Multi-digit Division

Teacher Guide | Grade 4 Mathematics | FAST Success Kit
Florida B.E.S.T. Standard:
MA.4.NSO.2.2 - Divide a whole number up to four digits by a one-digit whole number with procedural reliability. Represent remainders as fractional parts of the divisor.
🎯 Learning Objective 20-25 min lesson
Students will: Divide multi-digit numbers using partial quotients and the standard algorithm. They will interpret remainders appropriately based on context and express remainders as fractional parts when appropriate.
Key Understanding: Division asks "how many groups?" or "how many in each group?" The quotient tells us the answer, and the remainder tells us what's left over. Remainders must be interpreted based on the problem context.
📦 Materials Needed
⚠ Common Misconceptions to Address

Misconception #1: Forgetting Zeros in the Quotient

When dividing 4,208 / 4, students write 12 instead of 1,052 because they skip the 0 in the tens place.

How to Address:

Ask: "How many 4s in 0 tens?" Answer: 0 - write it! Every place needs a digit in the quotient. Use estimation first: 4,208 / 4 should be about 1,000, not 12.

Misconception #2: Remainder Larger Than Divisor

Students write 156 / 6 = 24 R 12 (remainder should be less than 6).

How to Address:

Rule: The remainder must ALWAYS be less than the divisor. If it's not, you can still take out more groups! 12 / 6 = 2 more, so the answer is 26.

Misconception #3: Ignoring Remainder Context

For "45 students need buses that hold 7. How many buses?" students write 6 R 3 instead of 7 buses.

How to Address:

Always ask: "What does the remainder mean in this problem?" Sometimes round up (buses), sometimes drop (full bags), sometimes express as fraction (sharing equally).

📋 Division Strategies

1. Partial Quotients (Most Flexible)

Subtract "chunks" of the divisor using friendly numbers. Students choose their own multiples.

Example: 846 / 6 846 - 600 (6 x 100) --> 100 246 - 240 (6 x 40) --> 40 6 - 6 (6 x 1) --> 1 0 ---- 141

2. Standard Algorithm (Most Efficient)

Divide, Multiply, Subtract, Bring down - repeat for each place.

141 ----- 6 | 846 6 (6 x 1 hundred = 6 hundreds) -- 24 (bring down 4 tens) 24 (6 x 4 tens = 24 tens) -- 06 (bring down 6 ones) 6 (6 x 1 = 6) -- 0
🔬 Interpreting Remainders

Three Ways to Handle Remainders:

  1. Round Up: "47 students, 8 per van. How many vans?" 47/8 = 5 R 7. Need 6 vans (can't leave 7 students behind!)
  2. Drop the Remainder: "48 stickers, 7 per page. How many full pages?" 48/7 = 6 R 6. Answer: 6 full pages.
  3. Express as Fraction: "Share 23 cookies among 4 friends equally." 23/4 = 5 R 3. Each gets 5 3/4 cookies.
📝 Lesson Steps
1

Connect to Multiplication (3 min)

Review division as the inverse of multiplication.

SAY THIS:

"If 6 x 7 = 42, what's 42 / 6? What's 42 / 7? Right! Knowing your multiplication facts helps you divide!"

2

Introduce Partial Quotients (6 min)

Model dividing 156 / 6 using partial quotients.

  • Ask: "How many 6s can we easily take out? 10? 20? Let's try 20."
  • 6 x 20 = 120. 156 - 120 = 36.
  • "How many 6s in 36?" 6 x 6 = 36. 36 - 36 = 0.
  • Add partial quotients: 20 + 6 = 26.
3

Teach Standard Algorithm (6 min)

Model the same problem with the standard algorithm, connecting each step.

SAY THIS:

"In partial quotients, we subtracted 6 x 20 first. In the standard algorithm, we work place by place. How many 6s in 15 tens? That's 2 tens, or 20! Same idea, different format."

4

Practice with Remainders (5 min)

Work through 157 / 6 together.

  • 156 / 6 = 26... but we have 157, so there's 1 left over.
  • 157 / 6 = 26 R 1 (check: 26 x 6 + 1 = 157)
5

Interpret Remainders in Context (4 min)

Present word problems and discuss how to handle the remainder.

6

Independent Practice

Distribute worksheets. Allow students to choose their preferred method.

💻 IXL Skills to Assign

Recommended IXL Practice:

Divide 2-digit by 1-digit Divide 3-digit by 1-digit Divide 4-digit by 1-digit Division with remainders Interpret remainders Division word problems
🏠 Differentiation

For struggling students: Start with 2-digit dividends. Use partial quotients with very friendly numbers (10, 20, 100). Provide multiplication charts.

For advanced students: Include larger dividends, introduce 2-digit divisors conceptually, work with mixed remainder interpretations.

For home: Practice equal sharing scenarios - dividing snacks, splitting collections, sharing time equally.

FAST Success Kit | Grade 4 | Multi-digit Division Standard: MA.4.NSO.2.2