Write and Evaluate Algebraic Expressions

Write expressions with variables from word phrases and evaluate them by substituting given values.

6.AT.B.6 · Numerical & Algebraic Expressions
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W

Warm-Up

2 questions
Warm-Up 1
Which expression represents "5 more than a number n"?
Vocabulary: A variable is a letter that stands for an unknown number. An algebraic expression uses numbers, variables, and operations but has no equal sign.
Hint: "More than" means addition.
✓Correct! "5 more than n" means you add 5 to n, giving n + 5.
✗Not quite. "More than" tells you to add. The answer is B: n + 5.
Warm-Up 2
True or false: The phrase "the product of 4 and x" is written as 4 + x.
Hint: The word product means the result of multiplication, not addition.
✓Correct! "Product" means multiply, so it should be 4x (or 4 × x), not 4 + x.
✗"Product" means multiplication. The correct expression is 4x, not 4 + x. The answer is False.
P

Practice

5 questions
Practice 1
Evaluate the expression 3x + 2 when x = 4.
What does evaluate mean? To evaluate an expression, replace the variable with the given number and calculate.
Try it: Replace x with 4 → 3(4) + 2 = ?
Show your substitution steps:

Sentence frame: "I substituted ___ for x. Then I calculated 3 × ___ + 2 = ___."

✓Correct! 3(4) + 2 = 12 + 2 = 14.
✗Substitute 4 for x: 3 × 4 = 12, then 12 + 2 = 14. The answer is B.
Practice 2
Evaluate each expression for the given value.
Strategy: Substitute means replace the variable with the number, then compute step by step.
a. 2n + 1 when n = 5 →
b. 20 − 3m when m = 4 →
c. k ÷ 2 + 6 when k = 10 →

Sentence frame: "When I replace ___ with ___, I get ___."

✓All correct! 2(5)+1 = 11, 20−3(4) = 8, 10÷2+6 = 11.
✗Some answers need another look. Substitute the value and follow the order of operations carefully.
Practice 3
Match each word phrase to the correct algebraic expression.
Key words: "sum" → add, "difference" → subtract, "product" → multiply, "quotient" → divide.
n + 7
n − 3
6n
n ÷ 2
7 more than n
3 less than n
The product of 6 and n
n divided by 2
✓All correct! You matched every phrase to its algebraic expression.
✗Some matches are off. Remember: "more than" = add, "less than" = subtract, "product" = multiply, "divided by" = divide.
Practice 4
A movie ticket costs $8. Which expression represents the total cost for n tickets plus a $5 service fee?
Think about it: Each ticket is $8, so n tickets cost 8 × n. Then add the one-time $5 fee.
Explain your reasoning:

Sentence frame: "Each ticket costs $___, so n tickets cost ___. Adding the $5 fee gives ___."

✓Correct! 8n represents the ticket cost, and +5 adds the service fee.
✗The ticket cost is 8 × n = 8n. Add the $5 fee: 8n + 5. The answer is B.
Practice 5
A gym charges a one-time signup fee of $10 plus $5 per visit. The total cost is 5n + 10. What is the total cost for 6 visits?
Strategy: Substitute n = 6 into the expression 5n + 10 and compute.
Show your work:

Sentence frame: "I substituted ___ for n. 5 × ___ = ___. Then ___ + 10 = ___."

✓Correct! 5(6) + 10 = 30 + 10 = $40.
✗Substitute 6: 5 × 6 = 30, then 30 + 10 = 40. The answer is C: $40.
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Challenge

1 question
Challenge
A store sells notebooks for $3 each and pens for $1 each. Write an algebraic expression for the total cost if you buy n notebooks and p pens. Then find the cost when n = 4 and p = 6.
Think about it: How much do n notebooks cost? How much do p pens cost? Add them together for the total.
Your expression:
Evaluate when n = 4 and p = 6. Show your work:

Sentence frame: "My expression is ___. When n = ___ and p = ___, the total cost is $___ because ___."