Whole Number Worksheet 1
Day 1 • Whole Number Foundations
Whole Number Power
Name:
Date:
Solve each problem using the standard algorithm. Keep your columns aligned and show all regrouping steps in the workspace.
A Multi-Digit Addition (Regrouping)
Align place values carefully
\( 47,859 + 28,476 \)
Answer:
\( 164,528 + 97,845 \)
Answer:
\( 532,194 + 389,908 \)
Answer:
\( 84,392 + 15,608 + 23,714 \)
Answer:
B Multi-Digit Subtraction (Regrouping Across Zeros)
Record borrow marks clearly
\( 64,215 - 37,849 \)
Answer:
\( 90,004 - 43,628 \)
Answer:
\( 405,200 - 168,435 \)
Answer:
\( 700,000 - 328,154 \)
Answer:
Digit Dynamo • Whole Number Operations Page 1 of 2
Day 1 • Continued
Multiplication & Long Division
Show all partial products and remainders
C Multi-Digit Multiplication
Record partial products
\( 4,827 \times 6 \)
Answer:
\( 348 \times 24 \)
Answer:
\( 615 \times 47 \)
Answer:
\( 582 \times 136 \)
Answer:
D Multi-Digit Long Division
State quotient and remainder if any
\( 3,745 \div 7 \)
Answer:
\( 5,892 \div 12 \)
Answer:
\( 7,654 \div 25 \)
Answer:
\( 14,832 \div 32 \)
Answer:
Digit Dynamo • Whole Number Operations Page 2 of 2
Whole Number Answer Key KEY
Teacher Solutions • Day 1
Whole Number Solutions
Answer Key
Review aligned column additions, regrouping indicators, and step-by-step subtraction checks.
A Multi-Digit Addition Solutions
Regrouping shown
\( 47,859 + 28,476 \)
¹ ¹ ¹ ¹
4 7 , 8 5 9
+ 2 8 , 4 7 6
7 6 , 3 3 5
Answer: 76,335
\( 164,528 + 97,845 \)
¹ ¹ ¹ ¹
1 6 4 , 5 2 8
+ 9 7 , 8 4 5
2 6 2 , 3 7 3
Answer: 262,373
\( 532,194 + 389,908 \)
¹ ¹ ¹ ¹ ¹
5 3 2 , 1 9 4
+ 3 8 9 , 9 0 8
9 2 2 , 1 0 2
Answer: 922,102
\( 84,392 + 15,608 + 23,714 \)
¹ ¹ ¹ ¹ (84,392 + 15,608 = 100,000)
1 0 0 , 0 0 0
+ 2 3 , 7 1 4
1 2 3 , 7 1 4
Answer: 123,714
B Multi-Digit Subtraction Solutions
Borrowing steps verified
\( 64,215 - 37,849 \)
5 (13) (11) (10) (15)
6 4 , 2 1 5
- 3 7 , 8 4 9
2 6 , 3 6 6
Answer: 26,366
\( 90,004 - 43,628 \)
8 9 9 9 (14)
9 0 , 0 0 4
- 4 3 , 6 2 8
4 6 , 3 7 6
Answer: 46,376
\( 405,200 - 168,435 \)
3 9 (14) (11) 9 (10)
4 0 5 , 2 0 0
- 1 6 8 , 4 3 5
2 3 6 , 7 6 5
Answer: 236,765
\( 700,000 - 328,154 \)
6 9 9 9 9 (10)
7 0 0 , 0 0 0
- 3 2 8 , 1 5 4
3 7 1 , 8 4 6
Answer: 371,846
Digit Dynamo • Solutions Day 1 Page 1 of 2
Teacher Solutions • Day 1 Continued
Multiplication & Division Solutions
Answer Key
C Multiplication Partial Products
Standard algorithm details
\( 4,827 \times 6 \)
⁴ ¹ ⁴
4,827
× 6
28,962
Answer: 28,962
\( 348 \times 24 \)
348 × 24
PP1: 348 × 4 = 1,392
PP2: 348 × 20 = 6,960
Total: 8,352
Answer: 8,352
\( 615 \times 47 \)
615 × 47
PP1: 615 × 7 = 4,305
PP2: 615 × 40 = 24,600
Total: 28,905
Answer: 28,905
\( 582 \times 136 \)
582 × 6 = 3,492
582 × 30 = 17,460
582 × 100 = 58,200
Sum = 79,152
Answer: 79,152
D Long Division Steps
Step verification
\( 3,745 \div 7 \)
• \(37 \div 7 = 5\) (rem 2)
• Bring down 4 → \(24 \div 7 = 3\) (rem 3)
• Bring down 5 → \(35 \div 7 = 5\) (rem 0)
• Exact quotient: 535
Answer: 535
\( 5,892 \div 12 \)
• \(58 \div 12 = 4\) (rem \(10\); \(4 \times 12 = 48\))
• Bring down 9 → \(109 \div 12 = 9\) (rem \(1\); \(9 \times 12 = 108\))
• Bring down 2 → \(12 \div 12 = 1\) (rem 0)
• Exact quotient: 491
Answer: 491
\( 7,654 \div 25 \)
• \(76 \div 25 = 3\) (rem 1)
• Bring down 5 → \(15 \div 25 = 0\) (rem 15)
• Bring down 4 → \(154 \div 25 = 6\) (rem 4)
• \(306 \text{ R } 4\) (or \(306.16\))
Answer: 306 R 4 (306.16)
\( 14,832 \div 32 \)
• \(148 \div 32 = 4\) (rem \(20\); \(4 \times 32 = 128\))
• Bring down 3 → \(203 \div 32 = 6\) (rem \(11\); \(6 \times 32 = 192\))
• Bring down 2 → \(112 \div 32 = 3\) (rem \(16\))
• \(463 \text{ R } 16\) (or \(463.5\))
Answer: 463 R 16 (463.5)
Digit Dynamo • Solutions Day 1 Page 2 of 2
Decimal Operations Worksheet 2
Day 2 • Decimal Operations Mastery
Decimal Precision
Name:
Date:
Line up decimal points vertically before adding or subtracting. Insert placeholder zeros when necessary and show your work clearly.
