Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.5

Lesson 6.3Explore Numerical Expressions with Exponents

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write and evaluate numbers in exponent form using a base and a power.

Why This Matters You're a sound engineer at a music studio. Each time you flip a switch, the volume doubles. The starting volume is 1 unit. After flipping the switch 3 times, the volume is 2³ = 2 × 2 × 2 = 8 units — that's 8 times louder! How loud does it get after more flips?

RememberExplore Numerical Expressions with Exponents

Powers & Exponents. Formula: Base^Exponent (b^n = b · b · ... · b n times) An exponent is a small raised number that tells you how many times to multiply a number by itself. We say 2³ as "two to the third power."

  1. Base is the factor being multiplied repeatedly.
  2. Exponent tells how many times to multiply the base by itself.
  3. Evaluate: 2³ = 2 × 2 × 2 = 8 (not 2 × 3 = 6)

Words: Exponent (Exponente)Base (Base)Power (Potencia)Evaluate (Evaluar)Repeated multiplication (Multiplicación repetida)

  1. 1Circle the letter of the best answer. Show how you know.

    12 is 25% of what number?

    1. A3
    2. B37
    3. C48
    4. D300
    0%50%100%
    Work
    1. 1Whole100% is what number?
    2. 2Find 10%Divide by 10.
    3. 3BuildAdd or multiply to the percent.
    4. 4CheckIs it under or over the whole?
  2. 2Circle the letter of the best answer. Show how you know.

    A team won 18 games, which is 60% of the games it played. How many games did it play?

    1. A10 games
    2. B28 games
    3. C30 games
    4. D48 games
    0%50%100%
    Work
    1. 1Whole100% is what number?
    2. 2Find 10%Divide by 10.
    3. 3BuildAdd or multiply to the percent.
    4. 4CheckIs it under or over the whole?
  3. 3Circle the letter of the best answer. Show how you know.

    Find the whole: 15 = 0.30 × n. What is n?

    1. A0.02
    2. B4.5
    3. C45
    4. D50
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    9 students are 10% of a grade. How many students are in the grade?

    1. A0.9 students
    2. B19 students
    3. C90 students
    4. D900 students
    0%50%100%
    Work
    1. 1Whole100% is what number?
    2. 2Find 10%Divide by 10.
    3. 3BuildAdd or multiply to the percent.
    4. 4CheckIs it under or over the whole?
  5. 5Circle the letter of the best answer. Show how you know.

    A music studio is recording tracks. Each track layer doubles the file size. A single track is 4 MB. The file size after n layers is given by 4 × 2ⁿ. What is 2⁵?

    1. A10
    2. B16
    3. C25
    4. D32
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
  6. 6Circle the letter of the best answer. Show how you know.

    A music studio is recording tracks. Each track layer doubles the file size. A single track is 4 MB. The file size after n layers is given by 4 × 2ⁿ. How big is the file after 5 layers?

    1. A20 MB
    2. B40 MB
    3. C64 MB
    4. D128 MB
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.

Explain your thinkingHow does the value change when you increase the exponent by 1? Why?

Sentence starter When the exponent increases by 1, the value is multiplied by ___ because the base is used as a factor ___ more time.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.5

Lesson 6.3Explore Numerical Expressions with Exponents

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write and evaluate numbers in exponent form using a base and a power.

Why This Matters You're a sound engineer at a music studio. Each time you flip a switch, the volume doubles. The starting volume is 1 unit. After flipping the switch 3 times, the volume is 2³ = 2 × 2 × 2 = 8 units — that's 8 times louder! How loud does it get after more flips?

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Drag each repeated-multiplication beat next to its matching exponential form.

    Groups: 7³ 6² 4⁴ 9²
    • 7 × 7 × 7
    • 6 × 6
    • 4 × 4 × 4 × 4
    • 9 × 9
  2. 2Write the letter of the matching item on each line.

    Match each power to the number of beats it plays (its value).

    1. 7³
    2. 6²
    3. 4⁴
    4. 9²
    5. 6³
    6. 7²
    • A343
    • B36
    • C256
    • D81
    • E216
    • F49
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A music studio is recording tracks. Each track layer doubles the file size. A single track is 4 MB. The file size after n layers is given by 4 × 2ⁿ. Why does the file grow so quickly?

    1. ABecause 4 MB is already large
    2. BBecause 5 is a big exponent
    3. CBecause the studio records faster each time
    4. DBecause each layer doubles the size instead of adding a fixed amount
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    The drum loop plays 3⁴ beats. What is the value of 3⁴?

    1. A7
    2. B12
    3. C27
    4. D81
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    A synth pattern repeats 7 × 7 × 7. How do you write that as a power?

    1. A3⁷
    2. B7³
    3. C7 × 3
    4. D21³
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    The bass line doubles for 2⁶ counts. What is the value of 2⁶?

    1. A12
    2. B32
    3. C36
    4. D64
    Show your work

Explain your thinkingHow does the value change when you increase the exponent by 1? Why?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help