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Evaluate Expressions

Students substitute values for variables and use the order of operations to find the value of numerical and algebraic expressions.

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Beginner 15–20 minutes Algebraic Expressions

Algebraic Expressions Page 4 of 5

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At a Glance

Evaluate Expressions

Binder SectionAlgebraic Expressions

DifficultyBeginner

Estimated Time15–20 minutes

PrerequisitesNone

Essential Question

How can substitution and structure help us find an expression’s value?

Build Understanding

To evaluate an expression, replace each variable with its given value and then simplify. Use parentheses around substituted negative numbers so their signs remain clear.

Follow the order of operations: grouping symbols; exponents; multiplication and division from left to right; addition and subtraction from left to right.

Worked example: Evaluate 3x² − 2y when x = −4 and y = 5. Substitute: 3(−4)² − 2(5). Exponent first: 3(16) − 10. Multiply: 48 − 10. Answer: 38.

For more than one variable, check every substitution before calculating. Evaluate 2a + 3b for a = 4 and b = −2: 2(4) + 3(−2) = 8 − 6 = 2.

Expressions can also represent formulas. If A = lw, then a rectangle with l = 8.5 and w = 3 has area A = 8.5(3) = 25.5 square units.

Common errors include ignoring exponents, performing addition before multiplication, losing a negative sign, or substituting a value for the wrong variable. A useful habit is to write the substituted expression on a separate line before simplifying.

Visual Model

4Thousands 3Hundreds 2Tens 7Ones

4,327 = 4,000 + 300 + 20 + 7

Goals

Learning Targets

Substitute each given value for its variable.
Place negative substitutions in parentheses.
Use the order of operations.
Multiplication and division share a level and proceed left to right.
Addition and subtraction share a level and proceed left to right.
Include units when evaluating a real-world formula.

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Interactive Vocabulary

Reveal one step at a time

Worked Examples

Example 1

Evaluate 3x+5 for x=4

Substitute 4.

Example 2

Evaluate 2a²−b for a=3,b=4

Exponent first.

Ask and explain

Common Questions

What does evaluate mean? Find the numerical value of an expression.

Why put parentheses around a negative value? They show that the negative sign belongs to the substituted number.

Do I multiply before exponents? No. Evaluate exponents first.

What if two variables have the same value? Substitute that value separately for each variable.

Can an expression have different values? Yes. Its value may change when the variables change.

Notice and correct

Common Misconceptions

Failing to use parentheses for negative substitutions

Replace x with (−3) so signs remain clear.

Multiplying before evaluating an exponent

Exponents are evaluated before multiplication.

Learn Through Video

Watch, pause, and explain

Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.

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Intro to Evaluating Algebraic Expressions

1 Intro to Evaluating Algebraic Expressions 2 Writing Algebraic Expressions 3 Algebraic Expressions Playlist

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Warm-Up Guided Independent Challenge

Quick Start

Warm-Up

Warm-up 1

Evaluate 2x+1 when x=5.

We Do

Guided Practice

Guided 1

Evaluate 5x + 2 when x = 6. Answer: 32.

Guided 2

Evaluate a² − 4 when a = −3. Answer: 5.

Guided 3

Evaluate 2m + 3n when m = 5 and n = −2. Answer: 4.

Guided 4

Evaluate 4(x − 3) when x = 10. Answer: 28.

Guided 5

Evaluate 18 ÷ (p + 1) when p = 2. Answer: 6.

Guided 6

Use C = 2πr to find the circumference when r = 4. Answer: 8π, about 25.13 units.

You Do

Independent Practice

Independent 1

Evaluate 5(a+2) for a=3.

Independent 2

Evaluate p/q+4 for p=18,q=3.

Stretch Your Thinking

Challenge & Real-World Practice

🧩 Challenge

Create an expression with two variables whose value is 24 when x=3 and y=2. Find a second pair that also produces 24 and verify both.

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Success Criteria

Before you begin, I can…

I can substitute every variable consistently.
I can preserve grouping around negative values.
I can show one order-of-operations step at a time.

Question 1

3x+5 when x=4 equals?

Question 2

2a² when a=3 equals?

Question 3

Why use parentheses around −3?

Question 4

5(m+2) when m=4 equals?

Question 5

If p=18,q=3, p/q+4 equals?