6.NOS.1 Lesson 6-11-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.11 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. A ribbon is 3/4 yard and each bow uses 1/4 yard. The total 3/4 is the dividend; 1/4 is the divisor.
  2. Equation: 3/4 ÷ 1/4. Keep, change, flip: 3/4 × 4/1 = 12/4 = 3.
  3. So we can make 3 bows. Check: 3 × 1/4 = 3/4. It matches, so it is reasonable.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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 ÷.
5Watch 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

    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. A4/5 ÷ 1/10
    2. B1/10 ÷ 4/5
    3. C4/5 × 1/10
    4. D4/5 + 1/10
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

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

    1. A4
    2. B1/16
    3. C16
    4. D1/4
    Rewrite each fraction
    Work it out
    Simplify
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem: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?
    2. 2A classmate at our table answered:6

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:A chemist has 3/4 liter of solution. Each test tube holds 1/8 liter. How many test tubes can be filled?
    2. 2Student's equation:3/4 ÷ 1/8 = 3/4 × 1/8
    3. 3Solve:3/4 × 1/8 = 3/32
    4. 4Answer:3/32 of a test tube

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Problem-Solving Error

    1. 1Problem:A tank has 3/4 gallon of water. Each bucket holds 1/6 gallon. How many buckets can be filled?
    2. 2Student's equation:1/6 ÷ 3/4
    3. 3Solve:1/6 × 4/3 = 4/18 = 2/9
    4. 4Answer:2/9 buckets

    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
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It