Standards - Mathematics

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.

Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.

Use tables, graphs, and equations to represent the relationship between independent and dependent variables.

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Generate expressions in equivalent forms based on context and explain how the quantities are related.

Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

Solve word problems leading to equations of the form $px + q = r$ and $p(x + q) = r$, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Solve word problems leading to inequalities of the form $px + q > r$ or $px + q < r$, where $p$, $q$, and $r$ are specific rational numbers. Graph the solution set of the inequality, and interpret it in the context of the problem.

Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

Use square root and cube root symbols to represent solutions to equations.

Evaluate square roots of perfect squares (less than or equal to 225) and cube roots of perfect cubes (less than or equal to 1000).

Explain that the square root of a non-perfect square is irrational.

Estimate and compare very large or very small numbers in scientific notation.

Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

Interpret scientific notation that has been generated by technology.

Determine whether a relationship between two variables is proportional or non-proportional.

Graph proportional relationships.

Interpret the unit rate of a proportional relationship, describing the constant of proportionality as the slope of the graph which goes through the origin and has the equation y = mx where m is the slope.

Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.