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

Lesson 6.26.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can divide a fraction by a fraction and divide with mixed numbers by multiplying by the reciprocal, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 6.2. 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
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 8/9 ÷ 2/9, 8/9 is the dividend.
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 8/9 ÷ 2/9, 2/9 is the divisor.
ReciprocalSpanish: Recíproco A fraction turned upside down. 2/9 → 9/2
QuotientSpanish: Cociente The answer when you divide. 8/9 ÷ 2/9 = 4
SimplifySpanish: Simplificar To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2. 8/12 → GCF is 4 → 8÷4 / 12÷4 = 2/3
Mixed numberSpanish: Número mixto A whole number and a fraction written together, like 2 1/2. It must be rewritten as an improper fraction before dividing. 2 1/2 = 5/2

How it worksWorked example

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

A pitcher has 2/3 liter of juice. Each cup holds 1/6 liter. How many cups can be filled?

  1. Write the division: 2/3 ÷ 1/6.
  2. Flip the divisor and multiply: 2/3 × 6/1 = 12/3.
  3. Simplify: 12/3 = 4. Check: 4 × 1/6 = 4/6 = 2/3.

Answer: 4 cups

Now you trySame steps, your turn

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

Find 1/2 ÷ 1/4. Then explain why the answer is bigger than 1/2.

Answer:

Say it and write itSentence starters

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

  • To divide by , I multiply by its reciprocal .
  • The quotient counts how many groups of fit inside .
  • I did not need a common denominator because .
  • After multiplying across, I simplified to .

Word bank reciprocaldividenddivisorquotientkeepchangeflipmultiply acrosssimplifygroupsfit insidetape diagram

Watch out!A common mistake

A common mistake in Divide Fractions is flipping the wrong fraction: students flip the dividend (the first fraction) instead of the divisor (the second fraction). For example, solving 3/4 ÷ 5/8 by flipping 3/4 to 4/3 and keeping 5/8 gives 4/3 × 5/8 = 20/24 = 5/6

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

Lesson 6.26.2 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can divide a fraction by a fraction and divide with mixed numbers by multiplying by the reciprocal, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 6.2. 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.
    sugar: 56 cupone batch: 13 cup = 26
    How many 26 parts fit in 56?

    Mo has 5/6 cup of sugar. One batch of cookies needs 1/3 cup. How many batches can he make?

    1. 1Keep, Change, Flip. Then multiply. What fraction do you get?
    2. 2Simplify. Write the answer as a mixed number.
    3. 3What does the 1/2 mean for Mo?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Piece lengthDivisionPieces
    56 foot52 ÷ 56?
    114 feet52 ÷ 54?
    Same board, two piece lengths.

    A board is 2 1/2 feet long. How many 5/6-foot pieces fit? How many 1 1/4-foot pieces fit?

    1. 1Write 2 1/2 as an improper fraction.
    2. 2Find 5/2 ÷ 5/6. How many pieces fit?
    3. 3Find 5/2 ÷ 5/4. How many pieces fit?
    4. 4Why does the longer piece give a smaller quotient?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find 9/10 ÷ 3/5. Write your answer as a mixed number.

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

    2/3 divided by a unit fraction is 8. A unit fraction has 1 on top. What is the unit fraction?

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

    A water jug holds 6 1/4 liters. Each bottle holds 1 1/2 liters. How many bottles can you fill? Give a mixed number.

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

    Lee says 4/5 ÷ 2/5 is less than 4/5, because division makes numbers smaller. Find the quotient.

    Show your work
    Final answer:

Explain your thinkingMo got 21/2 batches. What does the fraction part of a quotient tell you? Use Mo's sugar to explain.

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