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

Lesson 6.36.3 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can write and evaluate numbers in exponent form using a base and a power — one step at a time, with support.

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 examplewriting repeated multiplication as a power

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

Write 9 × 9 × 9 × 9 as a power. Then name its base and its exponent.

  1. Find the repeated factor. The factor is 9.
  2. Count how many times it is used. It is used 4 times.
  3. Write the base, then the exponent. 9 ^ 4
  4. Read it out loud. 9 to the 4th power

Answer: 9 × 9 × 9 × 9 = 9^4. The base is 9 and the exponent is 4.

Now you trySame steps, your turn

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

Write 6 × 6 × 6 as a power. Then name its base and its exponent.

  1. Find the repeated factor. The factor is .
  2. Count how many times it is used. times
  3. Write the base, then the exponent. ^
  4. Read it out loud. to the power
Answer:the power, its base, and its exponent

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 outA 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 — for example, thinking 2³ = 2 × 3 = 6 instead of 2³ = 2 × 2 × 2 = 8. Before you submit, rewrite the power as repeated multiplication first, then multiply step by step.

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

Lesson 6.36.3 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can write and evaluate numbers in exponent form using a base and a power — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    PowerFactorsValue
    4¹44
    4²4 × 416
    4³4 × 4 × 4?
    Each new factor of 4 adds one more × 4.

    Find the value of 4³.

    1. 1What is the base? What is the exponent?
    2. 2Write 4³ as repeated multiplication.
    3. 3Multiply two numbers at a time. What is the value?
    Final answer:
  2. 2Complete each step, then write the final answer.
    FactorsBaseExponent
    3 × 3 × 3 × 3 × 3??
    The base repeats. The exponent counts the factors.

    Write 3 × 3 × 3 × 3 × 3 as a power. Then find its value.

    1. 1What number is used as a factor? That is the base.
    2. 2How many times is 3 a factor? That is the exponent.
    3. 3Write the power.
    4. 4Multiply two numbers at a time. What is the value?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the value of 6².

    Show your work

    Hint The exponent 2 means use 6 as a factor 2 times.

    Final answer:
  4. 4Complete each step, then write the final answer.

    Find the value of 10³.

    Show your work

    Hint Use 10 as a factor 3 times. Multiply two numbers at a time.

    Final answer:
  5. 5Complete each step, then write the final answer.
    LevelFactors
    bags in a box5
    cups in all5 × 5
    beads in all5 × 5 × 5
    Each level uses 5 as a factor again.

    A box holds 5 bags. Each bag holds 5 cups. Each cup holds 5 beads. Write the number of beads in one box as a power. Then find the value.

    Show your work

    Hint 5 is used as a factor 3 times. Write 5³, then multiply.

    Final answer:
  6. 6Complete each step, then write the final answer.

    Sam says the value of 7² is 14. Is he right? Find the correct value.

    Show your work

    Hint Sam multiplied 7 by 2. What does the exponent 2 really tell you to do?

    Final answer:

Explain your thinkingWhy is 7² not the same as 7 × 2? Use the words base and exponent.

Sentence starter In 7², the base is ___ and the exponent is ___. · 7² means ___, so its value is ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help