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

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

Division of Fractions · Dividend · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What does it mean to divide by a fraction?
1Dividing by a fraction smaller than 1 gives a BIGGER answer, because many small pieces fit inside. Dividing a fraction BY a whole number gives a smaller answer, because one piece is being shared out.
  • 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. 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. I want to cut a 3-foot strip of tape into 1/4-foot pieces. I ask: how many 1/4-foot pieces fit into 3 feet?
  2. First I look at just 1 foot. How many 1/4-foot pieces fit in 1 foot? Four, because 4 fourths make one whole.
  3. Now I have 3 feet. So I do 3 groups of 4: 3 × 4 = 12.
  4. So 3 ÷ 1/4 = 12. There are 12 pieces. The answer is bigger than 3 because each piece is very small.
3Mathematical Word Bank
  • Division of Fractions (División de fracciones) — Finding how many groups of one fraction fit inside another amount.
  • Dividend (Dividendo) — The total number being divided into equal groups (the number inside the division bracket).
  • Divisor (Divisor) — The number of equal groups you are dividing into (the number outside the division bracket).
  • Quotient (Cociente) — The answer when you divide.
  • Reciprocal (Recíproco) — A fraction turned upside down.
  • Unit fraction (Fracción unitaria) — A fraction with 1 on top, like 1/4.
4Watch out
  • 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.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    What does 3 ÷ 1/4 mean?

    1. AHow many 1/4-size pieces fit into 3
    2. B3 groups of 1/4
    3. C3 minus 1/4
    4. D1/4 of 3
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which expression means 'how many 1/3-size pieces are in 2'?

    1. A2 ÷ 1/3
    2. B2 × 1/3
    3. C1/3 ÷ 2
    4. D2 + 1/3
    ✏️ Workspace & Solution Steps
  3. 3 DRAG SORT

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

    Target Categories: Quotient GREATER Than Dividend Quotient LESS Than Dividend
    • 4 MATCHING GAME

      Match each division expression to its quotient.

      1. 5 ÷ 1/2
      2. 6 ÷ 1/3
      3. 2 ÷ 1/6
      4. 4 ÷ 1/4
      5. 3 ÷ 1/5
      6. 7 ÷ 1/2
      • A10
      • B18
      • C12
      • D16
      • E15
      • F14
    SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 5 MULTIPLE CHOICE

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

      1. A8 pieces
      2. B2 pieces
      3. C4 pieces
      4. D1/2 piece
      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. 6 MULTIPLE CHOICE

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

      1. A1/8
      2. B2
      3. C4/2
      4. D1/2
      ✏️ Workspace & Solution Steps
    🗣️ 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