6th Grade Math (Ohio's Learning 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 as an amount per one and use rate language with ratios.
• 6.RP.3 Solve ratio and rate problems with tables, tape diagrams, double number lines or equations.
  • a. Make equivalent-ratio tables, find missing values, graph pairs and compare ratios.
  • b. Solve unit rate problems such as unit price and constant speed.
  • c. Find a percent of a quantity as a rate per 100; find the whole from a part.
  • d. Use ratio reasoning to convert units, handling units correctly.

The Number System (6.NS)

• 6.NS.1 Divide fractions by fractions, interpret quotients and solve word problems with models.
• 6.NS.2 Divide multi-digit whole numbers fluently with the standard algorithm.
• 6.NS.3 Add, subtract, multiply and divide multi-digit decimals fluently with standard algorithms.
• 6.NS.4 Find greatest common factors and least common multiples and factor sums with the distributive property.
• 6.NS.5 Use positive and negative numbers for quantities in opposite directions and explain what zero means.
• 6.NS.6 Understand rational numbers as points on the number line and in all four quadrants.
  • a. Opposite signs lie on opposite sides of 0; −(−3) = 3.
  • b. Read quadrants from coordinate signs; sign changes reflect points across axes.
  • c. Place integers and rational numbers on number lines and the coordinate plane.
• 6.NS.7 Understand ordering and absolute value of rational numbers.
  • a. Read inequalities as relative positions on a number line.
  • b. Write and explain order of rational numbers in real contexts.
  • c. Understand absolute value as distance from 0 and as size.
  • d. Tell comparing absolute values apart from ordering, e.g. debts.
• 6.NS.8 Graph points in all four quadrants and find distances using coordinates and absolute value.

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 in which letters stand for numbers.
  • a. Write expressions from phrases such as "subtract y from 5".
  • b. Name parts of expressions (sum, term, product, factor, coefficient).
  • c. Evaluate expressions and formulas, following order of operations.
• 6.EE.3 Use properties of operations to write equivalent expressions, e.g. applying the distributive property.
• 6.EE.4 Identify when two expressions are equivalent for any value substituted.
• 6.EE.5 Use substitution to check which values make an equation or inequality true.
• 6.EE.6 Use variables to stand for unknowns or any number in a set when writing expressions for problems.
• 6.EE.7 Solve real problems with equations x + p = q and px = q for nonnegative rational numbers.
• 6.EE.8 Write x > c or x < c inequalities for constraints and graph their solutions on a number line.
• 6.EE.9 Write equations linking dependent and independent variables and connect them to graphs and tables.

Geometry (6.G)

• 6.G.1 Find areas of triangles, quadrilaterals and polygons by composing or decomposing into shapes.
• 6.G.2 Find volumes of prisms with fractional edges by packing unit cubes and using formulas.
• 6.G.3 Draw polygons on the coordinate plane from vertices and find side lengths from coordinates.
• 6.G.4 Use nets of rectangles and triangles to represent 3D figures and find surface area.

Statistics and Probability (6.SP)

• 6.SP.1 Develop statistical reasoning through the GAISE process: question, collect, analyze, interpret.
  • a. Form statistical questions that expect variability in the data.
  • b. Plan and collect data suited to the question.
  • c. Choose displays and statistics that show variability.
  • d. Draw conclusions from the data that answer the question.
• 6.SP.2 Understand that data have a distribution described by center, spread and overall shape.
• 6.SP.3 Understand that a measure of center sums up data with one number and variation shows spread.
• 6.SP.4 Display numerical data on number lines in dot plots, histograms and box plots.
• 6.SP.5 Summarize numerical data in context.
  • a. Report the number of observations.
  • b. Describe what was measured, how and in what units.
  • c. Give center and spread and describe shape, gaps and outliers.
  • d. Choose measures of center and spread that suit the data's shape.