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15-Minute Lesson Plan: Writing Variable Expressions

Grade Level: 6–8
Time: 15 minutes
Topic: Translating Words Into Algebraic Expressions
Materials:

Learning Objective

Students will translate verbal phrases into algebraic expressions by identifying the unknown quantity, choosing a variable, and recognizing operation words.

1. Warm-Up — 3 Minutes

Write these phrases on the board:

a number plus 5

a number multiplied by 3

Ask students:

“How could we represent an unknown number?”

Introduce x as a variable.

Then translate together:

a number plus 5 → x + 5

a number multiplied by 3 → 3x

Remind students that a variable represents an unknown quantity.

2. Teacher Modeling — 4 Minutes

Write:

“Seven more than a number”

Ask students to identify:

  • Unknown number → x

  • “Seven more than” → + 7

Therefore:

x + 7

Model a second example:

“Four times a number decreased by 3”

Break it into parts:

  • “Four times a number” → 4x

  • “decreased by 3” → − 3

Expression:

4x − 3

Emphasize that students should translate the words one phrase at a time rather than trying to write the entire expression immediately.

3. Guided Practice — 3 Minutes

Give students these two examples:

1. Five less than a number

2. Twice a number plus 8

Have students write the expressions independently.

Answers:

1. x − 5

2. 2x + 8

Ask:

“Which words helped you decide which operation to use?”

Review common translation words:

Words Operation
sum, plus, more than +
difference, minus, less than −
product, times, twice ×
quotient, divided by ÷

4. Worksheet Practice — 3 Minutes

Give students the Math-Aids worksheet.

Have students begin with the first problems. Encourage them to use this three-step strategy:

1. Identify the unknown.
Choose a variable such as x.

2. Circle operation words.
Look for words such as plus, less, times, or divided by.

3. Write the expression.
Translate the phrase into mathematical symbols.

Circulate and ask:

  • “What is the unknown?”

  • “Which word tells you the operation?”

  • “What does ‘times’ tell you to do?”

  • “Does your expression match every part of the sentence?”

5. Exit Check — 2 Minutes

Write:

“Three more than twice a number”

Ask students to write the expression independently.

Answer: 2x + 3

Ask one student to explain how the words were translated.

Quick Success Check

Students should be able to say:

“I can identify the unknown, recognize operation words, and translate a verbal phrase into an algebraic expression.”

Differentiation

Students needing support:
Use the Easy worksheet setting, which focuses on one- and two-term expressions with a single variable. Provide an operation-word reference chart. (Math-Aids)

Students working at grade level:
Use the Medium setting and have students underline the operation words before writing each expression.

Students needing a challenge:
Use the Hard setting, which includes two- and three-term expressions with two variables. Ask students to explain why each variable represents a different unknown. (Math-Aids)

Assessment

During the lesson, check whether students can:

  • Identify an unknown quantity.

  • Select an appropriate variable.

  • Recognize mathematical operation words.

  • Translate a verbal phrase into an algebraic expression.

  • Explain how they determined the operation.

Success Criteria:
Students can accurately translate a verbal phrase into an algebraic expression and explain the meaning of each part.

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Posted: 8/21/2026

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