8.14 Algebraic Expressions

SOL

A) The student will evaluate an algebraic expression for given replacement values of the variables.

B) The student will simplify algebraic expressions in one variable.

Essential Knowledge

Properties page (if needed)

• An expression is a representation of an amount with no equals or inequality sign (=, <, >). They can contain numbers, variables, and/or operation symbols (addition, subtraction, etc.).

• Numerical expressions only have numbers and operations.

• Algebraic expressions must have variables; numbers and operations are not required.

• Both numerical and algebraic expressions are "simplified" instead of "solved."

• If you are given a value to "plug in" for the variable, then algebraic expressions are "evaluated."

• Expressions are always simplified or evaluated using the order of operations.

• Terms: numbers, variables, or number-variable products in an expression or equation.

  • Examples: 14, x, 6y

• Like terms can be "combined" through addition or subtraction to simplify the expression. These are terms that are either [1] numbers, or [2] variables where the letter of the variable and the exponent match.

Target Skills

• Use order of operations and properties to evaluate algebraic expressions for numbers that are "substituted" ("plugged in") for the variables. There may be multiple variables to substitute for.

• Represent algebraic expressions using physical objects (manipulatives) or pictures.

• Simplify algebraic expressions with a variable using order of operations and properties.

Desmos Tips

• When evaluating an algebraic expression, type the value you're "plugging in" in the calculator, then hit [enter]:

  • x = 5

• Then type in the expression exactly as it appears in the problem.

  • 3x - 2

• Desmos will evaluate the expression for you (see below pic).

• This is very helpful if you have multiple variables or need to plug in multiple values for a variable.

IXL Topics

• 6.Y.1-7, 15-17

• 7.R.1-8, 14, 17-19

• 8.V.1-7, 9, 15-17

• A.B.3, 7

• A.I.1, 3-4

Websites (Videos)

• Art of Problem Solving:

  • Simplifying Linear Expressions

  • Expressions with Fractions

  • Algebraic Expressions Number Game

• Virtual Nerd:

  • What Are Numerical & Algebraic Expressions?

  • Translating:

    • How Do You Translate Phrases into Numerical Expressions?

    • How Do You Translate A Phrase With One Variable And Number Into A Mathematical Expression?

    • How Do You Turn a Longer Verbal Phrase into an Algebraic Expression?

    • How Do You Turn a Simple Expression into Words?

  • Simplifying:

    • How Do You Simplify an Expression?

    • Which Operations Do You Do First in an Expression?

    • How Do You Simplify an Expression Using Order of Operations?

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  • Evaluating:

    • How Do You Evaluate an Algebraic Expression?

    • How Do You Evaluate an Algebraic Expression by Plugging in Values?

    • How Do You Evaluate an Algebraic Expression with One Variable?

    • How Do You Evaluate an Algebraic Expression with Two Variables?

Websites (Practice)

Websites (Games)