6th Grade Math (Utah Core Standards)

Ratios and Proportional Relationships (6.RP)

• 6.RP.1 Understand ratios and use ratio language to describe how two quantities relate.
• 6.RP.2 Understand a unit rate a/b for a ratio a:b (b ≠ 0) and use rate language.
• 6.RP.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. Find percents as rates per 100 and find a whole from a part and its percent.
  • d. Use ratio reasoning to convert measurement units.

The Number System (6.NS)

• 6.NS.1 Interpret and calculate fraction ÷ fraction and solve related word problems.
  • a. Compute quotients of fractions using visual models and equations.
  • b. Solve real-world problems that divide fractions by fractions (e.g. sharing chocolate).
  • c. Explain fraction quotients with story contexts and visual models.
• 6.NS.2 Divide multi-digit numbers fluently with the standard algorithm.
  • a. Divide decimals where the dividend or divisor is a whole number.
  • b. Divide one decimal by another using models and place value.
• 6.NS.3 Use standard algorithms fluently for all four operations with multi-digit decimals.
• 6.NS.4 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.
• 6.NS.5 Use positive and negative numbers for opposite quantities (temperature, elevation, credit/debit) and explain what 0 means.
• 6.NS.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.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.8 Graph points in all four quadrants to solve problems, using coordinates and absolute value for horizontal and vertical distances.

Expressions and Equations (6.EE)

• 6.EE.1 Write and evaluate numerical expressions with whole-number exponents.
• 6.EE.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.3 Use properties of operations to write equivalent expressions (e.g. 3(2 + x) = 6 + 3x).
• 6.EE.4 Recognize when two expressions are equivalent for every value of the variable.
• 6.EE.5 See solving an equation or inequality as finding which values make it true; use substitution to check.
• 6.EE.6 Use variables for numbers in problems, as an unknown or as any number in a set.
• 6.EE.7 Write and solve equations of the forms x + a = b and ax = b with nonnegative rational numbers.
• 6.EE.8 Write inequalities x > c or x < c for real conditions, know they have infinitely many solutions and graph them on a number line.
• 6.EE.9 Use variables for two related quantities, write an equation linking dependent and independent variables, and connect it to tables and graphs.

Geometry (6.G)

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

Statistics and Probability (6.SP)

• 6.SP.1 Recognize a statistical question as one that expects variation in the data.
• 6.SP.2 Know a data set has a distribution described by its center, spread and shape.
• 6.SP.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.4 Show numerical data in dot plots, histograms and box plots, choosing the most suitable display for the data.
• 6.SP.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.