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

Lesson 6.116.10 · 6.11 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 6.10 · 6.11 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 6.10 · 6.11: 6.10 Divide Mixed Numbers, 6.11 Fraction Division Problem Solving. Work one example from each lesson, then prove you're caught up in the mixed practice.

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.
ModelSpanish: Modelo A picture or math way to show a problem so you can solve it. A bar model showing 3/4 split into 1/8-size pieces, or the equation 3/4 ÷ 1/8 = 6

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 + 1 = 7 → 31/2 = 7/2
  2. Keep, change, flip. Then multiply: 7/2 × 4/1 = 28/2 = 14
  3. 31/2 ÷ 1/4 = 14. The route has 14 parts.
  4. Agent Torres has 2/3 gallon of dust. Each test uses 1/6 gallon. How many tests can she run?
  5. Write total ÷ size of one test: 2/3 ÷ 1/6
  6. Keep, change, flip. Then multiply: 2/3 × 6/1 = 12/3 = 4
  7. Check by multiplying back: 4 × 1/6 = 4/6 = 2/3
  8. She can run 4 tests.

Now you trySame steps, your turn

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

Find 11/2 ÷ 1/4.

Answer:

Say it and write itSentence starters

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

  • The total amount is the because it is being split into groups. The size of each group is the because we are dividing by that amount.

Word bank Mixed NumberImproper FractionConvertSimplifyReciprocalModeldividenddivisortotalgroupsplitequation

Watch out!A common mistake

A common mistake in Fraction Division Problem Solving is reversing which fraction is the dividend and which is the divisor when setting up the equation from a word problem. For example: a pitcher holds 3/4 cup of punch, and each serving is 1/8 cup

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

Lesson 6.116.10 · 6.11 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 6.10 · 6.11 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 6.10 · 6.11: 6.10 Divide Mixed Numbers, 6.11 Fraction Division Problem Solving. Work one example from each lesson, then prove you're caught up in the mixed practice.

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

    Find 1 1/4 ÷ 1/4.

    Show your work

    Hint Change 1 1/4 to 5/4. Then multiply by 4.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Find 2 1/2 ÷ 1/4.

    Show your work

    Hint Change 2 1/2 to 5/2. Then multiply by 4.

    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.

    A jug has 3/5 gallon of water. Each cup holds 1/5 gallon. How many cups can you fill?

    Show your work

    Hint Write total ÷ size of one cup.

    Final answer:
  2. 4Complete each step, then write the final answer.

    Agent Torres has 2 pounds of clay. Each cast uses 1/3 pound. How many casts can she make?

    Show your work

    Hint The total is 2 pounds. Divide 2 by 1/3.

    Final answer:

Explain your thinkingHow do you decide which value is the dividend and which is the divisor in a word problem?

Sentence starter The total amount is the ___ because it is being split into groups. The size of each group is the ___ because we are dividing by that amount.

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