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

Lesson 6.1Division Expressions with Fractions and Whole Numbers

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can explain what dividing with a whole number and a unit fraction means — how many groups fit, or how much is in one group — find the quotient with a model, and check it by multiplying.

Why This Matters Agent Reyes finds a 3-foot strip of tape at the crime scene. The lab needs the tape cut into 1/4-foot sections for analysis. How many sections can be made? The answer cracks the code to the locked evidence vault.

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. 1/4 → 4/1
QuotientSpanish: Cociente The answer when you divide. 8 ÷ 1/2 = 16 is the quotient.
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.
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.

Let's try 2 ÷ 1/3. The bar model counted 6 thirds inside 2 wholes — now let's see why.

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 6.1Division Expressions with Fractions and Whole Numbers

Level 0Most support · every hint printed

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

Learning target I can explain what dividing with a whole number and a unit fraction means — how many groups fit, or how much is in one group — find the quotient with a model, and check it by multiplying.

Why This Matters Agent Reyes finds a 3-foot strip of tape at the crime scene. The lab needs the tape cut into 1/4-foot sections for analysis. How many sections can be made? The answer cracks the code to the locked evidence vault.

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

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

    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
    Steps to try
    1. 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?
    2. Dividing by a fraction asks a counting question about pieces, not 'a part of.' Predict: should the result be bigger or smaller than 3?
    3. Picture a 3-foot tape cut into 1/4-foot pieces, then set it up: put a 1 under the 3 and flip the 1/4.
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    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
    Steps to try
    1. Find the two jobs: which number is the total being split, and which is the size of each piece?
    2. Division setups read total ÷ piece size. The total always sits in front of the ÷ sign.
    3. Here the total is 2 and each piece is 1/3. Build the expression with the total first, then check it against each choice.
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A rope is 4 feet long. How many 1/2-foot pieces can be cut from it?

    1. A1/2 piece
    2. B2 pieces
    3. C4 pieces
    4. D8 pieces
    Steps to try
    1. Note the numbers: the rope is 4 feet long, and every piece is 1/2 foot — smaller than a whole foot.
    2. Start small: figure out how many 1/2-foot pieces fit into just 1 foot of rope.
    3. Dividing by a fraction is the same as multiplying by its reciprocal: 4/1 × 2/1.
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
    1. 1Whole over 13 becomes 3/1.
    2. 2KeepThe first fraction does not move.
    3. 3Change · Flip÷ becomes ×; flip the second fraction.
    4. 4CheckDividing by a piece smaller than 1 gives a BIGGER answer.
  2. 4Circle the letter of the best answer. Show how you know.

    A half-pan of brownies is shared equally among 4 people. How much of the whole pan does each get?

    1. A1/8
    2. B1/2
    3. C2
    4. D8
    Steps to try
    1. Draw half a pan, then split that half into 4 equal parts.
    2. How many of those parts fit in the WHOLE pan?
    3. The whole number is second here. Put a 1 under the 4 to get 4/1, then flip it to 1/4 and multiply.
    Show your work

Explain your thinkingWhy does dividing by a unit fraction always give a number larger than the dividend?

Sentence starter Dividing by 1/3 means finding how many ___ fit into ___, so the quotient is ___ than the dividend.

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