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When you ask a question like, "How much should I add to 5 to make a total of 8?" you are talking out loud using an algebraic equation. We use algebra all the time in everyday life. When you ask your parents for money for an ice cream at lunch and they say how much do you need? You are using algebra to figure out the amount of money needed to buy an ice cream based on how much money you already have in your lunch account. In this unit you will learn how to write and solve algebraic equations.

Essential Questions

How are exponents useful in solving mathematical and real world problems?

How are properties of numbers helpful in computation?

What strategies can I use to help me understand and represent real situations using algebraic expressions and equations?

What properties and conventions do I need to understand in order to simplify and evaluate algebraic expressions?

Module Minute

Exponents are useful in solving mathematical and real world problems because multiplying the same number over and over again can get tiresome. The properties of numbers are helpful in computation to rearrange to make sums more manageable. I can use grouping strategies to help me understand and represent real situations using algebraic expressions and equations. I need to understand the distributive, associative, and commutative properties in order to simplify and evaluate algebraic expressions.

Key Words

Algebraic Expression: An expression involving at least one variable and sometimes numbers and operation symbols.

Associative Property of Addition : The sum of a set of numbers is the same no matter how the numbers are grouped. a + (b + c) = (a + b) + c

Associative Property of Multiplication: The product of a set of numbers is the same no matter how the numbers are grouped. a(bc)=(ab)c

Coefficient: A number multiplied by a variable in an algebraic expression.

Commutative Property of Addition: The sum of a group of numbers is the same regardless of the order in which the numbers are arranged. a + b = b + a

Commutative Property of Multiplication: The product of a group of numbers is the same regardless of the order in which the numbers are arranged. ab = ba

Constant: A quantity that does not change its value.

Distributive Property: If you multiply a sum by a number, you will get the same result if you multiply each addend by that number and add the products. a(b+c)=ab+bc

Exponent: The number of times a number or expression (called base) is used as a factor of repeated multiplication. Also called the power.

Term: A number, a variable, or a product of numbers and variables.

Like Terms: Terms in an algebraic expression that have the same variable raised to the same power. Only the coefficients of like terms are different.

Order of Operations: The rules to be followed when simplifying expressions.

Variable: A letter or symbol used to represent a number or quantities that vary.

Solve the crossword puzzle. There are no spaces for 2 or more words. You can click re-start and get a new puzzle.

A handout of these key words and definitions is also available in the sidebar
What To Expect

Using Properties Discussion

Exponents and Properties Homework Quiz 1

Expressions Quiz 1

Writing and Evaluating Expressions and Equivalent Expressions Homework Quiz 2

Expressions Quiz 2

Expressions Task

Expressions Test

To view the standards from this unit, please download the handout from the sidebar.

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When you ask a question like, "How much should I add to 5 to make a total of 8?" you are talking out loud using an algebraic equation. We use algebra all the time in everyday life. When you ask your parents for money for an ice cream at lunch and they say how much do you need?

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Intro to order of operations (video) | Khan Academy

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This example shows the steps and clarifies the purpose of order of operations: to have ONE way to interpret a mathematical statement.

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How Do You Use the Order of Operations? | Virtual Nerd

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.

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What's the Order of Operations? | Virtual Nerd

# data[].attributes.attachment_link.description
Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.