Lesson 6.5Write and Evaluate Algebraic Expressions
Start hereWords, worked example, and sentence starters
Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| VariableSpanish: Variable | A letter that stands for a number that is unknown or can change. | the m in 14m + 35 |
| Algebraic ExpressionSpanish: Expresión algebraica | A math phrase that has at least one letter. | 14m + 35 |
| CoefficientSpanish: Coeficiente | The number in front of a letter, like the 3 in 3x. | In 14m, the coefficient is 14. |
| ConstantSpanish: Constante | A fixed number in an expression or equation that does not change. | the 35 in 14m + 35 |
| Like termsSpanish: Términos semejantes | Terms with the same letter raised to the same power, like 2x and 5x. | 4x + 2x = 6x (like terms, same variable); but 4x + 2y cannot be combined (different variables) |
| SubstituteSpanish: Sustituir | To replace a variable with a given number before working out the value. | For s = 30: 4.25s + 23.50 → 4.25 × 30 + 23.50 |
How it worksWorked examplewriting an expression with a variable
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A club buys a $14 shirt for each member and pays one $35 setup fee. Write an expression for the total cost.
- Name the unknown. Let m = the number of members.
- Write the part that changes. $14 for each member → 14m
- Write the part that stays the same. one-time fee → 35
- Join them with the operation the story needs. 14m + 35
Answer: The expression is 14m + 35, where m stands for the number of members.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A camp charges $9 for each craft kit and one $20 registration fee. Write an expression for the total cost.
- Name the unknown. Let = the number of craft kits.
- Write the part that changes. $9 for each kit →
- Write the part that stays the same.
- Join them with the operation.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I let stand for .
- The coefficient shows the amount for each .
- The constant happens only .
- My expression for this situation is .
Word bank variablealgebraic expressioncoefficientconstanttermeachone-timeperstands fordefinetotalunknown
Watch outA common mistake
A common mistake in Write Algebraic Expressions is treating 'each' or 'per' as if it means add instead of multiply, and attaching the variable to the wrong number. For 'a $25 setup fee plus $8 per hour, h,' students often write 25 + 8 + h (adding all three numbers) or 25h + 8 (multiplying the flat fee by h) instead of the correct 8h + 25. Since $8 applies per hour, it must multiply the variable (8h), and the flat $25 fee is a constant added only once — check that the per-unit rate, not the flat fee, is the number multiplied by the variable.
Lesson 6.5Write and Evaluate Algebraic Expressions
Version ASupported practice
Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.
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1Circle the letter of the best answer. Show how you know.
Which expression represents 'the product of 6 and a number n'?
- A6n
- B6 + n
- Cn − 6
- Dn ÷ 6
Hint Underline the key word 'product.' Every operation has a code word — which operation does 'product' name?
Show your work -
2Circle the letter of the best answer. Show how you know.
Which expression represents '9 less than a number y'?
- Ay − 9
- B9 − y
- Cy + 9
- D9y
Hint 'Less than' is a tricky phrase — it flips the order of what you write.
Show your work -
3Circle the letter of the best answer. Show how you know.
Which expression represents 'the sum of a number m and 15'?
- Am + 15
- Bm − 15
- C15m
- Dm ÷ 15
Hint Circle the key word 'sum.' Which operation gives you a sum?
Show your work -
4Write the name of the correct group on each line.
Sort each key word by the operation it represents.
- sum
- more than
- difference
- less than
- product
- times
Hint Each word is a code for add, subtract, or multiply. Think about what result the word describes.
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5Circle the letter of the best answer. Show how you know.
Evaluate 4.25s + 23.50 when s = 10.
- A$47.75
- B$66.00
- C$66.75
- D$277.50
Hint Replace s with 10.
My work — one step per line What I did to both sides - 1LookWhat is done to the variable?
- 2UndoDo the opposite — both sides.
- 3SimplifyOne side at a time.
- 4CheckPut it back in.
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6Circle the letter of the best answer. Show how you know.
Which key word tells you to multiply?
- AProduct
- BSum
- CDifference
- DQuotient
Hint Think of a fact like 3 × 4 = 12. What do we call the number 12 in that fact?
Show your work
Explain your thinkingWhat key words helped you decide which operation to use? How can the same phrase be written differently?
Sentence starter The phrase '___ ' tells me to use ___ because the key word ___ means ___.
Lesson 6.5Write and Evaluate Algebraic Expressions
Version BCore practice
Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.
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1Write the name of the correct group on each line.
Match each word phrase to its correct algebraic expression.
- twice a number k → 2k
- a number b divided by 5 → b ÷ 5
- the sum of a number d and 15 → d + 15
- 10 decreased by a number r → 10 − r
- 4 more than triple a number c → 3c + 4
- half of a number h → h ÷ 2
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2Write the letter of the matching item on each line.
Match each word phrase to its algebraic expression.
- the product of 5 and n
- 8 less than a number w
- a number p increased by 12
- twice a number x, plus 3
- a number y divided by 4
- 7 more than a number z
- A5n
- Bw − 8
- Cp + 12
- D2x + 3
- Ey ÷ 4
- Fz + 7
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3Complete the table. Show how you found each value.
Write an algebraic expression for each real-world situation.
Situation Variable Expression Movie tickets cost $12 each t = number of tickets You had $50 and spent some money s = dollars spent Each student gets 3 pencils plus 2 erasers n = number of students A pizza is split equally among friends f = number of friends, pizza = 24 slices Show your work -
4Decide whether each pair balances. Check Yes or No, then explain.
Both expressions are equivalent by the commutative property of addition.
Left side Right side Balanced? Explain your choice
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5Circle the letter of the best answer. Show how you know.
The expression 8n + 15 gives the cost of n tickets plus a fee. What is the cost for 6 tickets?
- A$29
- B$48
- C$63
- D$138
My work — one step per line What I did to both sides
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6Find the mistake. Explain it, then show the correct work.
Spot the Common Mistake
- 1Phrase8 divided by a number m
- 2Student's expressionm ÷ 8
- 3ReasoningI saw 'divided by' so I wrote the variable first and then 8.
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer:
Explain your thinkingWhat key words helped you decide which operation to use? How can the same phrase be written differently?
Lesson 6.5Write and Evaluate Algebraic Expressions
ChallengeExtension
Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.
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1Complete the table. Show how you found each value.
Translate each two-step word phrase into an algebraic expression. Be careful with the order!
Word Phrase Algebraic Expression 5 more than triple a number x twice the sum of a number y and 4 10 less than the product of 7 and a number z Show your work
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2Find the mistake. Explain it, then show the correct work.
Find the Translation Error
- 1Phrase12 less than a number g
- 2Student's expression12 − g
- 3ReasoningI see 'less than' so I subtract, and 12 comes first in the phrase.
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer: -
3Answer in complete sentences.
Field day needs one $4.25 item per student plus a one-time $23.50 shipping fee. Write the expression, then find the cost for 30 students AND for 60 students. Does doubling the students double the cost? Explain.
Write your answer -
4Answer in complete sentences.
Write a real-world situation that could be modeled by the expression 4n + 10. Explain what the variable n represents, what the coefficient 4 means, and what the constant 10 represents.
Write your answer