Neft Teacher · Learn It

Unit 6 · Standard 6.AT.6a

Write and Evaluate Algebraic Expressions

Lesson 6-5 · Learn It — how the math works

Why we're learning this

Evelyn is helping to plan the sixth-grade field day. The committee will order the items shown for each student participating in field day. They do not yet know how many students will be participating. The shipping cost for all items is a one-time cost of $23.50. What expression can Evelyn use to determine how much the committee will need to purchase the items?

✱ Math Workbench

Learn It

How do we turn words into an expression?

An algebraic expression uses numbers, a variable (a letter for an unknown number), and operations. We read a word phrase and write it with math symbols.

Picture itSee what the math looks like before you read about it

Evelyn is booking a recording session at the music studio for her band. The studio charges the same price for every hour of recording time, plus a one-time setup fee of $23.50. The band does not yet know how many hours they will record.
Where you see this in real lifeEvelyn is booking a recording session at the music studio for her band. The studio charges the same price for every hour of recording time, plus a one-time setup fee of $23.50. The band does not yet know how many hours they will record.

Watch me solve itI do — read one step at a time

The problem looks like this
Tape diagram: total revenue is 12t from the tickets plus a flat $50 fee, so 12t + 50.12t + 5012t$12 each, t tickets50flat fee
  1. Tickets cost $12 each, plus a flat $50 venue fee. Let t be the number of tickets.
  2. "$12 each ticket" means 12 times t, which I write as 12t.
  3. The flat fee $50 is added once, so I add 50.
  4. I put them together: total revenue = 12t + 50.

Watch out — mistakes students make here

  • The expression is right, but the evaluation added before multiplying: (4.25 + 23.50) × 30. Multiplication comes first.
  • 'Product' is the result of multiplication. 6 times n is 6n.
  • n − 6 subtracts. 'Product' is the result of multiplying: 6 × n = 6n.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. The field day committee orders one $4.25 item for each student, plus a one-time $23.50 shipping fee. The number of students is unknown.
  2. Let s stand for the number of students. “$4.25 for each student” means 4.25 times s, written 4.25s.
  3. The shipping fee does not depend on how many students there are, so it is a that is added once: 4.25s + 23.50.
  4. The expression 4.25s + 23.50 has two : 4.25s, whose is 4.25, and the 23.50.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • The committee learns that 30 students signed up, so s = 30.
  • : replace s with 30 to get 4.25 × 30 + 23.50.
  • using the order of operations — which comes first, the multiplication or the addition?
  • Find the total cost, and say what your answer means for the committee.

Solve: The expression 8n + 15 gives the cost of n tickets plus a fee. What is the cost for 6 tickets?

My answer

Stuck? Open one hint at a time.

Hint 1

Replace n with 6.

Hint 2

8 × 6 = 48.

Hint 3

Then add the fee.

Check my answer
✅ Answer: $63
Substitute n = 6: 8 × 6 + 15 = 48 + 15 = $63.

Turn & TalkSay it out loud with a partner

The items cost $1.50, $12.95 and $0.65 per student, plus one $23.50 shipping fee. Which of those numbers gets multiplied by the number of students, and which does not — and why?

Try starting with:

  • I think ___ because ___.Pienso que ___ porque ___.
  • I agree / disagree with you because ___.Estoy / no estoy de acuerdo contigo porque ___.
Use these wordsWrite Algebraic ExpressionsVariableAlgebraic ExpressionCoefficientConstant