A Decimal Addition (Line Up Place Values)
Add placeholder zeros if digits don't match
\( 42.68 + 19.745 \)
Answer:
\( 156.4 + 28.937 \)
Answer:
\( 8.094 + 73.65 + 14.8 \)
Answer:
\( 340.25 + 98.765 \)
Answer:
B Decimal Subtraction (Regrouping with Decimals)
Write top zeros before regrouping
\( 85.4 - 38.67 \)
Answer:
\( 120.05 - 64.382 \)
Answer:
\( 50.00 - 27.638 \)
Answer:
\( 412.3 - 185.746 \)
Answer:
Digit Dynamo • Decimal Operations Page 1 of 2
Day 2 • Continued
Decimal Multiplication & Division
Count decimal places and shift divisors as needed
C Decimal Multiplication
Multiply as whole numbers, then place decimal point
\( 4.75 \times 8 \)
Answer:
\( 6.3 \times 4.8 \)
Answer:
\( 14.25 \times 3.6 \)
Answer:
\( 0.84 \times 0.29 \)
Answer:
D Decimal Division
Make divisor a whole number before dividing
\( 43.68 \div 6 \)
Answer:
\( 78.4 \div 0.8 \)
Answer:
\( 21.75 \div 1.5 \)
Answer:
\( 9.18 \div 0.27 \)
Answer:
Digit Dynamo • Decimal Operations Page 2 of 2
Decimal Operations Answer Key KEY
Teacher Solutions • Day 2
Decimal Addition & Subtraction Solutions
Answer Key
Review aligned place values, inserted placeholder zeros, and regrouping steps.
A Decimal Addition Solutions
Zero-padded alignment
\( 42.68 + 19.745 \)
¹ ¹ ¹
4 2 . 6 8 0
+ 1 9 . 7 4 5
6 2 . 4 2 5
Answer: 62.425
\( 156.4 + 28.937 \)
¹ ¹
1 5 6 . 4 0 0
+ 2 8 . 9 3 7
1 8 5 . 3 3 7
Answer: 185.337
\( 8.094 + 73.65 + 14.8 \)
¹ ¹ ¹
8 . 0 9 4
7 3 . 6 5 0
+ 1 4 . 8 0 0
9 6 . 5 4 4
Answer: 96.544
\( 340.25 + 98.765 \)
¹ ¹ ¹
3 4 0 . 2 5 0
+ 9 8 . 7 6 5
4 3 9 . 0 1 5
Answer: 439.015
B Decimal Subtraction Solutions
Regrouping with zeros
\( 85.4 - 38.67 \)
7 (14) . (13) (10)
8 5 . 4 0
- 3 8 . 6 7
4 6 . 7 3
Answer: 46.73
\( 120.05 - 64.382 \)
0 (11) 9 . 9 (14) (10)
1 2 0 . 0 5 0
- 6 4 . 3 8 2
5 5 . 6 6 8
Answer: 55.668
\( 50.00 - 27.638 \)
4 9 . 9 9 (10)
5 0 . 0 0 0
- 2 7 . 6 3 8
2 2 . 3 6 2
Answer: 22.362
\( 412.3 - 185.746 \)
3 (10) (11) . (12) 9 (10)
4 1 2 . 3 0 0
- 1 8 5 . 7 4 6
2 2 6 . 5 5 4
Answer: 226.554
Digit Dynamo • Solutions Day 2 Page 1 of 2
Teacher Solutions • Day 2 Continued
Decimal Multiplication & Division Solutions
Answer Key
C Decimal Multiplication Solutions
Decimal shift verification
\( 4.75 \times 8 \)
• Multiply: \( 475 \times 8 = 3,800 \)
• Decimals in factors: 2 places
• Move decimal 2 places left:
38.00 = 38
Operation Showdown Worksheet 3
Day 3 • Mixed Operations Challenge
Operation Showdown
Name:
Date:
Integrate all four operations with whole numbers and decimals. Check operations carefully and explain errors in the Error Lab.
