areas and other quantities.
• 7.AT.A.2 Recognize proportional relationships between quantities.
  • a. Test for proportionality with equivalent ratios in a table or a straight-line graph through the origin.
  • b. Find the constant of proportionality in tables, graphs, equations, diagrams and descriptions.
• 7.AT.A.3 Represent proportional relationships with equations and interpret points on their graphs.
  • a. Write equations for proportional relationships.
  • b. Explain what points on the graph mean in context, especially (0, 0) and (1, r) where r is the unit rate.
• 7.AT.A.4 Use proportional reasoning to solve ratio and percent problems such as interest, tax, markups and tips.

Algebraic Thinking – 7.AT.B: Rewrite expressions in equivalent forms

• 7.AT.B.5 Use properties of operations to add, subtract, factor and expand linear expressions with rational coefficients.
• 7.AT.B.6 Rewrite an expression in another form to show how quantities in a context are related.

Algebraic Thinking – 7.AT.C: Model with and solve equations and inequalities

• 7.AT.C.7 Decide whether an equation or an inequality better models a situation and justify the choice.
• 7.AT.C.8 Write and solve equations with variables to model relationships in context.
  • a. Write equations of the given two-step forms using specific rational numbers.
  • b. Solve them efficiently and explain how each step keeps the equality true.
  • c. Solve word problems leading to such equations and interpret the solution in context.
• 7.AT.C.9 Write and solve inequalities to model constraints and conditions in context.
  • a. Write inequalities of the given two-step forms.
  • b. Solve them and graph the solution set on a number line.
  • c. Interpret the solution set by saying which values are possible or sensible.

Geometric Reasoning and Measurement – 7.GR.A: Analyze geometric figures

• 7.GR.A.1 Solve scale drawing problems, including actual lengths and areas and redrawing at a different scale.
• 7.GR.A.2 Describe the plane shapes made by slicing solid figures and connect them to volume and surface area.

Geometric Reasoning and Measurement – 7.GR.B: Use geometric formulas in context

• 7.GR.B.3 Use the formulas for the area and circumference of a circle in context and explain informally how they relate.
• 7.GR.B.4 Solve area, surface area and volume problems, with or without context.
  • a. Solve problems with polygons and polyhedra such as triangles, quadrilaterals, cubes, prisms and pyramids.
  • b. Solve volume problems for cones, cylinders and spheres.
  • c. Justify solutions by comparing representations, estimating and explaining the result in context.

Reasoning with Data, Statistics and Probability – 7.DS.A: Statistical inquiry

• 7.DS.A.1 Decide when generalizing to a population is justified, based on how the sample was chosen.
  • a. Judge whether a sample represents the population and how selection affects accuracy.
  • b. Explain why random selection makes a representative sample more likely.
• 7.DS.A.2 Use data from random samples to estimate or predict population features and judge how reliable they are.
  • a. Estimate an unknown population feature from one random sample.
  • b. Compare several random samples of the same size to judge the reliability of the estimate.

Reasoning with Data, Statistics and Probability – 7.DS.B: Compare data with graphs and measures

• 7.DS.B.3 Compare two numerical distributions to draw informal inferences about differences between populations.
  • a. Compare range, shape and clustering using histograms and other graphs.
  • b. Use measures of center and variability to judge the size and importance of differences.
  • c. Use graphical and numerical comparisons to decide whether a difference matters in context.

Reasoning with Data, Statistics and Probability – 7.DS.C: Probability models and predictions

• 7.DS.C.4 Interpret probability as a number from 0 (impossible) to 1 (certain) and estimate the chance of events.
• 7.DS.C.5 Use long-run relative frequency to approximate probabilities and make predictions.
  • a. Approximate a probability by collecting data or simulating and watching long-run frequency.
  • b. Use a known or estimated probability to judge whether simulation results are reasonable.
  • c. Use bar graphs and circle graphs to compare and interpret probabilities.
• 7.DS.C.6 Build probability models, use them, and compare them with observed results.
  • a. Build a uniform model for equally likely outcomes and find event probabilities.
  • b. Build a model from observed frequencies to estimate probabilities.
  • c. Compare model probabilities with observed data and explain differences.