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

Lesson 6.36.3 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

Why This Matters This is your challenge small group for Lesson 6.3. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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.

Find the value of 5². Then explain why 5² is not 10.

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 6.36.3 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

Why This Matters This is your challenge small group for Lesson 6.3. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    PowerFactorsValue
    3⁴3 × 3 × 3 × 3?
    4³4 × 4 × 4?
    Same two numbers, switched places.

    Is 3⁴ greater than 4³? Find both values.

    1. 1Find the value of 3⁴.
    2. 2Find the value of 4³.
    3. 3Which is greater? By how much?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Divide by 5Result
    625 ÷ 5?
    ? ÷ 5?
    ? ÷ 5?
    ? ÷ 51
    Each division by 5 removes one factor of 5.

    Write 625 as a power of 5.

    1. 1Divide 625 by 5 again and again until you reach 1. List the results.
    2. 2How many times did you divide by 5? That is the exponent.
    3. 3Write 625 as a power.
    4. 4Why is 5⁴ not the same as 5 × 4?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the value of 0.3².

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

    Write 128 as a power of 2. What is the exponent?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    HoursCellsPower
    122¹
    242²
    382³
    The exponent matches the number of hours.

    One cell splits into 2 cells every hour. Each new cell splits too. You start with 1 cell. How many cells are there after 8 hours?

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

    How much greater is 2¹⁰ than 10²?

    Show your work
    Final answer:

Explain your thinkingDoes a bigger base always give a bigger power? Use 3⁴ and 4³ to explain your answer.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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