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

Lesson 6.3Explore Numerical Expressions with Exponents

Start hereWords, worked example, and sentence starters

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?

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
ExponentSpanish: Exponente A small number that tells how many times to multiply a number by itself. In 9^4, the exponent is 4.
BaseSpanish: Base The number that gets multiplied by itself. In 9^4, the base is 9.
PowerSpanish: Potencia A number written with a base and an exponent, like 2³. 9^4
EvaluateSpanish: Evaluar To find the value by putting numbers in for the letters. Evaluate 3⁴: write 3 × 3 × 3 × 3, then multiply step by step: 9 × 9 = 81
Repeated multiplicationSpanish: Multiplicación repetida Multiplying the same factor again and again. 9 × 9 × 9 × 9
Expanded formSpanish: Forma desarrollada A power written out as a product of its factors. 2^3 = 2 × 2 × 2

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Write 9 × 9 × 9 × 9 as a power.

  1. The repeated factor is 9, so the base is 9.
  2. Count the 9s: there are four, so the exponent is 4.
  3. Check: the exponent counts factors, not × signs (there are only 3 × signs).

Answer: 9⁴; base 9, exponent 4

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Now let's find 5². How many times do we multiply 5 by itself?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • In this power, the base is and the exponent is .
  • The exponent tells me to use the base as a factor times.
  • I read this power as to the power.
  • A power shows repeated , not repeated .

Word bank powerbaseexponentfactorrepeated multiplicationexpanded formsquaredcubedevaluateproductreadtimes

Watch out!A common mistake

A common mistake in Powers and Exponents is multiplying the base by the exponent instead of using the base as a repeated factor

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

Lesson 6.3Explore Numerical Expressions with Exponents

Level 0Most support · every hint printed

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?

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Write 9 × 9 × 9 × 9 as a power.

  1. The repeated factor is 9, so the base is 9.
  2. Count the 9s: there are four, so the exponent is 4.
  3. Check: the exponent counts factors, not × signs (there are only 3 × signs).

Answer: 9⁴; base 9, exponent 4

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Which expression shows 5³ as repeated multiplication?

    1. A3 × 3 × 3 × 3 × 3
    2. B5 × 5 × 5
    3. C5 × 3
    4. D5 + 5 + 5
    Steps to try
    1. In 5³ the base is 5 and the exponent is 3. Ask: which number repeats, and how many times?
    2. The exponent counts the factors. Look for the base written as a factor that many times.
    3. Say it out loud: 'use 5 as a factor 3 times.' Count the 5's in each choice — you need exactly three of them.
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    What is the value of 4³?

    1. A7
    2. B12
    3. C43
    4. D64
    Steps to try
    1. Look at the small raised 3. That exponent counts how many 4's get multiplied — it is not a number to multiply 4 by.
    2. Rewrite the power as repeated multiplication first, then multiply one step at a time.
    3. Write 4³ as 4 × 4 × 4. Multiply the first pair (4 × 4 = 16), then multiply that result by the last 4.
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    What is the value of 6²?

    1. A8
    2. B12
    3. C36
    4. D62
    Steps to try
    1. The little 2 is the exponent. It counts how many 6's you multiply — it's not a number to add or multiply by.
    2. Turn the power into repeated multiplication before you calculate anything.
    3. Rewrite 6² as 6 × 6, then multiply those two factors.
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Evaluate: 3 × (4 + 2)²

    1. A36
    2. B54
    3. C108
    4. D144
    Steps to try
    1. There are three jobs here: parentheses, an exponent, and multiplication. Order of operations decides which comes first.
    2. Do the parentheses first, then square that result, then multiply by 3 last.
    3. Start inside: 4 + 2 = 6. Now the problem becomes 3 × 6². Handle the exponent next.
    Rewrite the whole expression each lineWhat I simplified
    1. 1GroupingInside ( ) first.
    2. 2ExponentsThen powers.
    3. 3× ÷Left to right.
    4. 4+ −Left to right.

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