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

Lesson 6.1Division Expressions with Fractions and Whole Numbers

Set B · Version ASecond form · supported practice

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.

RememberDivision Expressions with Fractions and Whole Numbers

Dividing Whole Numbers & Fractions Dividing by a fraction asks one question: how many of that small piece fit inside the whole amount? For 3 ÷ 1/4, we ask how many 1/4-foot pieces fit into 3 feet.

  1. Name the question: 3 ÷ 1/4 asks how many 1/4s fit in 3, and 1/2 ÷ 4 asks how much is in each of 4 equal shares.
  2. Use the model: each whole holds 4 fourths, so 3 wholes hold 3 × 4 = 12 fourths, and 3 ÷ 1/4 =
  3. Check by multiplying: 12 × 1/4 =
  4. Shortcut: dividing by 1/4 gives the same answer as multiplying by its reciprocal, 4

Words: Reciprocal (Recíproco)Quotient (Cociente)Dividend (Dividendo)Divisor (Divisor)Unit fraction (Fracción unitaria)

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort each statement: does dividing by the fraction give a result GREATER than the dividend, or LESS than the dividend?

    Groups: Quotient GREATER Than Dividend Quotient LESS Than Dividend
    • 5 ÷ 1/3
    • 8 ÷ 1/2
    • 6 ÷ 1/4
    • 4 ÷ 2
    • 10 ÷ 5
    • 12 ÷ 3

    Hint Work out each quotient first, then compare it with the dividend — the number being divided.

Part 2Practice the skillshow every step
  1. 2Circle the letter of the best answer. Show how you know.

    What is 6 ÷ 1/5?

    1. A1
    2. B5/6
    3. C6/5
    4. D30

    Hint 6 ÷ 1/5 asks: how many 1/5-size pieces fit into 6 wholes? Predict first — more or fewer than 6?

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    What is 4.8 ÷ 2?

    1. A0.24
    2. B2.4
    3. C2.6
    4. D24
    Show your work
Part 3Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Agent Reyes has used 6 feet of evidence tape, and that is 1/2 of a full roll. How many feet of tape are on a full roll? (6 ÷ 1/2 asks how much is in ONE whole roll.)

    1. A3 feet
    2. B12 feet
    3. C6 1/2 feet
    4. D1/12 foot

    Hint The 6 feet is only part of the roll. Which part?

    Show your work
Part 4Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ProblemHow many 1/3-foot pieces fit into 4 feet of tape? Find 4 ÷ 1/3.
    2. 2Student writesDividing makes the answer smaller, so 4 ÷ 1/3 = 4 ÷ 3 ≈ 1.3 pieces.
    3. 3Student's answerAbout 1.3 pieces

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint How many 1/3-foot pieces fit inside just ONE foot?

    Correct work
    Correct answer:
  2. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ProblemHow many 1/5-cup scoops fill a 6-cup container? Find 6 ÷ 1/5.
    2. 2Student writesI will flip the first number instead of the divisor: 6 ÷ 1/5 = 1/6 × 5 = 5/6 scoop.
    3. 3Student's answer5/6 of a scoop

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Which number do you flip when you divide — the dividend (6) or the divisor (1/5)?

    Correct work
    Correct answer:

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

Lesson 6.1Division Expressions with Fractions and Whole Numbers

Set B · Version BSecond form · core practice

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.

Part 1Practice the skillshow every step
  1. 1Circle the letter of the best answer. Show how you know.

    What is 8.4 ÷ 0.7?

    1. A0.12
    2. B1.2
    3. C12
    4. D120
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    What is 14.4 ÷ 1.2?

    1. A0.12
    2. B1.2
    3. C12
    4. D120
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    What is 3.78 ÷ 0.6?

    1. A0.063
    2. B0.63
    3. C6.3
    4. D63
    Show your work
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A detective has 6 yards of crime scene tape. She needs to mark off sections that are each 1/3 of a yard. She wants to know how many sections she can mark. 6 ÷ 1/3 = ?

    1. A2
    2. B3
    3. C6
    4. D18
    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    A detective has 6 yards of crime scene tape. She needs to mark off sections that are each 1/3 of a yard. She wants to know how many sections she can mark. Why is the answer bigger than 6?

    1. ABecause the pieces are smaller than a whole yard, so many of them fit
    2. BBecause dividing always makes numbers bigger
    3. CBecause 1/3 is negative
    4. DBecause 6 × 3 is multiplication, not division
    Show your work
  3. 6Circle the letter of the best answer. Show how you know.

    A detective has 6 yards of crime scene tape. She needs to mark off sections that are each 1/3 of a yard. She wants to know how many sections she can mark. If each section were 1/2 yard instead, how many sections?

    1. A3
    2. B12
    3. C18
    4. D24
    Rewrite each fraction
    Work it out
    Simplify

Explain your thinkingWhy does dividing by a unit fraction always give a number larger 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