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

6.1 Small Group · Group 1

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

Division of Fractions · Dividend · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What does it mean to divide by a fraction?
1Dividing by a fraction smaller than 1 gives a BIGGER answer, because many small pieces fit inside. Dividing a fraction BY a whole number gives a smaller answer, because one piece is being shared out.
  • Dividing by a fraction asks one question: how many of that small piece fit inside the whole amount? For 3 ÷ 1/4, we ask how many 1/4-foot pieces fit into 3 feet. 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. I want to cut a 3-foot strip of tape into 1/4-foot pieces. I ask: how many 1/4-foot pieces fit into 3 feet?
  2. First I look at just 1 foot. How many 1/4-foot pieces fit in 1 foot? Four, because 4 fourths make one whole.
  3. Now I have 3 feet. So I do 3 groups of 4: 3 × 4 = 12.
  4. So 3 ÷ 1/4 = 12. There are 12 pieces. The answer is bigger than 3 because each piece is very small.
3Mathematical Word Bank
  • Division of Fractions (División de fracciones) — Finding how many groups of one fraction fit inside another amount.
  • 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).
  • Quotient (Cociente) — The answer when you divide.
  • Reciprocal (Recíproco) — A fraction turned upside down.
  • 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
SECTION 3 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 MULTIPLE CHOICE

    Picture clue: a 5-inch fingerprint strip is split into 1/6-inch slivers under the microscope. Which division does the picture show, and what is the count?

    1. A5 ÷ 1/6 = 30 slivers
    2. B5 ÷ 6 = 5/6 of a sliver
    3. C1/6 ÷ 5 = 1/30 sliver
    4. D5 × 1/6 = 5/6 of an inch
    ✏️ Workspace & Solution Steps
SECTION 4 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:How many 1/3-foot pieces fit into 4 feet of tape? Find 4 ÷ 1/3.
    2. 2Student writes:Dividing makes the answer smaller, so 4 ÷ 1/3 = 4 ÷ 3 ≈ 1.3 pieces.
    3. 3Student's answer:About 1.3 pieces

    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 — Which Question Is Being Asked?

    1. 1Case file:A 9-foot strip of evidence tape is cut into 1/4-foot pieces. How many pieces?
    2. 2Detective writes:This is 1/4 ÷ 9 — split the 1/4-foot piece among 9 sections.
    3. 3Detective's answer:1/36 of a foot per piece

    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