6.NOS.1 Lesson 6-11-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.11 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Fraction Division Problem Solving · Model · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I solve a fraction division word problem?
1Total goes first (dividend), group size goes second (divisor): total ÷ group size. Then check your answer by multiplying it back.
  • In a word problem, the total amount is the dividend (the number being split) and the size of each group is the divisor (what you divide by). Write the equation, solve with Keep, Change, Flip, then check that the answer makes sense. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. Agent Torres has 2/3 gallon of dust and each test uses 1/6 gallon. I ask: how many tests fit?
  2. The total 2/3 is the dividend. The size of each test 1/6 is the divisor. My equation is 2/3 ÷ 1/6.
  3. Keep 2/3, change to ×, flip 1/6 to 6/1: 2/3 × 6/1 = 12/3 = 4.
  4. So she can run 4 tests. I check by multiplying back: 4 × 1/6 = 4/6 = 2/3. It matches the total, so the answer is reasonable.
3Mathematical Word Bank
  • Fraction Division Problem Solving (Resolución de problemas de división de fracciones) — Use fraction division to find an unknown number of groups or the size of each group.
  • Model (Modelo) — A picture or math way to show a problem so you can solve it.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Solution (Solución) — A number that makes the equation or inequality true.
  • Reasonableness (Razonabilidad) — Checking if your answer makes sense.
  • Inverse operations (Operaciones inversas) — Two math actions that undo each other, like × and ÷.
4Watch out
  • 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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Marcus solved 2/3 ÷ 1/4 and got 8/3 = 2 2/3. He says 'That can't be right because I started with less than 1.' Is Marcus's math correct? Is his reasoning correct?

    1. AHis math is correct (2 2/3), but his reasoning is wrong — dividing by a small fraction gives a larger result
    2. BHis math and reasoning are both correct — the answer should be less than 1
    3. CHis math is wrong — the answer should be 1/6
    4. DHis math is wrong — the answer should be 8/12
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Room 1 — Evidence Locker: Agent Torres has 7/8 pound of casting clay to lift footprints. Each cast uses 1/8 pound. How many casts can she make to unlock the door?

    1. A7
    2. B6
    3. C8
    4. D1/7
    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. 3 MULTIPLE CHOICE

    Room 2 — Surveillance Map: A suspect's trail is 5/6 of a mile. Hidden checkpoints are spaced every 1/6 of a mile. How many checkpoints are on the trail?

    1. A5
    2. B6
    3. C1/5
    4. D4
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  4. 4 MULTIPLE CHOICE

    Room 5 — Final Keypad: The vault key code equals the number of 3/10-liter vials Torres can fill from a 9/10-liter bottle of fingerprint solution. What is the code?

    1. A3
    2. B9
    3. C1/3
    4. D6
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:A detective has 4/5 gallon of cleaning fluid. Each spray bottle holds 1/5 gallon. How many bottles can she fill?
    2. 2Student's equation:1/5 ÷ 4/5
    3. 3Solve:1/5 × 5/4 = 5/20 = 1/4
    4. 4Answer:1/4 of a bottle

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Level 2 Extension — Escape the Wrong Operation

    1. 1Problem:A tank holds 4/5 gallon of testing fluid. Each test uses 1/10 gallon. How many tests can be run to escape the lab?
    2. 2Student's equation:4/5 × 1/10
    3. 3Solve:4/5 × 1/10 = 4/50 = 2/25
    4. 4Answer:2/25 of a test

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It