6th Grade Math (West Virginia CCR Standards)

Ratios and Proportional Relationships – Ratio concepts and ratio reasoning

• M.6.1 Understand ratios and use ratio language to describe how two quantities are related.
• M.6.2 Understand the unit rate that goes with a ratio and use rate language to describe ratio relationships.
• M.6.3 Use ratio and rate reasoning to solve real-world problems with tables, tape diagrams, double number lines or equations.
  • a. Make tables of equivalent whole-number ratios, find missing values, plot the pairs and compare ratios.
  • b. Solve unit rate problems such as unit pricing and constant speed.
  • c. Find a percent of a quantity as a rate per 100 and find the whole from a part and the percent.
  • d. Use ratio reasoning to convert measurement units and handle units in calculations.

The Number System – Divide fractions by fractions

• M.6.4 Divide fractions by fractions and solve word problems about it using visual models and equations.

The Number System – Fluent multi-digit computation; common factors and multiples

• M.6.5 Divide multi-digit whole numbers fluently with the standard algorithm.
• M.6.6 Add, subtract, multiply and divide multi-digit decimals fluently with the standard algorithms.
• M.6.7 Find the greatest common factor (up to 100) and least common multiple (up to 12); use the distributive property to factor sums.

The Number System – The rational number system

• M.6.8 Use positive and negative numbers for opposite quantities in real situations and explain what 0 means there.
• M.6.9 Show rational numbers as points on number lines and on the coordinate plane, including negative coordinates.
  • a. See opposite signs as opposite sides of 0 and know the opposite of the opposite is the number itself.
  • b. Read the signs of an ordered pair as its quadrant and relate points differing only in signs as reflections.
  • c. Place integers and other rational numbers on number lines and pairs of them on the coordinate plane.
• M.6.10 Understand ordering and absolute value of rational numbers.
  • a. Read an inequality as the positions of two numbers on a number line.
  • b. Write, interpret and explain statements of order for rational numbers in real situations.
  • c. Understand absolute value as distance from 0 and as size in real situations.
  • d. Tell comparisons of absolute value apart from statements about order.
• M.6.11 Graph points in all four quadrants to solve problems, finding distances between points that share a coordinate.

Expressions and Equations – From arithmetic to algebraic expressions

• M.6.12 Write and evaluate numerical expressions with whole-number exponents.
• M.6.13 Write, read and evaluate expressions in which letters stand for numbers.
  • a. Write expressions that record operations with numbers and letters from verbal descriptions.
  • b. Name parts of an expression (sum, term, product, factor, quotient, coefficient) and treat a part as a single quantity.
  • c. Evaluate expressions, including formulas, for given values using the order of operations.
• M.6.14 Apply properties of operations to generate equivalent expressions.
• M.6.15 Identify two expressions as equivalent when they name the same number for any value substituted.

Expressions and Equations – One-variable equations and inequalities

• M.6.16 Understand solving as finding which values in a set make an equation or inequality true; test by substitution.
• M.6.17 Use variables for an unknown number or for any number in a set when solving problems.
• M.6.18 Solve real-world problems by writing and solving equations and inequalities with nonnegative rational numbers.
  • a. Solve equations of the forms x + p = q and px = q.
  • b. Solve inequalities of the forms x + p > q, x + p < q, px > q and px < q.
• M.6.19 Write inequalities such as x > c or x < c for constraints and show their solutions on a number line.

Expressions and Equations – Dependent and independent variables

• M.6.20 Write an equation giving a dependent quantity in terms of an independent one and analyze it with graphs and tables.

Geometry – Area, surface area and volume

• M.6.21 Find the area of triangles, quadrilaterals and other polygons by composing or decomposing them.
• M.6.22 Find the volume of right rectangular prisms with fractional edges using unit cubes and V = lwh and V = Bh.
• M.6.23 Draw polygons on the coordinate plane from given vertices and find side lengths that share a coordinate.
• M.6.24 Use nets made of rectangles and triangles to find the surface area of solid figures.

Statistics and Probability – Statistical variability

• M.6.25 Recognize a statistical question as one that expects variability in the answers.
• M.6.26 Understand that a data set has a distribution described by its center, spread and overall shape.
• M.6.27 Understand that a measure of center sums up a whole numerical data set with one number.

Statistics and Probability – Summarize and describe distributions

• M.6.28 Show numerical data on a number line with dot plots, histograms and box plots.
• M.6.29 Summarize numerical data sets in relation to their context.
  • a. Report the number of observations.
  • b. Describe the attribute studied, how it was measured and its units.
  • c. Give the median and/or mean and describe the overall pattern and any striking deviations.
  • d. Relate the choice of measure of center to the shape of the data and the context.