Ratios and Proportional Relationships

• Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
• Understand the concept of a unit rate a/b associated with a ratio a:b with b is not equal to 0, and use rate language in the context of a ratio relationship.
• Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

The Number System

• Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
• Fluently divide multi-digit numbers using the standard algorithm.
• Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
• Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
• Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
• Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
• Understand ordering and absolute value of rational numbers.
• Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Expressions and Equations

• Write and evaluate numerical expressions involving whole-number exponents.
• Write, read, and evaluate expressions in which letters stand for numbers.
• Apply the properties of operations to generate equivalent expressions.
• Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
• Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
• Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Statistics and Probability

• Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
• Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
• Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
• Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
• Summarize numerical data sets in relation to their context.