6.NOS.1 Lesson 6-1-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.1 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Visual Models · Division of Fractions · Dividend · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. Let's try 2 ÷ 1/3. The question it asks is: how many 1/3-size pieces fit into 2 wholes?
  2. How many thirds are in 1 whole? Three.
  3. We have 2 wholes, so 2 × 3 = 6. That means 2 ÷ 1/3 = 6.
  4. The answer is bigger than the 2 we started with, because each piece is smaller than one whole.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    Which expression means 'how many 1/3-size pieces are in 2'?

    1. A2 ÷ 1/3
    2. B2 × 1/3
    3. C1/3 ÷ 2
    4. D2 + 1/3
    ✏️ Workspace & Solution Steps
  2. 2 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
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A rope is 4 feet long. How many 1/2-foot pieces can be cut from it?

    1. A8 pieces
    2. B2 pieces
    3. C4 pieces
    4. D1/2 piece
    Write any whole number over 1
    Keep · Change · Flip
    Multiply across
    Simplify · label the units
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A rope is 4 feet long. How many 1/2-foot pieces can be cut from it?
    2. 2A classmate at our table answered:2 pieces

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:How many 1/5-cup scoops fill a 6-cup container? Find 6 ÷ 1/5.
    2. 2Student writes:I will flip the first number instead of the divisor: 6 ÷ 1/5 = 1/6 × 5 = 5/6 scoop.
    3. 3Student's answer:5/6 of a scoop

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Interpretation Error

    1. 1Problem:Interpret 4 ÷ 1/5
    2. 2Student says:4 ÷ 1/5 means 1/5 of 4
    3. 3Student's answer:4/5

    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
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