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

Lesson 6.106.10 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can divide mixed numbers by first changing them to improper fractions — 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
Mixed NumberSpanish: Número mixto A whole number plus a fraction, like 2 1/3. 2 1/3 means 2 wholes and 1/3 more — picture 2 full circles and 1/3 of another
Improper FractionSpanish: Fracción impropia A fraction where the top is bigger than or equal to the bottom, like 7/4. 7/3 is improper because 7 > 3. It equals 2 1/3 as a mixed number.
ConvertSpanish: Convertir To change a number to a new form but keep the same value. 2 1/3 → multiply 2 × 3 = 6, add 1 → 7/3. Same value, different form.
SimplifySpanish: Simplificar To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2. 8/6: GCF is 2 → 8÷2 / 6÷2 = 4/3 = 1 1/3
ReciprocalSpanish: Recíproco A fraction turned upside down. You use it in keep-change-flip. The reciprocal of 3/4 is 4/3. To divide by 3/4, multiply by 4/3.

How it worksWorked example

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

Agent Chen has a route that is 31/2 miles long. She cuts it into 1/4-mile parts. How many parts are there?

  1. Change 31/2 to an improper fraction: 3 × 2 = 6 → 6 + 1 = 7 → 31/2 = 7/2
  2. Keep 7/2, change ÷ to ×, and flip 1/4: 7/2 ÷ 1/4 = 7/2 × 4/1
  3. Multiply the tops. Multiply the bottoms: 7/2 × 4/1 = 28/2
  4. Simplify: 28/2 = 14
  5. 31/2 ÷ 1/4 = 14. The route has 14 parts.

Now you trySame steps, your turn

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

Find 21/2 ÷ 1/2.

Answer:

Say it and write itSentence starters

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

  • Before dividing, I convert 2 1/2 to because it is easier to with improper fractions.

Word bank Mixed NumberImproper FractionConvertSimplifyReciprocalimproper5/2convertmultiplyreciprocalkeep-change-flip

Watch outA common mistake

A common mistake in Divide Mixed Numbers is dividing the whole-number parts and fraction parts separately instead of converting first — for example, treating 4 1/2 ÷ 1 1/2 as (4 ÷ 1) + (1/2 ÷ 1/2) = 5. Always convert each mixed number to one improper fraction first, then divide using Keep, Change, Flip: 4 1/2 ÷ 1 1/2 = 9/2 ÷ 3/2 = 9/2 × 2/3 = 3.

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

Lesson 6.106.10 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 divide mixed numbers by first changing them to improper fractions — one step at a time, with support.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.
    145
    Count the fifths in 145.

    Find 1 4/5 ÷ 3/5.

    1. 1Change 1 4/5 to an improper fraction.
    2. 2Multiply by the reciprocal of 3/5. What do you get?
    3. 3Simplify. What is the quotient?
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find 4 1/2 ÷ 3/4.

    Show your work

    Hint Change 4 1/2 to an improper fraction. Then multiply by 4/3.

    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.
    1114
    Count the fourths in 214 feet.

    A rope is 2 1/4 feet long. You cut it into 1/4-foot pieces. How many pieces do you get?

    1. 1Change 2 1/4 to an improper fraction.
    2. 2Keep 9/4. Change ÷ to ×. What is the reciprocal of 1/4?
    3. 3Multiply 9/4 × 4/1 and simplify. How many pieces?
    Final answer:
  2. 4Complete each step, then write the final answer.

    Change the mixed number first. Then divide: 1 1/2 ÷ 1/2.

    Show your work

    Hint 1 1/2 is 3/2. Then keep, change, flip.

    Final answer:
  3. 5Complete each step, then write the final answer.

    A baker has 2 1/2 cups of butter. Each batch of cookies needs 5/8 cup. How many batches can the baker make?

    Show your work

    Hint Find 2 1/2 ÷ 5/8. Change 2 1/2 to halves first.

    Final answer:
  4. 6Circle the letter of the best answer. Show how you know.

    Which is the correct first step for 2 3/4 ÷ 1/4?

    1. AChange 2 3/4 to 11/4
    2. BChange 2 3/4 to 5/4
    3. CFlip 2 3/4
    4. DDrop the 3/4 and find 2 ÷ 1/4

    Hint What must you do to a mixed number before you keep, change, flip?

    Show your work

Explain your thinkingWhy must you change a mixed number to an improper fraction before you flip and multiply?

Sentence starter First I change ___ to ___ because ___. · Then I flip ___, not the first number, because ___.

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