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

Lesson 6.96.9 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can divide a whole number by a fraction 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 6.9. 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
Whole NumberSpanish: Número entero A counting number with no fraction or decimal, like 0, 1, 2, 3. 4 is a whole number; as a fraction it is 4/1
FractionSpanish: Fracción A number that shows part of a whole, like 3/4. 1/2 means 1 out of 2 equal parts — like cutting a sandwich in half and taking one piece
ReciprocalSpanish: Recíproco A fraction turned upside down. The reciprocal of 2/3 is 3/2. Flip the fraction to divide: 6 ÷ 2/3 = 6 × 3/2
Keep, Change, FlipSpanish: Mantener, cambiar, invertir A way to divide fractions: keep the first, change ÷ to ×, flip the second. 6 ÷ 1/3 → Keep 6, Change ÷ to ×, Flip 1/3 to 3/1 → 6 × 3 = 18
QuotientSpanish: Cociente The answer when you divide. In 4 ÷ 1/2 = 8, the quotient is 8

How it worksWorked example

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

Maya has 5 yards of ribbon. Each bow uses 3/4 yard. How many full bows can she make? How much ribbon is left?

  1. Write the division: 5 ÷ 3/4
  2. Multiply by the reciprocal of 3/4: 5 × 4/3 = 20/3
  3. Change 20/3 to a mixed number: 20/3 = 62/3
  4. Find the ribbon left after 6 bows: 6 × 3/4 = 18/4 = 41/2; 5 − 41/2 = 1/2
  5. She can make 6 full bows. 1/2 yard of ribbon is left.

Now you trySame steps, your turn

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

Find 3 ÷ 1/4. Then explain why the answer is greater than 3.

Answer:

Say it and write itSentence starters

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

  • 3 ÷ 1/4 = 12 because it takes jumps of to get from 0 to .

Word bank Whole NumberFractionReciprocalKeep, Change, FlipQuotient12fourthjumps3four timeseach whole

Watch out!A common mistake

A common mistake in Divide Whole Numbers by Fractions is doing 'Keep, Change' but skipping the 'Flip'

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

Lesson 6.96.9 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can divide a whole number by a fraction 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 6.9. 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.

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

    Find 12 ÷ 4/5.

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    0123434
    How many full jumps of 34 fit in 4?

    Sam has 4 yards of cord. Each bracelet uses 3/4 yard. How many full bracelets can he make? How much cord is left?

    1. 1Rewrite 4 ÷ 3/4 as a multiplication.
    2. 2Multiply. Write the answer as a mixed number.
    3. 3How many full bracelets? How much cord is left?
    Final answer:
  2. 3Complete each step, then write the final answer.
    01234561434
    Compare the two jump sizes.

    Find 6 ÷ 1/4 and 6 ÷ 3/4. Why is one answer three times the other?

    1. 1Find 6 ÷ 1/4.
    2. 2Find 6 ÷ 3/4.
    3. 3Why is 24 three times 8?
    Final answer:
  3. 4Complete each step, then write the final answer.

    A number divided by 2/3 is 12. What is the number?

    Show your work
    Final answer:
  4. 5Complete each step, then write the final answer.

    A board is 10 feet long. Each shelf needs 3/4 foot. How many full shelves can you cut?

    Show your work
    Final answer:
  5. 6Complete each step, then write the final answer.

    Ava says 5 ÷ 1/4 must be less than 5, because dividing always makes numbers smaller. Find 5 ÷ 1/4.

    Show your work
    Final answer:

Explain your thinkingSometimes the quotient is a mixed number, like 131/3 shelves. What does the fraction part mean? When do you drop it?

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