6.NOS.1 Lesson 6-2-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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6.2 Small Group · Group 1

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

Divide Fractions · Dividend · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I divide one fraction by another fraction?
1To divide fractions, multiply the first by the reciprocal of the second, then simplify. A mixed number has to become an improper fraction BEFORE that happens.
  • When you divide a fraction by a fraction, you keep the first fraction, change ÷ to ×, and flip the second fraction (the divisor) to its reciprocal. Then multiply and simplify. 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 Rivera has 3/4 pound and each portion is 1/8 pound. I want 3/4 ÷ 1/8.
  2. Keep 3/4. Change ÷ to ×. Flip the divisor 1/8 to its reciprocal 8/1.
  3. Multiply across: 3/4 × 8/1 = 24/4.
  4. Simplify: 24/4 = 6. So 3/4 ÷ 1/8 = 6. She can make 6 portions.
3Mathematical Word Bank
  • Divide Fractions (Dividir fracciones) — Multiply the first fraction by the reciprocal of the second fraction.
  • 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).
  • Reciprocal (Recíproco) — A fraction turned upside down.
  • Quotient (Cociente) — The answer when you divide.
  • Simplify (Simplificar) — To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2.
4Watch out
  • A common mistake in Divide Fractions is flipping the wrong fraction: students flip the dividend (the first fraction) instead of the divisor (the second fraction). For example, solving 3/4 ÷ 5/8 by flipping 3/4 to 4/3 and keeping 5/8 gives 4/3 × 5/8 = 20/24 = 5/6 — but only the divisor gets flipped. Keep 3/4, change ÷ to ×, and flip only the divisor 5/8 to its reciprocal 8/5: 3/4 × 8/5 = 24/20 = 6/5. Before you submit, check that the fraction you kept (the dividend) is still facing the same way it started.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each division: will the quotient be GREATER than 1 or LESS than 1?

    Target Categories: Quotient Greater Than 1 Quotient Less Than 1
    • 2 FILL TABLE

      Divide each pair of fractions using Keep, Change, Flip.

      ProblemKeep, Change, FlipQuotient
      1/2 ÷ 1/6
      3/4 ÷ 1/4
      2/3 ÷ 1/3
      5/8 ÷ 1/4
      ✏️ Scratchpad / Reasoning
    SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
    1. 3 MULTIPLE CHOICE

      What is 1/2 ÷ 1/4?

      1. A2
      2. B1/8
      3. C4
      4. D1/2
      ✏️ Workspace & Solution Steps
    2. 4 MULTIPLE CHOICE

      What is 3/4 ÷ 1/8?

      1. A6
      2. B3/32
      3. C8/3
      4. D24
      ✏️ Workspace & Solution Steps
    SECTION 3 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 5 MULTIPLE CHOICE

      What is the reciprocal of 3/5?

      1. A5/3
      2. B3/5
      3. C5/5
      4. D1/3
      Rewrite each fraction
      Work it out
      Simplify
      1. 1Same size piecesCommon denominator first.
      2. 2OperateOnly then add or subtract.
      3. 3SimplifyDivide out common factors.
    2. 6 MULTIPLE CHOICE

      What is the first step in evaluating 2 1/2 ÷ 1/4?

      1. ARewrite 2 1/2 as the improper fraction 5/2
      2. BFlip 2 1/2 to 1/2 2
      3. CDivide 2 by 1/4 and ignore the half
      4. DAdd 2 + 1/2 + 1/4
      ✏️ 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