6.NOS.1 Lesson 6-1-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.1 · Part II

Supported Application · Guided Entry to Today's Problem

Division of Fractions · Reciprocal

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.1 · Part II
1Dividing Whole Numbers & Unit Fractions
2Strategy Model — step by step
  1. Put a 1 under the whole number: 3 ÷ 1/4 = 3/1 ÷ 1/4
  2. Keep, Change, Flip: 3/1 ÷ 1/4 = 3/1 × 4/1
  3. Multiply across: 3/1 × 4/1 = 12/1 = 12
3Mathematical Word Bank
  • Division of Fractions (División de fracciones) — Finding how many groups of one fraction fit inside another amount.
  • Reciprocal (Recíproco) — A fraction turned upside down.
  • Quotient (Cociente) — The answer when you divide.
  • 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).
  • 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 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 1 MULTIPLE CHOICE

    What is 6 ÷ 1/5?

    1. A30
    2. B6/5
    3. C5/6
    4. D1
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 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
📐 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
6.NOS.1 Lesson 6-1-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.1 · Part II

On-Level Application · Standard Rigor

Division of Fractions · Reciprocal

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.1 · Part II
1Dividing Whole Numbers & Unit Fractions
2The Structural Procedure
  1. Put a 1 under the whole number: 3 ÷ 1/4 = 3/1 ÷ 1/4
  2. Keep, Change, Flip: 3/1 ÷ 1/4 = 3/1 × 4/1
  3. Multiply across: 3/1 × 4/1 = 12/1 = 12
3Mathematical Word Bank
  • Division of Fractions (División de fracciones) — Finding how many groups of one fraction fit inside another amount.
  • Reciprocal (Recíproco) — A fraction turned upside down.
  • Quotient (Cociente) — The answer when you divide.
  • 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).
  • 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

    A shelf is 5 feet long. Books are each 1/4 foot wide. How many books fit on the shelf? Which expression represents this?

    1. A5 ÷ 1/4 = 20 books
    2. B5 × 1/4 = 1 1/4 books
    3. C1/4 ÷ 5 = 1/20 book
    4. D5 + 1/4 = 5 1/4 books
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Agent Cole has 8 feet of evidence rope and cuts it into 1/3-foot pieces for tagging. What does 8 ÷ 1/3 mean?

    1. AHow many 1/3-foot pieces fit into 8 feet
    2. B1/3 of the 8 feet of rope
    3. C8 feet shortened by 1/3 of a foot
    4. D8 pieces that are each 1/3 foot long
    ✏️ Workspace & Solution Steps
SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 3 MULTIPLE CHOICE

    What is 6 ÷ 1/5?

    1. A30
    2. B6/5
    3. C5/6
    4. D1
    ✏️ Workspace & Solution Steps
📐 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
6.NOS.1 Lesson 6-1-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.1 · Part II

Extension & Non-Routine Application

Division of Fractions · Reciprocal

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.1 · Part II
1Dividing Whole Numbers & Unit Fractions
2The Structural Procedure
  1. Put a 1 under the whole number: 3 ÷ 1/4 = 3/1 ÷ 1/4
  2. Keep, Change, Flip: 3/1 ÷ 1/4 = 3/1 × 4/1
  3. Multiply across: 3/1 × 4/1 = 12/1 = 12
3Mathematical Word Bank
  • Division of Fractions (División de fracciones) — Finding how many groups of one fraction fit inside another amount.
  • Reciprocal (Recíproco) — A fraction turned upside down.
  • Quotient (Cociente) — The answer when you divide.
  • 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).
  • 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    What is the value of 6 ÷ 1/5?

    1. A30
    2. B6/5
    3. C1/30
    4. D11
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    Dividing 6 by 1/2 gives 12, but dividing 6 by 2 gives 3. How can dividing by a smaller number (1/2) give a bigger answer than dividing by a larger number (2)? Explain using a real-world example.

    ✏️ Mathematical Justification & Response
📐 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