6th Grade Math (Maryland MCCRS)

Number and Operation Sense – 6.NOS.A: Divide fractions by fractions

• 6.NOS.A.1 Divide fractions by fractions in real-world contexts.
  • a. Estimate to check that quotients are reasonable.
  • b. Use fraction models and equations to divide.
  • c. Explain the calculation by linking models and equations to the meaning of division.

Number and Operation Sense – 6.NOS.B: Fluent multi-digit computation; common factors and multiples

• 6.NOS.B.2 Divide multi-digit whole numbers fluently.
  • a. Estimate quotients to check reasonableness.
  • b. Use strategies such as partial quotients or inverse operations.
  • c. Use the standard division algorithm.
  • d. Decide which strategy or algorithm is most efficient.
• 6.NOS.B.3 Multiply and divide multi-digit decimals to thousandths in context.
  • a. Estimate products and quotients to check reasonableness.
  • b. Apply whole-number strategies to decimals.
  • c. Use the standard algorithms for multiplying and dividing decimals.
  • d. Decide which strategy or algorithm is most efficient.
• 6.NOS.B.4 Find common factors and multiples of two whole numbers.
  • a. Find the greatest common factor of two whole numbers up to 100.
  • b. Find the least common multiple of two whole numbers up to 12.
  • c. Use the distributive property to take a common factor out of a sum of numbers up to 100.

Number and Operation Sense – 6.NOS.C: The rational number system

• 6.NOS.C.5 Use positive and negative numbers for opposite quantities and explain what 0 means in each situation.
• 6.NOS.C.6 Show rational numbers, including negatives, as points on horizontal or vertical number lines.
  • a. Estimate using position, benchmarks and rounding.
  • b. Locate and interpret rational numbers on a number line.
  • c. Recognize that numbers with opposite signs lie on opposite sides of 0.
• 6.NOS.C.7 Use perpendicular number lines to build the four-quadrant coordinate plane.
  • a. Use the signs of the coordinates to tell where an ordered pair lies without plotting it.
  • b. Locate and interpret rational-number points, including how sign changes reflect points across axes into other quadrants.
• 6.NOS.C.8 Order rational numbers and find their absolute values.
  • a. Read inequalities as positions relative to each other on a number line.
  • b. Write, interpret and explain the order of rational numbers in context.
  • c. Use absolute value as distance from 0 to describe size in context.
• 6.NOS.C.9 Solve problems by graphing points in all four quadrants that share an x- or y-coordinate.
  • a. Explain that points sharing an x- or y-coordinate lie on the same vertical or horizontal line.
  • b. Use absolute value to find the length of vertical and horizontal segments.

Algebraic Thinking – 6.AT.A: Ratio concepts and ratio reasoning

• 6.AT.A.1 Use ratio language in context to describe part-to-part and part-to-whole relationships.
• 6.AT.A.2 Understand and use unit rates in context.
  • a. Use unit rate language for ratio situations.
  • b. Solve unit rate problems such as unit pricing and constant speed.
• 6.AT.A.3 Use ratio and rate reasoning with tables, tape diagrams, double number lines or the coordinate plane.
  • a. Make, compare and complete tables of equivalent ratios and unit rates.
  • b. Plot unit-rate pairs in the first quadrant and connect the representations.
  • c. Use ratio reasoning to convert measurement units.
• 6.AT.A.4 Find a percent of a quantity as a rate per 100, including finding the whole from a part and the percent.

Algebraic Thinking – 6.AT.B: From arithmetic to algebraic expressions

• 6.AT.B.5 Write numerical expressions with whole-number exponents and positive rational bases, and evaluate them using technology.
• 6.AT.B.6 Write, read and evaluate expressions in which letters stand for numbers.
  • a. Write expressions that record operations with numbers and letters.
  • b. Name the parts of an expression with math vocabulary and treat a part as a single quantity.
  • c. Evaluate expressions for given values, including those with exponents.
• 6.AT.B.7 Use properties of operations to write equivalent expressions and to tell when two expressions are equivalent.

Algebraic Thinking – 6.AT.C: One-variable equations and inequalities

• 6.AT.C.8 Solve problems in context by writing and solving equations and interpreting the solutions.
  • a. Explain a variable as an unknown and use substitution to test whether a value makes an equation true.
  • b. Write and solve one-step equations for nonnegative rational numbers.
  • c. Show the solutions on a number line.
• 6.AT.C.9 Write simple inequalities (variable compared with a constant) for constraints and show their infinitely many solutions on number lines.
• 6.AT.C.10 Solve problems in context by writing and solving inequalities and interpreting the solution sets.
  • a. Use substitution to test whether a value from a set makes an inequality true.
  • b. Write and solve one-step inequalities for nonnegative rational numbers.
  • c. Show the solutions on a number line.

Algebraic Thinking – 6.AT.D: Dependent and independent variables

• 6.AT.D.11 Use variables for two quantities that change in relation to each other.
  • a. Write a one-step equation giving the dependent variable in terms of the independent variable.
  • b. Analyze the relationship with graphs and tables and connect them to the equation.

Geometric Reasoning and Measurement – 6.GR.A: Area, surface area and volume

• 6.GR.A.1 Find the area of triangles, quadrilaterals and other polygons by composing or decomposing them.
• 6.GR.A.2 Find the volume of right rectangular prisms with fractional edge lengths.
  • a. Use packing with unit cubes and estimation to show volume equals the product of the edge lengths.
  • b. Apply the volume formulas to solve problems with fractional edge lengths.
• 6.GR.A.3 Draw polygons on the coordinate plane from vertex coordinates and find lengths of sides that share a coordinate.
• 6.GR.A.4 Use nets of rectangular and triangular prisms and pyramids to find surface area.

Reasoning with Data and Statistics – 6.DS.A: Statistical variability

• 6.DS.A.1 Recognize a statistical question as one that expects variability in the data.
• 6.DS.A.2 Use probability words (likely, unlikely, certain, impossible) to describe outcomes and anticipate variability.
• 6.DS.A.3 Explain that a data distribution can be described by its center, spread and overall shape.
• 6.DS.A.4 Know that a measure of center sums up data with one number and a measure of variation describes spread with one number.

Reasoning with Data and Statistics – 6.DS.B: Summarize and describe distributions

• 6.DS.B.5 Interpret numerical data shown on a number line, including line plots, histograms and box plots.
• 6.DS.B.6 Summarize numerical data sets in relation to their context.
  • a. Report the number of observations.
  • b. Describe the attribute measured, how it was measured and its units.
  • c. Give the center (median and/or mean) and variability (interquartile range) and describe outliers in context.
  • d. Link the choice of center and spread measures to the shape of the data and the context.