Making Meaning of the Code-Packet Process Mastery

A. Thinking about Definitions

B. Packet Process Part Two: Order of Operations:

The Order of operations is an established rule for evaluating an expression involving more
than one operation:
Step 1: Evaluate expressions inside grouping symbols.
Step 2: Evaluate powers.
Step 3: Multiply and divide from left to right.
Step 4: Add and subtract from left to right.

C. Expressions, Equations, and Inequalities

A variable is a letter used to represent one or more numbers. An algebraic expression
is made from numbers, variables, and algebraic operations.

The following examples describe how expressions can be evaluated, combined, written, and used to write algebraic equations and inequalities.

1. Evaluating Expressions (Part 3 of your review)
Evaluate an expression involves the following process:

Step 1: Substitute a number for the variable,
Step 2: Perform the operation(s), and
Step 3: Simplify the result if necessary.

D. Solving Problems with Variables on 1 Side:
A. Solving Equations in one Variable:
To solve an equation in one variable, isolate the variable on one side of the equation.

The following examples illustrate different ways to isolate the variable.
1. Solve an Equation Using Addition or Subtraction
Inverse operations Two operations that undo each other, such as addition and
subtraction or multiplication and division.
Equivalent equations: Equations that have the same solution(s).
Use addition or subtraction to solve the equation.
a. x + 9 = 3 b. x - 5 = 2 c. x + 4.1 = 6
Solution:
a. x + 9 = 3 S1: Write original equation.
x + 9 - 9 = 3 - 9 S2: Use subtraction property of equality. Subtract 9
from each side.
x=-6 S3: Simplify.
The solution is 26.

b. x - 5 = 2 S1: Write original equation.
x - 5 + 5 = 2 + 5 S2: Use addition property of equality. Add 5 to each side.
x = 7 S3: Simplify.
The solution is 7.

c. x + 4.1 = 6 S1: Write original equation.
x + 4.1 - 4.1 = 6 - 4.1 S2: Subtract 4.1 from each side.
x = 1.9 S3: Simplify.
The solution is 1.9.

Use addition or subtraction to solve the equation.
1. x + 5 = 4 2. c - 3 = 8 3. t + 6 = 10

2. Solving an Equation Using Multiplication or Division

Use multiplication or division to solve the equation.
a. x/6 = 3 b. -7x = -49 c. - 3/8x = 5

Solution:
a. x/6 = 3
Step 1: Write original equation.
Step 2: Multiply each side by 6.
Step 3: Simplify.
The solution is 18.


II. More Packet Process for You (Download a Copy of a Notetaking Guide for Algebra 1)

The Notetaking Guide models important steps to perform. Go the given sections (use the Table of Contents) and see how these steps are done. Fill in the blanks with any info relevant to your given problem.