2.6 · Part II

Supported Application · Guided Entry to Today's Problem

Algorithm · Dividend

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: 2.6 · Part II

1Algorithm: A step-by-step set of rules or instructions to solve a math problem. Long Division Algorithm: D (Divide), M (Multiply), S (Subtract), B (Bring Down)

2Strategy Model — step by step

D - Divide: write quotient digit above the bar
M - Multiply: digit × divisor
S - Subtract: find the difference
B - Bring down: next digit from dividend

3Mathematical Word Bank

Algorithm (Algoritmo) — A step-by-step set of rules or instructions to solve a math problem.
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.
Divide Multi-Digit Numbers (Dividir números de varias cifras) — Separate a multi-digit number into equal groups to find a quotient.

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.

1 MULTIPLE CHOICE
What is 1,125 ÷ 9?
1. A125
2. B115
3. C135
4. D124
1. 1DivideHow many fit?
2. 2MultiplyMultiply back.
3. 3SubtractWhat is left?
4. 4Bring downNext digit.

📐 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

2.6 · Part II

On-Level Application · Standard Rigor

Algorithm · Dividend

Name: Date: Period: Learning Goal:

■ ADVANCED CONCEPT ANCHOR: 2.6 · Part II

1Algorithm: A step-by-step set of rules or instructions to solve a math problem. Long Division Algorithm: D (Divide), M (Multiply), S (Subtract), B (Bring Down)

2The Structural Procedure

D - Divide: write quotient digit above the bar
M - Multiply: digit × divisor
S - Subtract: find the difference
B - Bring down: next digit from dividend

3Mathematical Word Bank

Algorithm (Algoritmo) — A step-by-step set of rules or instructions to solve a math problem.
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.
Divide Multi-Digit Numbers (Dividir números de varias cifras) — Separate a multi-digit number into equal groups to find a quotient.

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 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]

1 MULTIPLE CHOICE
What is 4,896 ÷ 12?
1. A408
2. B48
3. C480
4. D380
2 MULTIPLE CHOICE
What is 7,225 ÷ 25?
1. A289
2. B29
3. C2,890
4. D389

SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]

3 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

📐 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

2.6 · Part II

Extension & Non-Routine Application

Algorithm · Dividend

Name: Date: Period: Learning Goal:

■ ADVANCED CONCEPT ANCHOR: 2.6 · Part II

1Algorithm: A step-by-step set of rules or instructions to solve a math problem. Long Division Algorithm: D (Divide), M (Multiply), S (Subtract), B (Bring Down)

2The Structural Procedure

D - Divide: write quotient digit above the bar
M - Multiply: digit × divisor
S - Subtract: find the difference
B - Bring down: next digit from dividend

3Mathematical Word Bank

Algorithm (Algoritmo) — A step-by-step set of rules or instructions to solve a math problem.
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.
Divide Multi-Digit Numbers (Dividir números de varias cifras) — Separate a multi-digit number into equal groups to find a quotient.

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 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]

1 MULTIPLE CHOICE
What is 5,084 ÷ 31?
1. A164
2. B154
3. C174
4. D164 r2

SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]

2 MULTIPLE CHOICE
Use the long division algorithm to find 936 ÷ 4.
1. A234
2. B232
3. C243
4. D209

📐 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