6.NOS.1 Lesson 6-11-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.11 · Part II

Supported Application · Guided Entry to Today's Problem

Fraction Division Problem Solving · Model

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.11 · Part II
1Fraction Division Word Problems
2Strategy Model — step by step
  1. Identify the Dividend (total amount being split or shared)
  2. Identify the Divisor (size of each group or part)
  3. Divide: Total ÷ Size = Number of Groups (or Total ÷ Groups = Size per Group)
3Mathematical Word Bank
  • Fraction Division Problem Solving (Resolución de problemas de división de fracciones) — Use fraction division to find an unknown number of groups or the size of each group.
  • Model (Modelo) — A picture or math way to show a problem so you can solve it.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Solution (Solución) — A number that makes the equation or inequality true.
  • Reasonableness (Razonabilidad) — Checking if your answer makes sense.
  • Inverse operations (Operaciones inversas) — Two math actions that undo each other, like × and ÷.
4Watch out
  • A common mistake in Fraction Division Problem Solving is reversing which fraction is the dividend and which is the divisor when setting up the equation from a word problem. For example: a pitcher holds 3/4 cup of punch, and each serving is 1/8 cup — how many servings? The correct setup is total ÷ group size = 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 servings. A student who reverses the setup calculates 1/8 ÷ 3/4 = 1/8 × 4/3 = 4/24 = 1/6, an answer smaller than 1 that can't possibly be a serving count. Before you submit, check: does my answer make sense as a NUMBER OF GROUPS? If the setup gives a fraction less than 1 for a 'how many' question, you likely swapped the dividend and divisor.
  1. 1 MULTIPLE CHOICE

    A board is 5/6 foot long. Each shelf bracket needs 1/6 foot. How many brackets fit?

    1. A5
    2. B1/36
    3. C6
    4. D5/36
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
    1. 1Whole over 13 becomes 3/1.
    2. 2KeepThe first fraction does not move.
    3. 3Change · Flip÷ becomes ×; flip the second fraction.
    4. 4CheckDividing by a piece smaller than 1 gives a BIGGER answer.
  2. 2 MULTIPLE CHOICE

    (Lesson 6.10) What is 1 1/2 ÷ 3/4?

    1. A2
    2. B1 1/8
    3. C3/4
    4. D9/8
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 6.10) Convert 3 2/5 to an improper fraction.

    1. A17/5
    2. B15/5
    3. C6/5
    4. D32/5
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
📐 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 6-11-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.11 · Part II

On-Level Application · Standard Rigor

Fraction Division Problem Solving · Model

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.11 · Part II
1Fraction Division Word Problems
2The Structural Procedure
  1. Identify the Dividend (total amount being split or shared)
  2. Identify the Divisor (size of each group or part)
  3. Divide: Total ÷ Size = Number of Groups (or Total ÷ Groups = Size per Group)
3Mathematical Word Bank
  • Fraction Division Problem Solving (Resolución de problemas de división de fracciones) — Use fraction division to find an unknown number of groups or the size of each group.
  • Model (Modelo) — A picture or math way to show a problem so you can solve it.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Solution (Solución) — A number that makes the equation or inequality true.
  • Reasonableness (Razonabilidad) — Checking if your answer makes sense.
  • Inverse operations (Operaciones inversas) — Two math actions that undo each other, like × and ÷.
4Watch out
  • A common mistake in Fraction Division Problem Solving is reversing which fraction is the dividend and which is the divisor when setting up the equation from a word problem. For example: a pitcher holds 3/4 cup of punch, and each serving is 1/8 cup — how many servings? The correct setup is total ÷ group size = 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 servings. A student who reverses the setup calculates 1/8 ÷ 3/4 = 1/8 × 4/3 = 4/24 = 1/6, an answer smaller than 1 that can't possibly be a serving count. Before you submit, check: does my answer make sense as a NUMBER OF GROUPS? If the setup gives a fraction less than 1 for a 'how many' question, you likely swapped the dividend and divisor.
  1. 1 MULTIPLE CHOICE

    Marcus solved 2/3 ÷ 1/4 and got 8/3 = 2 2/3. He says 'That can't be right because I started with less than 1.' Is Marcus's math correct? Is his reasoning correct?

    1. AHis math is correct (2 2/3), but his reasoning is wrong — dividing by a small fraction gives a larger result
    2. BHis math and reasoning are both correct — the answer should be less than 1
    3. CHis math is wrong — the answer should be 1/6
    4. DHis math is wrong — the answer should be 8/12
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Room 1 — Evidence Locker: Agent Torres has 7/8 pound of casting clay to lift footprints. Each cast uses 1/8 pound. How many casts can she make to unlock the door?

    1. A7
    2. B6
    3. C8
    4. D1/7
    Rewrite each fraction
    Work it out
    Simplify
  3. 3 MULTIPLE CHOICE

    Room 2 — Surveillance Map: A suspect's trail is 5/6 of a mile. Hidden checkpoints are spaced every 1/6 of a mile. How many checkpoints are on the trail?

    1. A5
    2. B6
    3. C1/5
    4. D4
    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 6-11-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.11 · Part II

Extension & Non-Routine Application

Fraction Division Problem Solving · Model

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.11 · Part II
1Fraction Division Word Problems
2The Structural Procedure
  1. Identify the Dividend (total amount being split or shared)
  2. Identify the Divisor (size of each group or part)
  3. Divide: Total ÷ Size = Number of Groups (or Total ÷ Groups = Size per Group)
3Mathematical Word Bank
  • Fraction Division Problem Solving (Resolución de problemas de división de fracciones) — Use fraction division to find an unknown number of groups or the size of each group.
  • Model (Modelo) — A picture or math way to show a problem so you can solve it.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Solution (Solución) — A number that makes the equation or inequality true.
  • Reasonableness (Razonabilidad) — Checking if your answer makes sense.
  • Inverse operations (Operaciones inversas) — Two math actions that undo each other, like × and ÷.
4Watch out
  • A common mistake in Fraction Division Problem Solving is reversing which fraction is the dividend and which is the divisor when setting up the equation from a word problem. For example: a pitcher holds 3/4 cup of punch, and each serving is 1/8 cup — how many servings? The correct setup is total ÷ group size = 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 servings. A student who reverses the setup calculates 1/8 ÷ 3/4 = 1/8 × 4/3 = 4/24 = 1/6, an answer smaller than 1 that can't possibly be a serving count. Before you submit, check: does my answer make sense as a NUMBER OF GROUPS? If the setup gives a fraction less than 1 for a 'how many' question, you likely swapped the dividend and divisor.
  1. 1 MULTIPLE CHOICE

    A ribbon is 4 1/2 feet long. Marta cuts the whole ribbon into pieces that are each 3/4 foot long. How many pieces does she get?

    1. A6 pieces
    2. B3 3/8 pieces
    3. C1/6 of a piece
    4. D5 1/4 pieces
    ✏️ 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