Teacher Guide: Expressions & Equations

@ Learning Objective 5-10 min lesson

Students will: Write and evaluate algebraic expressions using variables, and solve one-step equations using inverse operations in mathematical and real-world contexts.

Why this matters for FAST: Understanding variables and solving equations is the foundation of algebra. Students must translate between words and symbols, evaluate expressions by substitution, and apply inverse operations to solve equations.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Algebra tiles (optional)
Index cards
Balance scale visual
Calculator (for checking)

Key Vocabulary

Variable: A letter that represents an unknown number (like x, n, or y)
Expression: A mathematical phrase with numbers, variables, and operations (like 3x + 5)
Equation: A statement that two expressions are equal (like 2x + 3 = 11)
Evaluate: To find the value of an expression by substituting numbers for variables
Inverse Operations: Operations that undo each other (addition/subtraction, multiplication/division)

! Common Misconceptions to Address

Misconception #1: Thinking 3x Means 3 + x

Students see 3x and think it means "3 plus x" instead of "3 times x".

How to Address:

"When a number is right next to a variable with no sign between them, it means MULTIPLY! 3x = 3 times x. We just skip the multiplication sign to save space."

Misconception #2: Operating on Only One Side of an Equation

Students add 5 to one side of an equation but forget to add 5 to the other side.

How to Address:

"An equation is like a balance scale. Whatever you do to one side, you MUST do to the other side to keep it balanced! If you add 5 to the left, add 5 to the right too."

Misconception #3: Using the Wrong Inverse Operation

Students try to solve x + 5 = 12 by adding 5 instead of subtracting 5.

How to Address:

"Ask yourself: What operation is being done TO the variable? Then do the OPPOSITE to undo it! If 5 is being added to x, we subtract 5 to get x alone."

$ Lesson Steps

Activate Prior Knowledge (1 min)

Ask: "I'm thinking of a number. If I add 3, I get 10. What's my number?" (7) "How did you figure that out?" (Subtracted 3 from 10) "That's solving an equation!"

Introduce Variables (2 min)

SAY THIS:

"A variable is a letter that stands for an unknown number. Instead of saying 'a number plus 3 equals 10,' we write 'x + 3 = 10' where x is the mystery number we're trying to find!"

Writing Expressions (2 min)

Translate words to algebra:

"5 more than a number" = x + 5

"3 times a number" = 3x

"A number divided by 4" = x / 4 or x/4

"7 less than a number" = x - 7

Evaluating Expressions (1 min)

SAY THIS:

"To evaluate an expression, substitute the given value for the variable, then calculate. If x = 4, then 3x + 2 = 3(4) + 2 = 12 + 2 = 14."

Solving One-Step Equations (3 min)

Use inverse operations:

Addition equation: x + 5 = 12

Subtract 5 from both sides: x = 7

Multiplication equation: 3x = 15

Divide both sides by 3: x = 5

Always check: 3(5) = 15? Yes!

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"Solve: 4x = 20"

A) x = 80 B) x = 16 C) x = 5 D) x = 24

Correct answer: C) x = 5

Work: 4x = 20, divide both sides by 4, x = 5. Check: 4(5) = 20. Yes!

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Write variable expressions Evaluate expressions Solve one-step equations with addition Solve one-step equations with multiplication Write equations from word problems

^ Differentiation & Extension

For struggling students: Use algebra tiles or a balance scale model. Start with simple equations like x + 1 = 5 before moving to larger numbers.

For advanced students: Challenge with two-step equations or equations with fractions. Have them write their own word problems for classmates to solve.

For home: Send Parent Activity sheet. Families can play "mystery number" games that naturally use algebraic thinking.