6.NOS.1 Lesson 6-11-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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6.11 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each word problem: should you DIVIDE or MULTIPLY to solve it?

    Target Categories: Division Problem Multiplication Problem
    • 2 FILL TABLE

      Solve each word problem by writing and solving an equation.

      ProblemEquationSolution
      A board is 7/8 foot long. Each shelf bracket needs 1/4 foot. How many brackets fit?
      A jug holds 5/6 liter. Each cup holds 1/3 liter. How many cups can be filled?
      A path is 3/4 mile long. A runner does laps of 3/8 mile. How many laps fit?
      ✏️ Scratchpad / Reasoning
    SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 3 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. 4 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
      1. 1Same size piecesCommon denominator first.
      2. 2OperateOnly then add or subtract.
      3. 3SimplifyDivide out common factors.
    3. 5 MULTIPLE CHOICE

      A trail is 3/4 mile long. A jogger runs laps of 1/4 mile each. How many laps does the jogger complete?

      1. A3 laps
      2. B1/3 lap
      3. C4 laps
      4. D3/16 lap
      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. 6 MULTIPLE CHOICE

      A board is 5/6 foot long. Each shelf bracket needs 1/6 foot. How many brackets fit?

      1. A5
      2. B1/36
      3. C6
      4. D5/36
      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.
    🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

    Group Discussion Prompt: How does your visual model justify your mathematical solution?

    🗣️ Partner A:
    Partner A: "I modeled this by identifying the relationship and..."
    👂 Partner B:
    Partner B: "I agree with your step because the standard mathematical rule states..."
    ✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

    Complete each sentence stem to demonstrate precise mathematical reasoning:

    BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
    BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
    SO The quantities follow the standard rule, so the final result is verified with certainty.
    📐 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