Standards - Mathematics

Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

Use unit rates to represent and describe ratio relationships.

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Interpret and compute quotients of fractions using visual models and equations to represent problems.

Use quotients of fractions to analyze and solve problems.

Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.

Add, subtract, multiply, and divide decimals using a standard algorithm.

Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

Use factors and multiples to determine prime factorization.

Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.

Locate integers and other rational numbers on a horizontal or vertical line diagram.

Define opposites as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

Find the position of pairs of integers and other rational numbers on the coordinate plane.

Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

Identify (a,b) and (a,-b) as reflections across the x-axis.

Identify (a,b) and (-a,b) as reflections across the y-axis.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts.

Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.

Write, evaluate, and compare expressions involving whole number exponents.

Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

Interpret a variable as an unknown value for any number in a specified set, depending on the context.

Write expressions to represent verbal statements and real-world scenarios.

Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.

Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.

Determine whether two expressions are equivalent and justify the reasoning.

Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.

Write and solve an equation in the form of x+p=q or px=q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematical problems.

Interpret the solution of an equation in the context of the problem.

Write and solve inequalities in the form of $x > c$, $x < c$, $x ge c$, or $x le c$ to represent a constraint or condition in a real-world or mathematical problem.

Interpret the solution of an inequality in the context of a problem.

Represent the solutions of inequalities on a number line and explain that the solution set may contain infinitely many solutions.