6th Grade Math (Arizona Mathematics Standards)

Ratios and Proportional Relationships (RP)

• 6.RP.A.1 Understand ratios and use ratio language to describe how two quantities relate.
• 6.RP.A.2 Understand a unit rate a/b for a ratio a:b (b ≠ 0) and use rate language.
• 6.RP.A.3 Solve ratio and rate problems using tables, tape diagrams, double number lines or equations.
  • a. Make tables of equivalent ratios, fill in missing values, plot the pairs and compare ratios.
  • b. Solve unit rate problems, including unit price and constant speed.
  • c. Treat a percent as a rate per 100 and solve percent problems whichever value is unknown.
  • d. Use ratio reasoning to convert measurement units.

The Number System (NS)

• 6.NS.A.1 Interpret and calculate fraction ÷ fraction and solve related word problems.
• 6.NS.B.2 Divide multi-digit numbers fluently with the standard algorithm.
• 6.NS.B.3 Use standard algorithms fluently for all four operations with multi-digit decimals.
• 6.NS.B.4 Use factors and multiples to find greatest common factors and least common multiples and apply the distributive property.
  • a. Find the GCF of two whole numbers no greater than 100.
  • b. Find the LCM of two whole numbers no greater than 12.
  • c. Use the distributive property to factor a common factor out of a sum of two numbers from 1 to 100.
• 6.NS.C.5 Use positive and negative numbers for opposite quantities (temperature, elevation, credit/debit) and explain what 0 means.
• 6.NS.C.6 See rational numbers as points on the number line and extend number lines and axes to negative numbers.
  • a. Know opposite signs mean opposite sides of 0 and that the opposite of the opposite is the number itself.
  • b. Use signs in ordered pairs to tell the quadrant and see that sign changes give reflections across the axes.
  • c. Locate integers and other rationals on number lines and pairs of them on the coordinate plane.
• 6.NS.C.7 Understand order and absolute value of rational numbers.
  • a. Read inequalities as positions on a number line (e.g. −3 > −7 means −3 is to the right).
  • b. Write and explain order statements for rational numbers in real contexts.
  • c. Understand absolute value as distance from 0 and as size of a quantity in context.
  • d. Tell comparisons of absolute value apart from statements of order (e.g. debt sizes).
• 6.NS.C.8 Graph points in all four quadrants to solve problems, using coordinates and absolute value for horizontal and vertical distances.

Expressions and Equations (EE)

• 6.EE.A.1 Write and evaluate numerical expressions with whole-number exponents.
• 6.EE.A.2 Write, read and evaluate expressions with letters standing for numbers.
  • a. Write expressions for operations with numbers and variables (e.g. 5 − y).
  • b. Name parts of an expression (sum, term, product, factor, quotient, coefficient) and treat a part as one quantity.
  • c. Evaluate expressions, including formulas, for given values, following the order of operations.
• 6.EE.A.3 Use properties of operations to write equivalent expressions (e.g. 3(2 + x) = 6 + 3x).
• 6.EE.A.4 Recognize when two expressions are equivalent for every value of the variable.
• 6.EE.B.5 See solving an equation or inequality as finding which values make it true; use substitution to check.
• 6.EE.B.6 Use variables for numbers in problems, as an unknown or as any number in a set.
• 6.EE.B.7 Write and solve equations of the forms x + p = q, x − p = q, px = q and x/p = q with nonnegative rational numbers.
• 6.EE.B.8 Write inequalities x > c, x < c, x ≥ c or x ≤ c for real conditions and graph their solutions on a number line.
• 6.EE.C.9 Use variables for two related quantities, write an equation linking dependent and independent variables, and connect it to tables and graphs.

Geometry (G)

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

Statistics and Probability (SP)

• 6.SP.A.1 Recognize a statistical question as one that expects variation in the data.
• 6.SP.A.2 Know a data set has a distribution described by its center, spread and shape.
• 6.SP.A.3 Know a measure of center sums up the data in one number while a measure of variation describes spread in one number.
• 6.SP.B.4 Show numerical data in dot plots, histograms and box plots.
• 6.SP.B.5 Summarize numerical data sets in context.
  • a. State the number of observations.
  • b. Describe the attribute studied, how it was measured and its units.
  • c. Give median or mean and IQR or mean absolute deviation, and describe overall patterns and striking outliers.
  • d. Link the choice of center and spread measures to the data's shape and context.