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.

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 outA common mistake

A common mistake in Divide Whole Numbers by Fractions is doing 'Keep, Change' but skipping the 'Flip' — students multiply by the divisor as it is instead of by its reciprocal. For example, for 6 ÷ 3/4, a student might write 6 × 3/4 = 4 1/2 and stop there, but the divisor 3/4 must be flipped to 4/3 first: 6 × 4/3 = 24/3 = 8. Before you submit, check: did I flip the second fraction (the divisor) upside down before multiplying?

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.

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.

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