6.NOS.1 Lesson 6-2-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.2 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

Divide Fractions · Dividend · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — 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 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.
3Second Model — Try it together — then prove it
  1. Let's try 1/2 ÷ 1/4. Keep 1/2, change to ×, flip 1/4 to 4/1.
  2. Multiply: 1/2 × 4/1 = 4/2.
  3. Simplify: 4/2 = 2. So 1/2 ÷ 1/4 = 2.
  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
  • 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.
5Watch 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 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
  2. 2 MATCHING GAME

    Match each fraction division to its quotient.

    1. 4/5 ÷ 2/5
    2. 3/4 ÷ 3/8
    3. 5/6 ÷ 1/3
    4. 2/3 ÷ 1/6
    5. 7/8 ÷ 1/4
    6. 1/2 ÷ 3/4
    • A2
    • B2
    • C2 1/2
    • D4
    • E3 1/2
    • F2/3
SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 3 MULTIPLE CHOICE

    What is (3/4) ÷ (1/2)?

    1. A3/2
    2. B3/8
    3. C1/2
    4. D2/3
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
  2. 4 MULTIPLE CHOICE

    What is (2/3) ÷ (4/9)?

    1. A3/2
    2. B8/27
    3. C2/3
    4. D9/4
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
  3. 5 MULTIPLE CHOICE

    What is (5/6) ÷ (5/12)?

    1. A2
    2. B1/2
    3. C25/72
    4. D12/5
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
  4. 6 MULTIPLE CHOICE

    What is (7/8) ÷ (1/4)?

    1. A7/2
    2. B7/32
    3. C1/2
    4. D4/7
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
🗣️ 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
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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It