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

2.6 Small Group · Group 2

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

Divide Multi-Digit Numbers · Dividend · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do you divide big numbers?
1Repeat the cycle Divide → Multiply → Subtract → Bring Down until no digits are left to bring down; what is left at the end is the remainder — 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 1,344 ÷ 12. The dividend is 1,344 and the divisor is 12, so 12 goes outside the bracket and 1,344 goes inside.
  2. DIVIDE: 12 does not fit into 1, so I look at 13. How many 12s fit into 13? One. I write 1 above the 3.
  3. MULTIPLY: 1 × 12 = 12. I write 12 underneath the 13.
  4. SUBTRACT: 13 − 12 = 1. That is what is left so far.
  5. BRING DOWN: I bring the next digit, 4, down next to the 1 to make 14. Now I repeat the cycle.
  6. REPEAT: 14 ÷ 12 → 1 (written above the 4), 1 × 12 = 12, 14 − 12 = 2, and I bring down the last 4 to make 24.
  7. REPEAT: 24 ÷ 12 → 2 (written above the last 4), 2 × 12 = 24, 24 − 24 = 0. Nothing is left to bring down, so the remainder is 0.
  8. The digits I wrote are 1, 1, 2, so 1,344 ÷ 12 = 112. I check by multiplying: 12 × 112 = 1,344.
3Second Model — Try it together — then prove it
  1. Let's do 384 ÷ 8. DIVIDE: 8 does not fit into 3, so we look at 38. How many 8s fit into 38? (4 — write it above the 8.)
  2. MULTIPLY: 4 × 8 = ? (32 — write it under the 38.) SUBTRACT: 38 − 32 = ? (6.)
  3. BRING DOWN: bring the 4 down to make 64, then repeat. DIVIDE: 64 ÷ 8 = ? (8.) MULTIPLY: 8 × 8 = 64. SUBTRACT: 64 − 64 = 0.
  4. Nothing is left to bring down, so the remainder is 0 and 384 ÷ 8 = 48. Check: 8 × 48 = 384.
  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
  • Divide Multi-Digit Numbers (Dividir números de varias cifras) — Separate a multi-digit number into equal groups to find a quotient.
  • 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.
  • Remainder (Residuo) — What is left over when a number does not divide evenly.
  • Long division (División larga) — A method that repeats four steps — divide, multiply, subtract, bring down — until there are no digits left to bring down.
5Watch out
  • A common mistake in Divide Multi-Digit Numbers is skipping a placeholder zero in the quotient when a digit doesn't divide evenly, which shifts every digit after it out of place. For example, dividing 3,216 ÷ 3: 3 ÷ 3 = 1, but the next digit 2 doesn't divide by 3, so a 0 must be written before continuing — bring down the 1 to make 21 ÷ 3 = 7, then bring down 6 ÷ 3 = 2, giving the correct quotient 1,072. A student who skips writing that 0 and jumps straight to 21 ÷ 3 = 7 ends up with 172 instead of 1,072 — an answer off by a factor of ten. Always check: does a digit in your quotient go missing every time you 'can't divide'? If so, you dropped a placeholder zero.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Path 2: A side corridor displays 6,045 ÷ 9. Which door is correct?

    1. A671 R 6
    2. B671
    3. C672 R 3
    4. D67 R 6
    96045
  2. 2 MULTIPLE CHOICE

    A warehouse has 2,184 items to pack into boxes of 14. How many boxes are needed?

    1. A156 boxes
    2. B146 boxes
    3. C166 boxes
    4. D155 boxes
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Path 2: A side corridor displays 6,045 ÷ 9. Which door is correct?
    2. 2A classmate at our table answered:67 R 6

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 4 OPEN RESPONSE

    You already found 4,896 ÷ 12 = 408. WITHOUT dividing again, work out 4,896 ÷ 24 and 4,896 ÷ 6, and state the rule that connects them. Then say what happens to the quotient if the DIVIDEND doubles instead of the divisor.

    ✏️ Mathematical Justification & Response
  3. 5 ERROR ANALYSIS

    Spot the Mistake in 2,058 ÷ 14

    1. 1Problem:Divide 2,058 ÷ 14 with long division. Dividend = 2,058, divisor = 14.
    2. 2Divide, Multiply, Subtract:14 does not fit into 2, so start with 20. 20 ÷ 14 → 1. 1 × 14 = 14, and 20 − 14 = 6
    3. 3Bring down, repeat:Bring down the 5 to make 65. 65 ÷ 14 → 4. 4 × 14 = 56, and 65 − 56 = 9
    4. 4Bring down, repeat:Bring down the 8 to make 98. 98 ÷ 14 → 8. 8 × 14 = 112, and 98 − 112 = −14
    5. 5Final answer:Quotient = 148

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 ERROR ANALYSIS

    Find Sonia's Mistake

    1. 1Problem:1,536 ÷ 16
    2. 2Divide:16 does not fit into 1 or 15, so start with 153. 153 ÷ 16 → 9, written above the 3
    3. 3Multiply:9 × 16 = 144, written under the 153
    4. 4Subtract:153 − 144 = 19
    5. 5Bring down:Bring down the 6 to make 196
    6. 6Final answer:Quotient = 9 with 196 left over

    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