How might representation of a sequence provide insight into change?

Students relate terms to position within an arithmetic sequence.

A table of values representing an arithmetic sequence lists the position in the first column or row and the corresponding term in the second column or row.

Points representing an arithmetic sequence on a coordinate grid fit on a straight line.

An algebraic expression can describe the relationship between the positions and terms of an arithmetic sequence.

Each term of an arithmetic sequence corresponds to a natural number indicating position in the sequence.

How can expressions enhance communication of number?

Students interpret numerical and algebraic expressions.

Numerical expressions with multiple operations may include parentheses to group numbers and operations.

The conventional order of operations includes performing operations in parentheses before other operations.

Expressions that include variables are called algebraic expressions.

A variable can be interpreted as a specific unknown value and is represented symbolically with a letter.

Products with variables are expressed without the multiplication sign.

Quotients with variables are expressed using fraction notation.

An algebraic term is the product of a number, called a coefficient, and a variable.

A constant term is a number.

A variable can be replaced by a given number in order to evaluate an expression.

The process of applying inverse operations can be used to solve an equation.

The value of the variable obtained by solving an equation is the solution.

Numerical expressions represent a quantity of known value.

Parentheses change the order of operations in a numerical expression.

Algebraic expressions use variables to represent quantities of unknown value.

Algebraic expressions may be composed of one algebraic term or the sum of algebraic and constant terms.

Equality is preserved by applying inverse operations to algebraic expressions on each side of an equation.

The expressions on each side of an equation will be equal when evaluated using the correct solution.