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

6.2 Small Group · Group 2

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

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Lock 1 — Crack the code: What is (1/2) ÷ (1/4) in simplest form?

    1. A2
    2. B1/8
    3. C4
    4. D1/2
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
  2. 2 MULTIPLE CHOICE

    Lock 2 — The vault dial reads a fraction problem: What is (2/3) ÷ (1/6) in simplest form?

    1. A4
    2. B1/9
    3. C2/18
    4. D9/2
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
  3. 3 MULTIPLE CHOICE

    A recipe needs 2/3 cup of sugar. You only have a 1/6-cup scoop. How many scoops do you need?

    1. A4 scoops
    2. B3 scoops
    3. C6 scoops
    4. D2 scoops
    Rewrite each fraction
    Work it out
    Simplify
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A recipe needs 2/3 cup of sugar. You only have a 1/6-cup scoop. How many scoops do you need?
    2. 2A classmate at our table answered:2 scoops

    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:2/3 ÷ 1/2
    2. 2Change ÷ to × (but forgot to flip):2/3 × 1/2
    3. 3Multiply:2/6
    4. 4Simplify:1/3

    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 Division Error

    1. 1Problem:2/5 ÷ 3/4
    2. 2Keep, Change, Flip:2/5 × 3/4
    3. 3Multiply:6/20
    4. 4Simplify:3/10

    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