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.

Why This Matters This is your challenge small group for Lesson 6.1. 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 ÷ 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 example

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

A cook has 4 cups of broth. How many 1/3-cup servings can she pour?

  1. Write the division: 4 ÷ 1/3.
  2. Keep 4, change ÷ to ×, flip 1/3 to 3: 4 × 3 = 12.
  3. Check: 12 × 1/3 = 4 cups.

Answer: 12 servings

Now you trySame steps, your turn

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

Find 2 ÷ 1/3. Then explain why the answer is bigger than 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 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 out!A 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.

Why This Matters This is your challenge small group for Lesson 6.1. 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.
    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.

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