6.NOS.1 Lesson 6-9-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.9 Small Group · Group 2

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

Divide Whole Numbers by Fractions · Whole Number · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do I divide a whole number by a fraction?
1Dividing by a fraction is the same as multiplying by its reciprocal (the fraction flipped over) — 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 Park has 4 pounds of powder and each bag holds 1/2 pound. I want 4 ÷ 1/2.
  2. Keep the 4. Change ÷ to ×. Flip 1/2 to make 2/1, which is just 2.
  3. Now I multiply: 4 × 2 = 8.
  4. So 4 ÷ 1/2 = 8. He can fill 8 bags. That makes sense: each pound fills 2 bags, and 4 pounds × 2 = 8.
3Second Model — Try it together — then prove it
  1. Let's try 3 ÷ 1/4 together. What do we keep? The 3.
  2. Change ÷ to ×, then flip 1/4 to 4/1, which is 4.
  3. Multiply: 3 × 4 = 12. So 3 ÷ 1/4 = 12.
  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 Whole Numbers by Fractions (Dividir números enteros entre fracciones) — Find how many fractional groups fit in a whole number by multiplying by the reciprocal.
  • Whole Number (Número entero) — A counting number with no fraction or decimal, like 0, 1, 2, 3.
  • Fraction (Fracción) — A number that shows part of a whole, like 3/4.
  • Reciprocal (Recíproco) — A fraction turned upside down.
  • Keep, Change, Flip (Mantener, cambiar, invertir) — A way to divide fractions: keep the first, change ÷ to ×, flip the second.
  • Quotient (Cociente) — The answer when you divide.
5Watch out
  • A common mistake in Divide Whole Numbers by Fractions is doing 'Keep, Change' but skipping the 'Flip' — students multiply by the divisor as it is instead of by its reciprocal. For example, for 6 ÷ 3/4, a student might write 6 × 3/4 = 4 1/2 and stop there, but the divisor 3/4 must be flipped to 4/3 first: 6 × 4/3 = 24/3 = 8. Before you submit, check: did I flip the second fraction (the divisor) upside down before multiplying?
SECTION 1 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 1 MULTIPLE CHOICE

    What is 6 ÷ 1/3?

    1. A18
    2. B2
    3. C6/3
    4. D3
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    What is 6 ÷ 2/3?

    1. A9
    2. B4
    3. C12
    4. D2/18
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 ERROR ANALYSIS

    Level 2 Extension — Catch the Catering Mistake

    1. 1Problem:6 cups of soup ÷ 3/4-cup bowls
    2. 2Keep, Change, Flip:6 × 3/4
    3. 3Multiply:18/4
    4. 4Simplify:4 1/2 bowls

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:What is 6 ÷ 2/3?
    2. 2A classmate at our table answered:2/18

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  3. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:8 ÷ 3/4
    2. 2Keep, Change, Flip:Flipped the wrong number — wrote 1/8 × 3/4 instead of 8 × 4/3
    3. 3Multiply:1/8 × 3/4 = 3/32

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 ERROR ANALYSIS

    Find the Division Error

    1. 1Problem:6 ÷ 2/3
    2. 2Keep, Change, Flip:6 × 2/3
    3. 3Multiply:12/3
    4. 4Simplify:4

    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