Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.16.1 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use models to divide a whole number by a fraction and a fraction by a whole number, explain why the method works, and use it on a problem I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 8 ÷ 1/2, 8 is the dividend.
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 8 ÷ 1/2, 1/2 is the divisor.
QuotientSpanish: Cociente The answer when you divide. 8 ÷ 1/2 = 16 is the quotient.
ReciprocalSpanish: Recíproco A fraction turned upside down. 1/4 → 4/1
Unit fractionSpanish: Fracción unitaria A fraction with 1 on top, like 1/4. 1/3, 1/8, 1/10
Multiplicative inverseSpanish: Inverso multiplicativo Two numbers whose product is 1; each is the reciprocal of the other. 4 and 1/4 · 2/3 and 3/2

How it worksWorked exampledividing a whole number by a unit fraction

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

An 11-foot ribbon is cut into pieces that are each 1/6 foot long. How many pieces are there?

  1. Write the whole number over 1. 11 ÷ 1/6 = 11/1 ÷ 1/6
  2. Keep, Change, Flip. Keep 11/1, change ÷ to ×, flip the divisor: 6/1
  3. Multiply across. 11/1 × 6/1 = 66/1
  4. Simplify. 66/1 = 66 pieces

Answer: The ribbon makes 66 pieces that are each 1/6 foot long.

Now you trySame steps, your turn

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

A 7-foot rope is cut into pieces that are each 1/9 foot long. How many pieces are there?

  1. Write the whole number over 1. ÷ 1/9 = / 1 ÷ 1/9
  2. Keep, Change, Flip. / 1 × /
  3. Multiply across. /
  4. Simplify. pieces
Answer:number of 1/9-foot pieces

Say it and write itSentence starters

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

  • To divide by a fraction, I multiply by its .
  • I wrote over 1 so both numbers are fractions.
  • The quotient is because that many groups fit inside.
  • Dividing by a fraction smaller than one whole makes the quotient .

Word bank reciprocalquotientdividenddivisorunit fractionkeepchangeflipmultiplygroupsfit insidelarger

Watch outA common mistake

A common mistake in Interpret Division of Fractions is assuming that dividing always makes the answer smaller. For 4 ÷ 1/3, students reason 'dividing shrinks the number' and compute 4 ÷ 3 ≈ 1.3 instead of asking how many 1/3-foot pieces fit into 4 feet (each whole foot holds 3 thirds, so 4 × 3 = 12). Before you submit, check: if the divisor is a fraction smaller than 1, the quotient must be BIGGER than the dividend, not smaller.

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.1

Lesson 6.16.1 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can use models to divide a whole number by a fraction and a fraction by a whole number, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    123
    Count the eighths in 3 wholes.

    Find 3 ÷ 1/8 and 1/8 ÷ 3. Which quotient is greater?

    1. 1Write 3 over 1. Keep, Change, Flip. What is 3 ÷ 1/8?
    2. 2Now write 3 as 3/1 in 1/8 ÷ 3. What is the quotient?
    3. 3Which quotient is greater?
    Final answer:
  2. 2Complete each step, then write the final answer.
    1 whole = 4 fourths
    Each whole gives 4 pieces.

    A number divided by 1/4 is 28. What is the number?

    1. 1How many 1/4 pieces are in 1 whole?
    2. 2Each whole gives 4 pieces. How many wholes give 28 pieces?
    3. 3Check: find 7 ÷ 1/4 with Keep, Change, Flip.
    4. 4Why do you divide 28 by 4 to work backward?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find 6/7 ÷ 3. Simplify your answer.

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

    A fraction divided by 5 is 1/10. What is the fraction?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    Six families share 9/10 kilogram of rice equally. How much rice does each family get?

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

    Nia says dividing always makes a number smaller. Find 7 ÷ 1/2 to test her idea.

    Show your work
    Final answer:

Explain your thinkingWithout solving, how do you know 8 ÷ 1/4 is greater than 8, but 1/4 ÷ 8 is less than 1/4?

ChallengeWrite your own problem

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

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