Write and evaluate numerical expressions involving whole-number exponents.
Write, read, and evaluate expressions in which letters stand for numbers.
Write expressions that record operations with numbers and with letters standing for numbers.
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
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.
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Use variables to represent quantities in a real-world or mathematical problem and construct simple 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.
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
Solve linear equations in one variable.
Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
How much an object’s velocity changes over a certain time, or the rate at which an object increases its speed.
A mathematical phrase that contains ordinary numbers, variables (like x or y) and mathematical operations.
A mathematical sentence with an equal sign where the value of the variable cannot be changed
The peak altitude or highest point of a rocket’s flight.
A value or number that does not change.
How far something has gone.
How far something has gone from where it started (includes direction).
When terms have the same algebraic factors and are raised to the same power.
The amount of matter in an object.
The rate of change of position or how far something went in a certain amount of time.
A number, variable, or quotient of numbers and variables in an algebraic expression or equation.
The propulsive force that moves something forward.
When terms have different algebraic factors or are raised to different powers.
A placeholder for a quantity that may change in an algebraic expression or equation.
The speed and direction of an object.