A Mixed Operation Sprint
Whole numbers & decimals
1. [ + ] \( 846.7 + 59.84 + 1,208.45 \)
Answer:
2. [ − ] \( 5,002.4 - 1,876.85 \)
Answer:
3. [ × ] \( 31.8 \times 4.25 \)
Answer:
4. [ ÷ ] \( 136.08 \div 5.4 \)
Answer:
B Error Lab • Find and Fix the Glitch
Spot the conceptual flaw and recalculate
Incorrect Student Work
18.4 + 2.75 = ?
Student thought:
(Treated decimals as whole numbers)
Explain the error:
Correct Solution:
Incorrect Student Work
2.4 × 0.15 = ?
\( 24 \times 15 = 360 \)
(Counted only 1 decimal place)
Explain the error:
Correct Solution:
Digit Dynamo • Mixed Operations Showdown Page 1 of 2
Day 3 • Continued
Multi-Step Real-World Challenges
Identify the operations required, show work, and include units
Problem 5 • Event Budgeting Multiplication • Subtraction
The student council bought 25 boxes of festival wristbands at $14.75 per box. They also spent $138.50 on banners. If the school gave them a total budget of $600.00, how much money do they have remaining?
Remaining Budget:
Problem 6 • Lab Distribution Addition • Division
A chemistry teacher combines three flasks containing 124.6 mL, 88.75 mL, and 146.65 mL of saline solution. The teacher then divides the total mixture equally among 16 student test beakers. Exactly how many milliliters will each beaker receive?
Milliliters per Beaker:
Problem 7 • Material Logistics Multiplication • Division
A builder orders 18 crates of wood tiles. Each crate weighs 42.5 kilograms. The builder transports the total weight across 4 equal truck trips. What is the cargo weight transported on each individual truck trip?
Weight per Trip:
Digit Dynamo • Mixed Operations Showdown Page 2 of 2
Operation Showdown Answer Key KEY
Teacher Solutions • Day 3
Mixed Operations Solutions
Answer Key
Review multi-operation execution, decimal alignment, place-value analysis, and conceptual error diagnostics.
A Mixed Operation Sprint Solutions
Algorithmic steps
1. [ + ] \( 846.7 + 59.84 + 1,208.45 \)
8 4 6 . 7 0
5 9 . 8 4
+ 1,2 0 8 . 4 5
2,1 1 4 . 9 9
Answer: 2,114.99
2. [ − ] \( 5,002.4 - 1,876.85 \)
5,0 0 2 . 4 0
- 1,8 7 6 . 8 5
Regroup across zeros:
3,1 2 5 . 5 5
Answer: 3,125.55
3. [ × ] \( 31.8 \times 4.25 \)
• \( 318 \times 425 = 135,150 \)
• Total decimals: 1 + 2 = 3 places
• Shift decimal: 135.150
• Total: 135.15
Answer: 135.15
4. [ ÷ ] \( 136.08 \div 5.4 \)
• Shift 1 place: \( 1,360.8 \div 54 \)
• \( 136 \div 54 = 2 \) (rem 28)
• \( 280 \div 54 = 5 \) (rem 10)
• \( 108 \div 54 = 2 \) → Quotient: 25.2
Answer: 25.2
B Error Lab Solutions • Diagnosis & Fix
Teacher diagnosis notes
Error Diagnosis
The student treated the decimal parts (.4 and .75) as whole numbers rather than place values. They added 4 + 75 = 79 instead of aligning tenths (.40 + .75 = 1.15).
¹ ¹ (Pad 18.4 with a trailing zero)
1 8 . 4 0
+ 2 . 7 5
2 1 . 1 5
Correct Solution: 21.15
Error Diagnosis
The student only counted 1 decimal place from 2.4 and completely ignored the 2 decimal places in 0.15. The product requires a total of 1 + 2 = 3 decimal places.
• Multiply: \( 24 \times 15 = 360 \)
• Total decimal places: 1 + 2 = 3 places
• Shift decimal 3 places left: \( 0.360 = 0.36 \)
Correct Solution: 0.36 (or 0.360)
Digit Dynamo • Solutions Day 3 Page 1 of 2
Teacher Solutions • Day 3 Continued
Multi-Step Real-World Solutions
Answer Key
Problem 5 • Event Budgeting Solution Multiplication • Addition • Subtraction
25 boxes of wristbands at $14.75 each, plus $138.50 banners, from a $600.00 budget.
• Step 1 (Wristbands): \( 25 \times \$14.75 = \$368.75 \)
• Step 2 (Total Expenses): \( \$368.75 + \$138.50 = \$507.25 \)
