2.6 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.

Dividing means splitting a total into equal groups. Long division finds the quotient one digit at a time by repeating the same four steps: divide, multiply, subtract, bring down. 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

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.

3Mathematical 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.

4Watch 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]

SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]

🗣️ 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

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