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

Lesson 6.26.1 · 6.2 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 6.1 · 6.2 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
ReciprocalSpanish: Recíproco A fraction turned upside down. 2/9 → 9/2
QuotientSpanish: Cociente The answer when you divide. 8/9 ÷ 2/9 = 4
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 8/9 ÷ 2/9, 8/9 is the dividend.
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 8/9 ÷ 2/9, 2/9 is the divisor.
Unit fractionSpanish: Fracción unitaria A fraction with 1 on top, like 1/4. 1/2, 1/3, 1/4, 1/5 — each represents one equal part of a whole
SimplifySpanish: Simplificar To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2. 8/12 → GCF is 4 → 8÷4 / 12÷4 = 2/3

How it worksWorked exampledividing a fraction by a fraction

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

A pitcher holds 8/9 liter of lemonade. Each glass takes 2/9 liter. How many glasses can be filled?

  1. Write the division. 8/9 ÷ 2/9
  2. Keep, Change, Flip. Keep 8/9, change ÷ to ×, flip the divisor to 9/2
  3. Multiply across. 8/9 × 9/2 = 72/18
  4. Simplify. 72/18 = 4 glasses

Answer: The pitcher fills 4 glasses that each hold 2/9 liter.

Now you trySame steps, your turn

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

A roll holds 6/7 meter of tape. Each label uses 2/7 meter. How many labels can be made?

  1. Write the division. ÷
  2. Keep, Change, Flip. 6/7 × /
  3. Multiply across. /
  4. Simplify. labels
Answer:number of labels

Say it and write itSentence starters

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

  • To divide by , I multiply by its reciprocal .
  • The quotient counts how many groups of fit inside .
  • I did not need a common denominator because .
  • After multiplying across, I simplified to .

Word bank reciprocaldividenddivisorquotientkeepchangeflipmultiply acrosssimplifygroupsfit insidetape diagram

Watch outA common mistake

A common mistake in Divide Fractions is flipping the wrong fraction: students flip the dividend (the first fraction) instead of the divisor (the second fraction). For example, solving 3/4 ÷ 5/8 by flipping 3/4 to 4/3 and keeping 5/8 gives 4/3 × 5/8 = 20/24 = 5/6 — but only the divisor gets flipped. Keep 3/4, change ÷ to ×, and flip only the divisor 5/8 to its reciprocal 8/5: 3/4 × 8/5 = 24/20 = 6/5. Before you submit, check that the fraction you kept (the dividend) is still facing the same way it started.

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

Lesson 6.26.1 · 6.2 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 6.1 · 6.2 by using each lesson's big idea in mixed practice.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 6.1) What does 3 ÷ 1/4 mean?

    1. AHow many 1/4-size pieces fit into 3
    2. B1/4 of 3
    3. C3 groups of 1/4
    4. D3 minus 1/4

    Hint Re-read the expression: 3 is the total amount and 1/4 is the size of one piece. What question could that setup be asking?

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 6.1) Which expression means 'how many 1/3-size pieces are in 2'?

    1. A1/3 ÷ 2
    2. B2 ÷ 1/3
    3. C2 × 1/3
    4. D2 + 1/3

    Hint Find the two jobs: which number is the total being split, and which is the size of each piece?

    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    (Lesson 6.2) What is the reciprocal of 3/5?

    1. A1/3
    2. B3/5
    3. C5/3
    4. D5/5

    Hint Re-read 'reciprocal' — it's about the two numbers of the fraction trading places.

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  2. 4Circle the letter of the best answer. Show how you know.

    (Lesson 6.2) What is 1/2 ÷ 1/4?

    1. A1/8
    2. B1/2
    3. C2
    4. D4

    Hint This asks how many 1/4-size pieces fit inside 1/2 — the pieces are smaller than the amount.

    Show your work

Explain your thinkingWhy does 5/6 ÷ 1/12 = 10? How does the bar model show this?

Sentence starter 5/6 ÷ 1/12 = 10 because 5/6 is the same as ___ twelfths, and ___ twelfths divided by 1 twelfth = ___.

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