Expression Blueprint

Mastering Algebraic Expressions

Phase: Study Guide

Sheet: 01 / 03

Student Name: ____________________________

Date: __________

The Foundation: Vocabulary

Before we build, we need to know our materials. Every algebraic expression is made of specific parts.

Variable

A letter (like \(x\), \(y\), or \(n\)) that represents an unknown number. Its value can change.

Constant

A number that stands alone. It does not have a variable attached. Its value never changes.

Coefficient

The number being multiplied by a variable. It is "attached" to the front of the letter.

Term

Parts of an expression separated by plus (+) or minus (-) signs.

\(5x + 3y - 12\)

Term 1

5 = Coefficient
x = Variable

Term 2

3 = Coefficient
y = Variable

Term 3

-12 = Constant

Drafting: Translating Phrases

Operation	Key Words	Example Expression
Addition (+)	sum, plus, increased by, more than	\(x + 5\)
Subtraction (-)	difference, minus, decreased by, less than*	\(x - 5\)
Multiplication (·)	product, times, twice, of	\(5x\)
Division (÷)	quotient, divided by, split into	\(\frac{x}{5}\)

*WATCH OUT! "Less than" and "Subtracted from" are switch words.
"5 less than \(x\)" is written as \(x - 5\), NOT \(5 - x\).

Expression Blueprint

Evaluating and Substituting

Phase: Study Guide

Sheet: 02 / 03

The Assembly: Evaluating Expressions

1

Substitute

Replace the variable with the given number. Use parentheses to keep things clean, especially for multiplication!

2

Simplify (GEMDAS)

Follow the order of operations to solve the numerical expression.

G (Groups)

E (Exponents)

MD (Mult/Div)

AS (Add/Sub)

Construction Example

Evaluate \(3x^2 + 4\) when \(x = 2\)

Step 1: \(3(2)^2 + 4\)

Step 2: \(3(4) + 4\)

Step 3: \(12 + 4\)

Solution: 16

Field Work: Try It!

1. Evaluate \(8n - 3\) if \(n = 5\)

2. Evaluate \(\frac{24}{y} + 2\) if \(y = 4\)

3. Evaluate \(w^2 + 10\) if \(w = 3\)

Expression Blueprint

Equivalent Expressions

Phase: Study Guide

Sheet: 03 / 03

Expansion: The Distributive Property

Multiply the number on the outside by each term on the inside of the parentheses.

\(a(b + c) = ab + ac\)

\(3(x + 4) = 3x + 12\)

Think of the 3 "visiting" both the x and the 4!

Renovation: Combining Like Terms

You can only add or subtract terms that are "like" (they must have the exact same variable and exponent).

Like Terms

\(4x\) and \(7x\)

Both have "x"

NOT Like Terms

\(4x\) and \(4y\)

Variables don't match

Example: Simplify \(5x + 3 - 2x + 7\)

1. Group the \(x\) terms: \(5x - 2x = 3x\)

2. Group the constants: \(3 + 7 = 10\)

Result: \(3x + 10\)

Project Review Checklist

I can identify constants, coefficients, and variables.

I know my "switch words" for subtraction.

I can evaluate by following GEMDAS.

I can simplify expressions using the Distributive Property.

Ready for inspection? Flip this over and try a practice set!

Expression Blueprint

Expression Blueprint Study Guide

Expression Blueprint Quiz

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