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

Lesson 6.16.1 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can use models to divide a whole number by a fraction and a fraction by a whole number — 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
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 1

Group 1Supported practice

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

Learning target With my small group, I can use models to divide a whole number by a fraction and a fraction by a whole number — one step at a time, with support.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    Find 3 ÷ 1/2.

    Show your work

    Hint Write 3 as 3/1. Then keep, change, flip.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Find 3/5 ÷ 2.

    Show your work

    Hint Write 2 as 2/1. Flip only the number you divide by.

    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.
    1 foot1 foot1 foot
    Each foot holds 3 pieces.

    A rope is 3 feet long. You cut it into pieces that are 1/3 foot long. How many pieces do you get? Find 3 ÷ 1/3.

    1. 1Put a 1 under the whole number. What do you get?
    2. 2Keep, Change, Flip. What is the new problem?
    3. 3Multiply the tops. Multiply the bottoms. How many pieces?
    Final answer:
  2. 4Complete each step, then write the final answer.
    25 yard
    Split 25 into 3 equal pieces.

    Ana has 2/5 yard of ribbon. She cuts it into 3 equal pieces. How long is each piece? Find 2/5 ÷ 3.

    1. 1Put a 1 under the whole number. What do you get?
    2. 2Keep, Change, Flip. What is the new problem?
    3. 3Multiply across. How long is each piece?
    Final answer:
  3. 5Complete each step, then write the final answer.

    Jamal has 6 cups of trail mix. He puts 1/4 cup in each bag. How many bags can he fill?

    Show your work

    Hint Find how many 1/4-cup parts fit in 6 cups. Find 6 ÷ 1/4.

    Final answer:
  4. 6Complete each step, then write the final answer.

    Leo says 1/2 ÷ 4 is 8. He flipped the 1/2 and multiplied: 2 × 4 = 8. Is he right? Find the correct answer.

    Show your work

    Hint Keep the first number. Flip only the number you divide by. Write 4 as 4/1 first.

    Final answer:

Explain your thinkingWhy does 3 ÷ 1/3 give a big answer, but 2/5 ÷ 3 gives a small answer?

Sentence starter Dividing by {1/3} gives more pieces because ___. · Dividing by 3 makes each piece ___ because ___.

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