Algebra 1 · Unit 1 · Lesson 1 · A1-U1-WS1
Understanding Algebraic Expressions
Learn the language of algebra by identifying expressions, equations, variables, coefficients, constants, operations, and terms.
I canidentify the parts of an algebraic expression and explain what the expression means.
4x+7coefficient · variable · operation · constant
Why should I care?
Expressions Describe Real Situations
Algebraic expressions can describe a phone plan, hourly pay, a streaming subscription, a game score, or any situation where an amount can change.
1
First decision
Expression or Equation?
A mathematical phrase. It has numbers, variables, and operations, but no equal sign.
A mathematical statement saying that two expressions have the same value. It contains an equal sign.
How do you know? It is an ______ because it ______.
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1 of 6Expression or Equation?
3x + 7
2
Learn the language
Parts of an Expression
coefficient4
variablex
+constant7
Variable
A letter that represents a number that can vary, or change. That is why it is called a variable.
Coefficient
A number that multiplies a variable. It works together with the variable to tell how many groups there are.
Constant
A number without a variable. It is called a constant because its value stays constant—it does not change.
Operation
The mathematical action being performed, such as addition, subtraction, multiplication, or division.
CHECK YOUR UNDERSTANDING
1 of 6Label the Parts
What is the coefficient in 6x + 9?
3
Break it into pieces
Identify and Count the Terms
A term is one mathematical piece of an expression, equation, or formula.
Terms are separated by a + or − sign. When subtraction separates terms, the negative sign stays with the term that follows it.
5x²+−3x+8Term 1Term 2Term 3
A term may contain: a number, a variable, or numbers and variables being multiplied or divided. A term may also include an exponent.
Why terms matter: Terms are the building blocks of expressions, equations, and formulas. Identifying them helps you find like terms, understand what each part represents, and later simplify or solve.
Remember: Multiplication and division do not separate terms. For example, 6ab and x/2 are each one term. An expression inside parentheses can contain its own terms.
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1 of 6Identify and Count Terms
How many terms are in 4x + 7?
4
Move between two languages
Translate Words and Algebra
How to read 3x + 5
3xSay: “three times x” or “three times a number.”
You must name what is multiplied by 3.+5Say: “plus five.”
You must name what is multiplied by 3.+5Say: “plus five.”
Put the two pieces together: “Three times x, plus five.”
Three times a number, plus five.
Seven less than twice a number.
2x − 7twice ×2product multiplyquotient divideless than subtract aftermore than add
CHECK YOUR UNDERSTANDING
1 of 8Translate Words and Algebra
Write 3x + 5 in words.
5
Connect algebra to life
Explain What an Expression Means
12starting fee
constant
+constant
3cost each month
coefficient
coefficient
mnumber of months
variable
Total subscription costvariable
The variable represents ______.The coefficient tells us ______.The constant represents ______.The expression calculates ______.
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1 of 6Explain What It Means
A music service costs 12 + 3m dollars. What does 12 represent?
6
Put everything together
Complete Lesson Practice
This practice combines expressions, equations, vocabulary, terms, translation, and real-world meaning.
CHECK YOUR UNDERSTANDING
1 of 12Complete Lesson Check
Is 7x - 4 an expression or equation?
Printable practice · A1-U1-WS1
Understanding Algebraic Expressions Worksheet
Questions 1–10 provide the core assignment. Questions 11–16 extend the lesson with application and explanation.