Write, Read, and Evaluate Expressions

Lesson 1 of 1: Variables and Algebraic Expressions

In this lesson:

• Translate between words and algebraic expressions
• Name the parts of an expression with precise vocabulary
• Evaluate expressions by substituting values

Learning Objectives for This Lesson

By the end of this lesson, you will:

1. Translate verbal phrases into algebraic expressions and vice versa
2. Identify parts of an expression: sum, term, product, factor, quotient, coefficient
3. View a sub-expression as a single entity and as a sum of parts
4. Evaluate expressions by substituting values and applying order of operations
5. Apply formulas like and with fractional values

From Boxes to Variables — Making the Connection

Same question — same idea. The letter works just like the box.

Variables: Letters That Stand for Numbers

• A variable is a letter standing in for a number
• , , all mean the same thing
• means "some number plus 4" — can be any value
• Variables represent unknowns, changing quantities, or formula inputs

Translating Verbal Phrases into Algebraic Expressions

Watch Out: Subtraction Order Matters

• "Subtract from 5" → ✓ (start at 5, remove )
• "Subtract from 5" → ✗ (starts at the wrong value)
• "8 less than " → , not

From Expressions Back to Words

The expression can be described in multiple ways:

• "One less than twice a number"
• "Two times a number, minus one"
• "The difference of and 1"

Try it: How would you say in words?

Check-In: Write Expressions from Verbal Phrases

Write an algebraic expression for each phrase:

1. A number divided by 4
2. 8 less than a number
3. The product of 6 and a number
4. Subtract from 12

Answers: — — —

The Language of Expressions: Key Vocabulary

Coefficient: the number multiplying a variable — in , coefficient = 3

Anatomy of an Expression: 2(8 + 7)

Zoom out: a product of two factors. Zoom in: a sum of two terms.

Worked Example: Naming Parts of 3x + 5

The expression is a sum of two terms:

• First term: — itself a product; coefficient is 3, variable is
• Second term: — a constant (no variable)

Coefficient: 3 (the number multiplied by the variable)

Guided Practice: Label These Expressions

1. — product of two factors; is a sum
2. — sum of two terms; is a quotient
3. — sum of two terms; coefficient of is 4

Check-In: Name the Parts of an Expression

For the expression :

1. How many terms?
2. What is the coefficient of ?
3. Sum or product?

Answers: 3 terms — coefficient of is 5 — it is a sum

A sub-expression is one thing from outside, many things inside.

Evaluating Expressions: The Three-Step Method

Step 1: Write the expression
Step 2: Replace each variable with its value in parentheses
Step 3: Compute — apply order of operations

Parentheses prevent the 25-vs-10 error.

Worked Example: Two Variables and Exponents

Evaluate when and .

Step 1: Write the expression:

Step 2: Replace with and with :

Step 3: Compute — exponents first, then multiply, then subtract:

Watch Out: Order of Operations with Exponents

Evaluate when .

Correct:

Common error:

The exponent applies only to , not to the whole expression. Substitute first, then follow PEMDAS.

Guided Practice: Evaluate with Parentheses

when :

Your turn: when .

Answer:

Check-In: Evaluation and Error Alert

Evaluate when .

A student wrote: . What went wrong?

Correct:

In algebra, means . Use parentheses: , not .

Formulas as Expressions: The Cube Model

• : all three side lengths equal , so volume =
• : six faces, each with area

Worked Example: Cube Formulas at s = 3

When :

Volume:

Surface Area:

Worked Example: Cube Formulas at s = ½

— exponents first, then multiply:

Worked Example: Rectangle Perimeter Formula

when , :

Substitute:

Multiply:

Add: units

Check-In: Apply the Triangle Area Formula

Use to find the area when and .

Try first, then check. Formulas are expressions — substitution makes them powerful.

Summary: Key Takeaways from This Lesson

✓ A variable is a letter that stands for a number — the flexible version of a box placeholder

✓ "From 5" means 5 is written first: "subtract from 5" =

✓ Vocabulary: sum (+ terms), product (× factors), quotient (÷), coefficient (number × variable)

✓ To evaluate: substitute in parentheses, then apply order of operations

✓ Formulas are expressions — substitution makes them give real answers

Watch out: "Subtract from 5" = , not

Watch out: means ; writing with → , not

Watch out: Exponents first — at is , not

Watch out: Role depends on context — 3 is a coefficient in , a term in

What's Coming Next: Equivalent Expressions

Next lesson — 6.EE.A.3: Generating equivalent expressions

• Distributive property:
• Combining like terms:
• Recognizing equivalent expressions for all values of the variable

Today's vocabulary — terms, factors, coefficients — is exactly the foundation you need.