6.NOS.1 Lesson 6-10-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.10 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Divide Mixed Numbers · Mixed Number · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I divide with mixed numbers?
1Always convert a mixed number to an improper fraction first, then divide using Keep, Change, Flip.
  • A mixed number, like 3 1/2, has a whole part and a fraction part. Before you can divide, you change each mixed number into an improper fraction (top heavier than bottom). Then you use Keep, Change, Flip. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. Agent Chen has a 3 1/2-mile route cut into 1/4-mile segments. I want 3 1/2 ÷ 1/4.
  2. First I convert 3 1/2. Multiply the whole by the bottom: 3 × 2 = 6. Add the top: 6 + 1 = 7. So 3 1/2 = 7/2.
  3. Now Keep, Change, Flip: keep 7/2, change ÷ to ×, flip 1/4 to 4/1.
  4. Multiply: 7/2 × 4/1 = 28/2.
  5. Simplify: 28/2 = 14. So 3 1/2 ÷ 1/4 = 14 segments.
3Mathematical Word Bank
  • Divide Mixed Numbers (Dividir números mixtos) — Change mixed numbers to improper fractions, then multiply by the reciprocal.
  • Mixed Number (Número mixto) — A whole number plus a fraction, like 2 1/3.
  • Improper Fraction (Fracción impropia) — A fraction where the top is bigger than or equal to the bottom, like 7/4.
  • Convert (Convertir) — To change a number to a new form but keep the same value.
  • Simplify (Simplificar) — To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2.
  • Reciprocal (Recíproco) — A fraction turned upside down. You use it in keep-change-flip.
4Watch out
  • A common mistake in Divide Mixed Numbers is dividing the whole-number parts and fraction parts separately instead of converting first — for example, treating 4 1/2 ÷ 1 1/2 as (4 ÷ 1) + (1/2 ÷ 1/2) = 5. Always convert each mixed number to one improper fraction first, then divide using Keep, Change, Flip: 4 1/2 ÷ 1 1/2 = 9/2 ÷ 3/2 = 9/2 × 2/3 = 3.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A baker has 2 1/4 cups of butter. Each batch of cookies needs 3/4 cup of butter. How many batches can the baker make?

    1. A3 batches
    2. B1 1/2 batches
    3. C2 batches
    4. D6 batches
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Mission 1: The stakeout shift is 4 1/2 hours long. Each agent covers a 1 1/2-hour watch. How many agent watches fill one shift?

    1. A3
    2. B6
    3. C2 1/2
    4. D4 1/2
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Mission 2: A surveillance route is 3 miles long, split into 1 1/2-mile patrol sections. How many sections are on the route?

    1. A2
    2. B1 1/2
    3. C4 1/2
    4. D3
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Mission 3: There are 7 1/2 feet of caution tape to seal a crime scene. Each doorway needs 2 1/2 feet. How many doorways can be sealed?

    1. A3
    2. B5
    3. C2 1/2
    4. D10
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:1 1/2 ÷ 3/4
    2. 2Convert:1 1/2 = 3/2
    3. 3Keep, Change, Flip:3/2 × 3/4
    4. 4Multiply:9/8 = 1 1/8

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Level 2 Extension — The Rookie Detective's Mistake

    1. 1Problem:4 1/2 ÷ 1 1/2
    2. 2Divide the whole parts:4 ÷ 1 = 4
    3. 3Divide the fraction parts:1/2 ÷ 1/2 = 1
    4. 4Combine:4 + 1 = 5 watches

    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
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