6.NOS.1 Lesson 6-9-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.9 · Part II

Supported Application · Guided Entry to Today's Problem

Divide Whole Numbers by Fractions · Whole Number

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.9 · Part II
1Dividing Fractions by Fractions
2Strategy Model — step by step
  1. Rewrite division as multiplication by the reciprocal of the divisor
  2. Cross-cancel common factors before multiplying
  3. Multiply numerators, multiply denominators, and simplify
3Mathematical 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.
4Watch 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?
  1. 1 MULTIPLE CHOICE

    What is 5 ÷ 1/2?

    1. A10
    2. B5/2
    3. C2.5
    4. D7
    ✏️ 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 6-9-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.9 · Part II

On-Level Application · Standard Rigor

Divide Whole Numbers by Fractions · Whole Number

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.9 · Part II
1Dividing Fractions by Fractions
2The Structural Procedure
  1. Rewrite division as multiplication by the reciprocal of the divisor
  2. Cross-cancel common factors before multiplying
  3. Multiply numerators, multiply denominators, and simplify
3Mathematical 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.
4Watch 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 ÷ 2/3?

    1. A9
    2. B4
    3. C12
    4. D2/18
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Detective Park has 4 cups of flour. Each batch of evidence-cookies needs 1/2 cup. How many batches can he make?

    1. A8
    2. B2
    3. C4
    4. D6
    Rewrite each fraction
    Work it out
    Simplify
  2. 3 MULTIPLE CHOICE

    The crew has 8 quarts of sports drink. Each detective's water bottle holds 4/5 of a quart. How many bottles can be filled?

    1. A10
    2. B5
    3. C32/5
    4. D12
    Rewrite each fraction
    Work it out
    Simplify
📐 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 6-9-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.9 · Part II

Extension & Non-Routine Application

Divide Whole Numbers by Fractions · Whole Number

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.9 · Part II
1Dividing Fractions by Fractions
2The Structural Procedure
  1. Rewrite division as multiplication by the reciprocal of the divisor
  2. Cross-cancel common factors before multiplying
  3. Multiply numerators, multiply denominators, and simplify
3Mathematical 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.
4Watch 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    What is the value of 6 ÷ 3/4?

    1. A8
    2. B4 1/2
    3. C2
    4. D2/9
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    A pizza shop has 8 whole pizzas. Each serving is 2/3 of a pizza. How many servings can they make? Write and solve an equation, then explain why the answer is greater than 8.

    ✏️ 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