Neft Teacher · Learn It

Unit 6 · Standard 6.AT.6c

Write and Evaluate Numerical Expressions with Exponents

Lesson 6-4 · Learn It — how the math works

Why we're learning this

The studio's booking sheet lists a price for each kind of seat. Writing one numerical expression for the whole order — and evaluating it in the right order — is faster and easier to check than adding costs one at a time. Some counts are written as powers, so the exponent has to be handled before any multiplying. The booking sheet lists a $150 base fee plus $12 for each speaker rented. Write one expression for the cost of renting 5 speakers.

✱ Math Workbench

Learn It

Write the expression, then evaluate it in order

A numerical expression is a math phrase made of numbers and operations, with no equal sign. Writing one for a whole situation keeps every part visible; evaluating it means finding its single value, following the order of operations.

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

You are the music producer from the story. Your concert cost is given by the expression 150 + 12s, where s is the number of speakers you rent.
Where you see this in real lifeYou are the music producer from the story. Your concert cost is given by the expression 150 + 12s, where s is the number of speakers you rent.

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

The problem looks like this
Tape diagram: 2 × 15 = 30, 4 × 20 = 80 and 8 × 2 = 16 add to 126 dollars.126302 × 15804 × 20168 × 2
  1. Sofia buys 2 member tickets at $15, 4 non-member tickets at $20, and 8 student tickets at $2 each. I write one expression for each ticket type: 2 × 15, 4 × 20, and 8 × 2.2 × 15, 4 × 20
  2. The whole order is the three costs added together:2 × 15 + 4 × 20 + 8 × 2
  3. Now I . There are no and no yet, so multiplication comes first, left to right:30 + 80 + 16
  4. Then I add: 30 + 80 + 16 = 126. The tickets cost $126.30 + 80 + 16 = 126

Watch out — mistakes students make here

  • 126 uses $2 student tickets instead of 2³ = $8 each.
  • 158 treats 2³ as 2 × 3 = 6, giving 30 + 80 + 48. An exponent means repeated multiplication: 2³ = 8.
  • 1,392 multiplies the total by 8 again — the 8 got used one extra time. Evaluate 2³ = 8 once, multiply each pair, then add 30 + 80 + 64.

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

Same steps, new numbers.

  1. Suppose the student tickets cost 2³ dollars each instead of $2. The expression becomes 2 × 15 + 4 × 20 + 8 × 2³.2 × 15 + 4 × 20 + 8
  2. come before multiplying, so 2³ first:2 × 2 × 2 = 8
  3. Now multiply, left to right:30 + 80 + 64
  4. Then add: 30 + 80 + 64 = 174. The order now costs $174.30 + 80 + 64 = 174

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Seven friends split a bill. The pizzas cost 3² dollars each and they order 4 of them, plus a $6 delivery fee.
  • Write ONE for the total bill.
  • it: which do you handle first, the or the multiplication?
  • Then divide the total among the 7 friends, and say what each step meant.

Solve: What is the total of 2 × 15 + 4 × 20 + 8 × 2³?

My answer

Stuck? Open one hint at a time.

Hint 1

Evaluate the power first.

Hint 2

Then do all three multiplications.

Hint 3

Add the three costs.

Check my answer
✅ Answer: 174
Power first: 2³ = 8. Multiply: 30, 80, 64. Add: 30 + 80 + 64 = 174.

Turn & TalkSay it out loud with a partner

The concert cost is 150 + 12s, where s is the number of speakers. How do you find the cost for 5 speakers, and why does this one expression work for any number of speakers?

Try starting with:

  • I substitute s = 5 into 150 + 12s to get ___.Sustituyo s = 5 en 150 + 12s para obtener ___.
  • One expression works for any show because s ___.Una expresión sirve para cualquier concierto porque s ___.
Use these wordsVariableExpressionEvaluateSubstitute