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

Lesson 6.36.1–6.3 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 6.1–6.3 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Division of FractionsSpanish: División de fracciones Finding how many groups of one fraction fit inside another amount. 3 ÷ 1/2 asks how many halves fit in 3; the answer is 6.
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 3 ÷ 1/4 = 12, the dividend is 3 — it is the total being split
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 3 ÷ 1/4 = 12, the divisor is 1/4 — it is the size of each piece
QuotientSpanish: Cociente The answer when you divide. In 3 ÷ 1/4 = 12, the quotient is 12 — there are 12 quarter-size pieces in 3
ReciprocalSpanish: Recíproco A fraction turned upside down. The reciprocal of 1/4 is 4/1 = 4. Multiplying by the reciprocal gives the same result as dividing.
Unit fractionSpanish: Fracción unitaria A fraction with 1 on top, like 1/4. 1/2, 1/3, 1/4, 1/5 — each represents one equal part of a whole

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 6.36.1–6.3 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 6.1–6.3 by using each lesson's big idea in mixed practice.

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

    (Lesson 6.1) What does 3 ÷ 1/4 mean?

    1. AHow many 1/4-size pieces fit into 3
    2. B1/4 of 3
    3. C3 groups of 1/4
    4. D3 minus 1/4

    Hint Re-read the expression: 3 is the total amount and 1/4 is the size of one piece. What question could that setup be asking?

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 6.1) Which expression means 'how many 1/3-size pieces are in 2'?

    1. A1/3 ÷ 2
    2. B2 ÷ 1/3
    3. C2 × 1/3
    4. D2 + 1/3

    Hint Find the two jobs: which number is the total being split, and which is the size of each piece?

    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    (Lesson 6.2) What is the reciprocal of 3/5?

    1. A1/3
    2. B3/5
    3. C5/3
    4. D5/5

    Hint Re-read 'reciprocal' — it's about the two numbers of the fraction trading places.

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  2. 4Circle the letter of the best answer. Show how you know.

    (Lesson 6.2) What is 1/2 ÷ 1/4?

    1. A1/8
    2. B1/2
    3. C2
    4. D4

    Hint This asks how many 1/4-size pieces fit inside 1/2 — the pieces are smaller than the amount.

    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    (Lesson 6.3) What is the value of 4³?

    1. A7
    2. B12
    3. C43
    4. D64

    Hint Look at the small raised 3. That exponent counts how many 4's get multiplied — it is not a number to multiply 4 by.

    Show your work

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.

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