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Variables and Expressions
Students identify variables, constants, coefficients, factors, and terms; translate words into algebraic expressions; and interpret what expressions mean.
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Beginner
15–20 minutes
Algebraic Expressions
Algebraic Expressions
Page 2 of 5
Inside Cover
Variables and Expressions
At a Glance
Binder SectionAlgebraic Expressions
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How can an algebraic expression represent a quantity that can change?
Build Understanding
A variable is a letter or symbol that represents a number. A constant is a number without a variable. A coefficient is the numerical factor multiplying a variable. In 5x + 12, x is the variable, 5 is the coefficient, and 12 is the constant.
Terms are separated by addition or subtraction signs. The expression 4x² − 3x + 8 has three terms: 4x², −3x, and 8. A factor is a quantity being multiplied. In 6ab, the factors are 6, a, and b.
Translate words carefully. “Seven more than n” is n + 7. “Seven less than n” is n − 7. “Seven less than three times n” is 3n − 7. The phrase “the quotient of x and 4” is x/4.
Worked example: Write an expression for a $12 entrance fee plus $5 per game. Let g represent the number of games. The total cost is 5g + 12. The variable can change, but the entrance fee is constant.
An expression names a value and has no equals sign. An equation states that two expressions are equal and includes an equals sign. A common error is treating an expression like an equation. You simplify or evaluate an expression; you solve an equation.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- A variable represents a number that can change or may be unknown.
- A coefficient multiplies a variable.
- A constant has no variable.
- Terms are separated by addition or subtraction.
- An expression does not contain an equals sign.
- Translate phrases in their stated order, especially “less than.”
Click each word
Interactive Vocabulary
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Reveal one step at a time
Worked Examples
Example 1
Translate words
1
Five more than three times n.
2
Three times n is 3n; then add 5.
3
3n+5.
Example 2
Interpret
1
12+4m
2
12 is constant; 4 is coefficient; m is variable.
3
Two terms.
Ask and explain
Common Questions
Is a variable always x? No. Any letter or symbol may represent a number.
Is 1 a coefficient in x? Yes. x means 1x.
How many terms are in 3x + 2y − 7? Three.
What is the difference between an expression and an equation? An equation includes an equals sign; an expression does not.
Why does “5 less than n” become n − 5? “Less than” reverses the order from the way the words are spoken.
Notice and correct
Common Misconceptions
Reversing subtraction phrases
'Five less than n' means n−5.
Adding an equals sign
An expression names a quantity; an equation states equality.
Learn Through Video
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Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
Write an expression for 7 more than x.
2
We Do
Guided Practice
Identify the coefficient in 8m + 3. Answer: 8.
List the terms in 4x² − 2x + 9. Answer: 4x², −2x, and 9.
Write “six more than twice n.” Answer: 2n + 6.
Write “the quotient of p and 5.” Answer: p/5.
A taxi charges $4 plus $2 per mile. Write the cost for m miles. Answer: 2m + 4.
Is 3x + 7 = 19 an expression or equation? Answer: Equation.
3
You Do
Independent Practice
Write 12 less than 5m.
How many terms are in 4a+3b−8?
4
Stretch Your Thinking
Challenge & Real-World Practice
Create a real situation modeled by 15+3x. Define the variable, identify every term, and explain how the value changes when x increases by 1.
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Before you begin, I can…
- I can distinguish an expression from an equation.
- I can preserve the order of verbal subtraction.
- I can interpret every symbol and operation in context.
1
Question 1
Coefficient in 6x+4?
2
Question 2
Five less than n is?
3
Question 3
Which is an expression?
4
Question 4
Terms in 3a+2b−9?
5
Question 5
Twice p plus 1 is?
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