Decimal Division Decoders Worksheet
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Decimal Division Decoders
Level 1: Dividing Decimals by Whole Numbers
Name:
Date:
Golden Rule for Level 1:
Float the decimal point straight up onto the quotient line. Then divide just like whole numbers!
Divide → Multiply → Subtract → Bring Down
1 14.4 ÷ 4 Guided Model
Follow the 3 scaffolded steps
Step A: Estimate
Round $14.4$ to a friendly number that divides by $4$:
12 ÷ 4 = 3
My answer should be close to 3.
Step B: Divide with Grid
.
4
1 4 . 4
Step C: Check
Decimal placed up
Divided digits
Matches estimate?
Final Quotient:
2 25.8 ÷ 6 Independent Try
Show your full division steps
Estimate First
Pick a multiple of $6$ close to $25.8$:
____ ÷ 6 ≈ ____
Reminder: Put the decimal dot directly above the dot in $25.8$ before dividing!
Work Area Setup: 6 ) 2 5 . 8
6 2 5 . 8
25.8 ÷ 6 =
Checkpoint #1: Did you line up your decimal straight into the quotient?
How confident do you feel?
😄 Ready 🤔 Need Help
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Decimal Division Decoders
Level 2: The Power of 10 Shift (Decimal Divisors)
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Shift Rule: Never divide by a decimal! Multiply both numbers by 10 to move the decimal right:
× 10 = Jump 1 Spot →
0.5 ↷ (×10) 5 (Whole divisor!)
7.5 ↷ (×10) 75 (Shift dividend too!)
3 7.5 ÷ 0.5
Step 1: Shift → Step 2: Divide
1. Jump the Decimals
Divisor: 0.5 → 5
Dividend: 7.5 → 75
Equivalent Problem: 75 ÷ 5
2. Show Your Work
7.5 ÷ 0.5 =
4 9.6 ÷ 0.3
Jump both decimals 1 place right
Rewrite Problem:
New whole divisor:
New dividend:
Hint: Both hop right 1 time.
Division Workspace
9.6 ÷ 0.3 =
5 Real-World Mission: Ribbon Cutting
Word Problem
Maya has a spool of ribbon that is 4.8 meters long. Each ribbon bookmark she makes requires 0.6 meters of ribbon. How many bookmarks can Maya cut?
Visual Strip Model
Total Length: 4.8 meters
0.6m
0.6m
0.6m
... ?
Equation: 4.8 ÷ 0.6 = _____
Answer Sentence:
Maya can make bookmarks.
Mission Complete! Check your work: Did you shift both numbers equally?
Teacher Stamp / Initials:
Decimal Division Decoders Answer Key
Decimal Division Decoders
Teacher Answer Key & Diagnostic Guide • Level 1
TEACHER RESOURCE
Grades 6–7 IEP Support
Key Teaching Focus: Ensure students place the decimal point on the quotient line prior to initiating standard division. If a student calculates $36$ instead of $3.6$, revisit the estimation anchor immediately ($12 \div 4 = 3$).
1 14.4 ÷ 4 Exact Answer: 3.6
Scaffolded Model
Step-by-Step Breakdown:
Step A (Estimate): $12 \div 4 = 3$. Student verifies quotient is near 3.
Step B (Place Decimal): Put the decimal straight up above the decimal in $14.4$.
Step C (Divide Digits):
- $4$ goes into $14$ three times ($4 \times 3 = 12$). Subtract: $14 - 12 = 2$.
- Bring down $4$ to make $24$.
- $4$ goes into $24$ six times ($4 \times 6 = 24$). Remainder: $0$.
3.6
4 14.4
- 12
24
- 24
0
2 25.8 ÷ 6 Exact Answer: 4.3
Independent Practice
Step-by-Step Breakdown:
Estimate: $24 \div 6 = 4$. Quotient must be just above 4.
Division Steps:
- Float decimal straight up above the dot in $25.8$.
- $6$ goes into $25$ four times ($6 \times 4 = 24$). Remainder $1$.
- Bring down $8$ to make $18$.
- $6$ goes into $18$ three times ($6 \times 3 = 18$). Remainder: $0$.
4.3
6 25.8
- 24
18
- 18
0
Level 1 Diagnostic & Prompting Guide
Common Misconception:
Student writes $0.36$ or $36$ because they forget to place the decimal dot first or shift digits sideways.
Prompting Questions:
"What was your estimate? If you have about $14$ dollars split among 4 friends, could each friend get $36$ dollars? Where should the dot go?"
IEP Accommodation Tip:
Provide a colored highlighter to draw a vertical "elevator beam" directly from the dividend's decimal up to the quotient before pencil touches paper.
Sensory / Motor Support:
Use graph paper turned sideways or grid boxes to align the ones and tenths columns strictly.
Decimal Division Decoders
Teacher Answer Key & Diagnostic Guide • Level 2
PAGE 2 SOLUTIONS
