6th Grade Math (Colorado Academic Standards)

Standard 1: Number and Quantity

• MA.6.RP.A Understand ratios and use ratio reasoning to solve problems.
  • 1. Understand ratios and use ratio language to describe how two quantities relate.
  • 2. Understand a unit rate a/b for a ratio a:b (b ≠ 0) and use rate language.
  • 3. Solve ratio and rate problems using tables, tape diagrams, double number lines or equations.
  • 3.a. Make tables of equivalent ratios, fill in missing values, plot the pairs and compare ratios.
  • 3.b. Solve unit rate problems, including unit price and constant speed.
  • 3.c. Find percents as rates per 100 and find a whole from a part and its percent.
  • 3.d. Use ratio reasoning to convert measurement units.
• MA.6.NS.A Extend multiplication and division to dividing fractions by fractions.
  • 1. Interpret and calculate fraction ÷ fraction and solve related word problems.
• MA.6.NS.B Compute fluently with multi-digit numbers and find common factors and multiples.
  • 1. Divide multi-digit numbers fluently with the standard algorithm.
  • 2. Use standard algorithms fluently for all four operations with multi-digit decimals.
  • 3. Find the GCF of two numbers up to 100 and the LCM of two numbers up to 12; use the distributive property to factor out a common factor.
• MA.6.NS.C Extend number understanding to the rational numbers.
  • 1. Use positive and negative numbers for opposite quantities (temperature, elevation, credit/debit) and explain what 0 means.
  • 2. See rational numbers as points on the number line and extend number lines and axes to negative numbers.
  • 2.a. Know opposite signs mean opposite sides of 0 and that the opposite of the opposite is the number itself.
  • 2.b. Use signs in ordered pairs to tell the quadrant and see that sign changes give reflections across the axes.
  • 2.c. Locate integers and other rationals on number lines and pairs of them on the coordinate plane.
  • 3. Understand order and absolute value of rational numbers.
  • 3.a. Read inequalities as positions on a number line (e.g. −3 > −7 means −3 is to the right).
  • 3.b. Write and explain order statements for rational numbers in real contexts.
  • 3.c. Understand absolute value as distance from 0 and as size of a quantity in context.
  • 3.d. Tell comparisons of absolute value apart from statements of order (e.g. debt sizes).
  • 4. Graph points in all four quadrants to solve problems, using coordinates and absolute value for horizontal and vertical distances.

Standard 2: Algebra and Functions

• MA.6.EE.A Extend arithmetic to algebraic expressions.
  • 1. Write and evaluate numerical expressions with whole-number exponents.
  • 2. Write, read and evaluate expressions with letters standing for numbers.
  • 2.a. Write expressions for operations with numbers and variables (e.g. 5 − y).
  • 2.b. Name parts of an expression (sum, term, product, factor, quotient, coefficient) and treat a part as one quantity.
  • 2.c. Evaluate expressions, including formulas, for given values, following the order of operations.
  • 3. Use properties of operations to write equivalent expressions (e.g. 3(2 + x) = 6 + 3x).
  • 4. Recognize when two expressions are equivalent for every value of the variable.
• MA.6.EE.B Reason about and solve one-variable equations and inequalities.
  • 1. See solving an equation or inequality as finding which values make it true; use substitution to check.
  • 2. Use variables for numbers in problems, as an unknown or as any number in a set.
  • 3. Write and solve equations x + p = q and px = q with nonnegative rational numbers in problems.
  • 4. Write inequalities x > c or x < c for real conditions, know they have infinitely many solutions and graph them on a number line.
• MA.6.EE.C Show and analyze relationships between dependent and independent variables.
  • 1. Use variables for two related quantities, write an equation linking dependent and independent variables, and connect it to tables and graphs.

Standard 3: Data, Statistics, and Probability

• MA.6.SP.A Understand statistical variability.
  • 1. Recognize a statistical question as one that expects variation in the data.
  • 2. Know a data set has a distribution described by its center, spread and shape.
  • 3. Know a measure of center sums up the data in one number while a measure of variation describes spread in one number.
• MA.6.SP.B Summarize and describe distributions.
  • 1. Show numerical data in dot plots, histograms and box plots.
  • 2. Summarize numerical data sets in context.
  • 2.a. State the number of observations.
  • 2.b. Describe the attribute studied, how it was measured and its units.
  • 2.c. Give median or mean and IQR or mean absolute deviation, and describe overall patterns and striking outliers.
  • 2.d. Link the choice of center and spread measures to the data's shape and context.

Standard 4: Geometry

• MA.6.G.A Solve problems with area, surface area and volume.
  • 1. Find areas of triangles, special quadrilaterals and polygons by composing rectangles or decomposing into triangles; solve problems.
  • 2. Find volumes of rectangular prisms with fraction edge lengths by packing small cubes and by using the volume formulas.
  • 3. Draw polygons on the coordinate plane from vertex coordinates and find side lengths with shared coordinates.
  • 4. Use nets of rectangles and triangles to show 3-D shapes and find surface area.