Grade 6 Math (New York Next Generation)

Ratio and Proportional Reasoning

• Understand ratio concepts and use ratio reasoning to solve problems
• NY-6.RP.1 Understand ratios and use ratio language to describe a relationship between two quantities.
• NY-6.RP.2 Understand unit rates associated with ratios and use rate language.
• NY-6.RP.3 Use ratio and rate reasoning (tables, tape diagrams, number lines, equations) to solve problems.
• NY-6.RP.3a Make tables of equivalent ratios, find missing values, plot pairs on the coordinate plane and compare ratios.
• NY-6.RP.3b Solve unit rate problems, including unit pricing and constant speed.
• NY-6.RP.3c Find a percent of a quantity as a rate per 100, and find the whole from a part and the percent.
• NY-6.RP.3d Use ratio reasoning to convert measurement units and handle units when multiplying or dividing.

The Number System

• Apply and extend previous understandings of multiplication and division to divide fractions by fractions
• NY-6.NS.1 Compute quotients of fractions and solve word problems with visual models, algorithms and equations.
• Compute fluently with multi-digit numbers and find common factors and multiples
• NY-6.NS.2 Fluently divide multi-digit whole numbers using a standard algorithm.
• NY-6.NS.3 Fluently add, subtract, multiply and divide multi-digit decimals using a standard algorithm.
• NY-6.NS.4 Find greatest common factors and least common multiples and use the distributive property to rewrite sums.
• Apply and extend previous understandings of numbers to the system of rational numbers
• NY-6.NS.5 Use positive and negative numbers for opposite quantities in real contexts and explain the meaning of zero.
• NY-6.NS.6 Understand rational numbers as points on the number line and on coordinate axes.
• NY-6.NS.6a Understand opposite signs as opposite sides of 0, and that the opposite of the opposite is the number itself.
• NY-6.NS.6b Use signs in ordered pairs to identify quadrants; points differing only in sign are reflections across axes.
• NY-6.NS.6c Find and position integers and other rational numbers on number lines and the coordinate plane.
• NY-6.NS.7 Understand ordering and absolute value of rational numbers.
• NY-6.NS.7a Interpret inequality statements as the relative positions of two numbers on a number line.
• NY-6.NS.7b Write, interpret and explain order statements for rational numbers in real-world contexts.
• NY-6.NS.7c Understand absolute value as distance from 0 and as the size of a positive or negative quantity.
• NY-6.NS.7d Distinguish comparisons of absolute value from statements about order (e.g. debts).
• NY-6.NS.8 Graph points in all four quadrants to solve problems, using coordinates and absolute value for distances.

Expressions and Equations (Inequalities)

• Apply and extend previous understandings of arithmetic to algebraic expressions
• NY-6.EE.1 Write and evaluate numerical expressions with whole-number exponents.
• NY-6.EE.2 Write, read and evaluate expressions in which letters stand for numbers.
• NY-6.EE.2a Write expressions recording operations with numbers and letters standing for numbers.
• NY-6.EE.2b Identify parts of an expression (sum, term, product, factor, quotient, coefficient) and view parts as single entities.
• NY-6.EE.2c Evaluate expressions, including formulas, for given values using the order of operations.
• NY-6.EE.3 Apply properties of operations to generate equivalent expressions.
• NY-6.EE.4 Identify when two expressions are equivalent for any value substituted.
• Reason about and solve one-variable equations and inequalities
• NY-6.EE.5 Understand solving an equation or inequality as finding which values from a set make it true.
• NY-6.EE.6 Use variables to represent an unknown number or any number in a set when writing expressions.
• NY-6.EE.7 Solve problems by writing and solving one-step equations of the forms x + p = q, x - p = q, px = q, x/p = q.
• NY-6.EE.8 Write inequalities of the form x > c, x >= c, x < c or x <= c for constraints and graph solutions on number lines.
• Represent and analyze quantitative relationships between dependent and independent variables
• NY-6.EE.9 Use variables for two changing quantities, identify dependent and independent variables, and analyze graphs and tables.

Geometry

• Solve real-world and mathematical problems involving area, surface area, and volume
• NY-6.G.1 Find areas of triangles, trapezoids and other polygons by composing or decomposing into simpler shapes.
• NY-6.G.2 Find volumes of right rectangular prisms with fractional edge lengths.
• NY-6.G.3 Draw polygons from vertex coordinates and find side lengths that share a coordinate.
• NY-6.G.4 Represent 3-D figures with nets of rectangles and triangles and use them to find surface area.
• NY-6.G.5 Use area and volume models to explain perfect squares and perfect cubes.

Statistics and Probability

• Develop understanding of statistical variability
• NY-6.SP.1a Recognize a statistical question as one that expects variability in the data.
• NY-6.SP.1b Understand that samples can give information about a population when they are representative.
• NY-6.SP.1c Understand how sampling method and size affect samples, and generate several samples to see variation.
• NY-6.SP.2 Describe a data distribution by its center, spread and overall shape.
• NY-6.SP.3 Recognize that a measure of center summarizes data with one number and a measure of variation describes spread.
• Summarize and describe distributions
• NY-6.SP.4 Display numerical data in plots on a number line, including dot plots and histograms.
• NY-6.SP.5 Summarize numerical data sets in relation to their context.
• NY-6.SP.5a Report the number of observations.
• NY-6.SP.5b Describe the attribute investigated, how it was measured and its units.
• NY-6.SP.5c Give measures of center and variation and describe overall patterns and striking deviations.
• NY-6.SP.5d Relate the choice of measures of center and variation to the shape of the data and its context.
• Investigate chance processes and develop, use, and evaluate probability models
• NY-6.SP.6 Understand that a probability is a number from 0 to 1 that shows how likely an event is.
• NY-6.SP.7 Estimate probabilities from long-run relative frequencies and predict frequencies from probabilities.
• NY-6.SP.8 Develop probability models for simple events, compare with observed frequencies and explain differences.
• NY-6.SP.8a Develop a uniform probability model (equal probability for every outcome).
• NY-6.SP.8b Develop a probability model from observed frequencies of a chance process.