2.6 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

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

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

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.
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.
MULTIPLY: 1 × 12 = 12. I write 12 underneath the 13.
SUBTRACT: 13 − 12 = 1. That is what is left so far.
BRING DOWN: I bring the next digit, 4, down next to the 1 to make 14. Now I repeat the cycle.
REPEAT: 14 ÷ 12 → 1 (written above the 4), 1 × 12 = 12, 14 − 12 = 2, and I bring down the last 4 to make 24.
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.
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

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.)
MULTIPLY: 4 × 8 = ? (32 — write it under the 38.) SUBTRACT: 38 − 32 = ? (6.)
BRING DOWN: bring the 4 down to make 64, then repeat. DIVIDE: 64 ÷ 8 = ? (8.) MULTIPLY: 8 × 8 = 64. SUBTRACT: 64 − 64 = 0.
Nothing is left to bring down, so the remainder is 0 and 384 ÷ 8 = 48. Check: 8 × 48 = 384.
Now prove it: say why that move had to work at all — not just that it did.
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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

1 FILL TABLE

Complete each division problem.

Division Problem Quotient
672 ÷ 8
2,208 ÷ 16
2,016 ÷ 14
1,560 ÷ 15
3,276 ÷ 12

✏️ Scratchpad / Reasoning
2 MATCHING GAME
Match each division problem to its quotient.
1. 450 ÷ 18
2. 1,008 ÷ 16
3. 1,440 ÷ 24
4. 2,100 ÷ 15
5. 864 ÷ 12
6. 1,825 ÷ 25
- A25
- B63
- C60
- D140
- E72
- F73

Division Problem	Quotient
672 ÷ 8
2,208 ÷ 16
2,016 ÷ 14
1,560 ÷ 15
3,276 ÷ 12

SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]

3 MULTIPLE CHOICE
What is 4,896 ÷ 12?
1. A408
2. B48
3. C480
4. D380
4 MULTIPLE CHOICE
What is 5,084 ÷ 31?
1. A164
2. B154
3. C174
4. D164 r2

SECTION 3 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]

5 MULTIPLE CHOICE
A school orders 3,648 pencils packed 24 to a box. How many boxes are there?
1. A152
2. B148
3. C160
4. D144
✏️ Workspace & Solution Steps
6 MULTIPLE CHOICE
Path 1: The first arcade door shows 4,928 ÷ 7. Which quotient lights the correct path?
1. A704
2. B74
3. C740
4. D703 r7

🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."

👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."

✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.

BUT An estimate provides a quick benchmark, but an exact proof is required for precision.

SO The quantities follow the standard rule, so the final result is verified with certainty.

📐 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.

✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key

Student Mastery Self-Assessment:

1 · Need More Support

2 · Getting Closer

3 · Got It / Solid

4 · Master / Can Teach It