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.

Start hereWords for this lesson

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

WordWhat it meansExample
Divide Mixed NumbersSpanish: Dividir números mixtos Change mixed numbers to improper fractions, then multiply by the reciprocal. 2 1/2 ÷ 1 1/4 = 5/2 ÷ 5/4 = 5/2 × 4/5 = 2
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.

Lesson 6.10 — Divide Mixed Numbers: Always convert a mixed number to an improper fraction first, then divide using Keep, Change, Flip.

  1. Lesson 6.11 — Fraction Division Problem Solving: Total goes first (dividend), group size goes second (divisor): total ÷ group size. Then check your answer by multiplying it back.

Now you trySame steps, your turn

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

From 6.10: Let's try 2 1/2 ÷ 1/2. First convert 2 1/2: 2 × 2 = 4, plus 1 = 5, so 2 1/2 = 5/2.

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 Divide Mixed NumbersMixed NumberImproper FractionConvertSimplifyReciprocaldividenddivisortotalgroupsplitequation

Watch outA 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 — how many servings? The correct setup is total ÷ group size = 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 servings. A student who reverses the setup calculates 1/8 ÷ 3/4 = 1/8 × 4/3 = 4/24 = 1/6, an answer smaller than 1 that can't possibly be a serving count. Before you submit, check: does my answer make sense as a NUMBER OF GROUPS? If the setup gives a fraction less than 1 for a 'how many' question, you likely swapped the dividend and divisor.

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.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 6.10) What is 1 1/2 ÷ 3/4?

    1. A1 1/8
    2. B2
    3. C3/4
    4. D9/8

    Hint 1 1/2 is a mixed number — it has to become one improper fraction before you divide.

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

    (Lesson 6.10) Convert 3 2/5 to an improper fraction.

    1. A6/5
    2. B15/5
    3. C17/5
    4. D32/5

    Hint Converting keeps the denominator 5 the same — only the top number changes.

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

    (Lesson 6.11) A ribbon is 4/5 of a yard long. Each bow uses 1/10 of a yard. Which equation finds how many bows can be made?

    1. A1/10 ÷ 4/5
    2. B4/5 ÷ 1/10
    3. C4/5 × 1/10
    4. D4/5 + 1/10

    Hint Name the roles: 4/5 yard is ALL the ribbon; 1/10 yard is what one bow uses.

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 6.11) A detective has 1/2 gallon of solution. Each test uses 1/8 gallon. How many tests can be run?

    1. A1/16
    2. B1/4
    3. C4
    4. D16

    Hint The total is 1/2 gallon; each test drains 1/8 gallon — you're counting tests.

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.

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.

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