Double Digit Practice Worksheet
N1
Double Digit Power • Evening Practice
Night 1 • Lessons 4-1 & 4-2: Multiples of 10 & Base-Ten Models
Name:
Date:
Quick Tip
Multiply basic facts first, then count zeros! Example: For \(40 \times 60\), multiply \(4 \times 6 = 24\), then attach two zeros \(\rightarrow 2,400\).
A Multiplication Patterns with Multiples of 10
- Basic fact: \(5 \times 3 = 15\)
\(50 \times 30 = \text{______}\)
Think: \((\text{\_\_} \times \text{\_\_}) \times 100 = \text{\_\_\_\_\_\_}\)
- Basic fact: \(7 \times 8 = 56\)
\(70 \times 80 = \text{______}\)
Answer: _________________
- Calculate mentally
\(90 \times 40 = \text{______}\)
Answer: _________________
- Watch the zeros!
\(50 \times 60 = \text{______}\)
Answer: _________________
B Use Place-Value Breakdown to Solve
5. Find \(24 \times 30\)
Break down \(24\) into tens and ones:
\(20 \times 30 = \text{\_\_\_\_\_\_}\)
\(4 \times 30 = \text{\_\_\_\_\_\_}\)
Total Product =
6. Find \(36 \times 20\)
Break down \(36\) into tens and ones:
\(30 \times 20 = \text{\_\_\_\_\_\_}\)
\(6 \times 20 = \text{\_\_\_\_\_\_}\)
Total Product =
C Word Problem Challenge
- The school cafeteria ordered 30 crates of crisp apples. Each crate holds 48 apples. How many total apples did the school order? Show your thinking in the space below.
Final Answer: apples
Self-Reflection: Easy! 😄 Just Right 🙂 Need Help 🤔
Page 1 of 4 • Grade 4 Math Home Reinforcement
N2
Double Digit Power • Evening Practice
Night 2 • Lesson 4-3: Estimate with Rounding & Compatible Numbers
Name:
Date:
Two Strategies
Rounding: Round each factor to the nearest ten (e.g., \(48 \times 32 \approx 50 \times 30 = 1,500\)).
Compatible Numbers: Pick nearby numbers that are easy to multiply mentally (e.g., \(25 \times 40 = 1,000\)).
A Estimate by Rounding to the Nearest Ten
1. \(38 \times 52\) Round each
\(38 \rightarrow\) rounds to:
\(52 \rightarrow\) rounds to:
Estimated Product:
2. \(79 \times 41\) Round each
\(79 \rightarrow\) rounds to:
\(41 \rightarrow\) rounds to:
Estimated Product:
3. \(63 \times 28\) Round each
\(63 \rightarrow\) rounds to:
\(28 \rightarrow\) rounds to:
Estimated Product:
4. \(91 \times 69\) Round each
\(91 \rightarrow\) rounds to:
\(69 \rightarrow\) rounds to:
Estimated Product:
B Reasoning: Overestimate or Underestimate?
- Maya estimates \(53 \times 74\) by rounding to \(50 \times 70 = 3,500\).
Is her estimate an overestimate or an underestimate? Explain why without finding the exact answer:
C Estimation in Action
- A community sports center has 26 rows of bleacher seats. Each row seats 48 spectators. About how many spectators can sit in the bleachers?
About spectators
Self-Reflection: Easy! 😄 Just Right 🙂 Need Help 🤔
Page 2 of 4 • Grade 4 Math Home Reinforcement
N3
Double Digit Power • Evening Practice
Night 3 • Lessons 4-4 & 4-5: Area Models & Partial Products
Name:
Date:
Area Model
Split both 2-digit factors into tens and ones. Calculate the area of all 4 smaller rectangles, then add them together to find the total product!
1 Complete the Area Model for \(34 \times 27\)
30 4
20 7
\(20 \times 30\) 600
\(20 \times 4\) ______
\(7 \times 30\) ______
\(7 \times 4\) ______
Add the 4 Partial Products:
600
+ ____ (tens \(\times\) ones)
+ ____ (ones \(\times\) tens)
+ ____ (ones \(\times\) ones)
Total = _______
2 Draw Your Own Area Model to Solve \(45 \times 23\)
Label dimensions (\(40 + 5\) and \(20 + 3\)) and draw the 4 boxes:
List Partial Products:
1. ________
2. ________
3. ________
4. ________
Product = _________
3 Matching Partial Products
For \(56 \times 32\):
Which are the four partial products?
A) 1500, 100, 180, 12 B) 1500, 180, 100, 12 C) 150, 10, 18, 12
Area Model Application:
A garden plot is 28 feet wide and 62 feet long. What is the total square footage?
Show work:
Area = ________ sq ft
Self-Reflection: Easy! 😄 Just Right 🙂 Need Help 🤔
Page 3 of 4 • Grade 4 Math Home Reinforcement
N4
Double Digit Power • Evening Practice
Night 4 • Lessons 4-6 & 4-7: Partial Products & Problem Solving
Name:
Date:
Persevere
Make Sense of Problems: 1. What do I know? 2. What am I solving for? 3. Does my answer make sense when compared to my estimate?
A Multiply Using Partial Products
1. Calculate \(43 \times 26\) Estimate: \(40 \times 30 \approx 1,200\)
43
× 26
______
______
______
______
______
\(6 \times 3\) (ones \(\times\) ones)
\(6 \times 40\) (ones \(\times\) tens)
\(20 \times 3\) (tens \(\times\) ones)
\(20 \times 40\) (tens \(\times\) tens)
Sum of partials
2. Calculate \(58 \times 34\) Estimate: \(60 \times 30 \approx 1,800\)
58
× 34
______
______
______
______
______
\(4 \times 8\) = ______
\(4 \times 50\) = ______
\(30 \times 8\) = ______
\(30 \times 50\) = ______
Sum = ______
B Persevere: Multi-Step Problem Solving
- The 4th grade is hosting a read-a-thon. There are 24 students in Mrs. Kim's class and each student read 35 pages. In Mr. Patel's class, 22 students each read 40 pages. Which class read more total pages, and by how many?
Mrs. Kim's Class:
Total = _________
Mr. Patel's Class:
Total = _________
Class with more pages: Difference: pages
- A bookstore receives 16 boxes of hardcovers with 18 books per box, and 25 boxes of paperbacks with 32 books per box. How many books did the bookstore receive in all?
Total Books Received:
Packet Complete! Rate your confidence: Ready for Test! 🚀 Need Review 📖
Page 4 of 4 • Grade 4 Math Home Reinforcement
Double Digit Study Guide
SG
Double Digit Study Guide
Topic 4 Test Preparation • 2-Digit by 2-Digit Multiplication
Student:
Test Date:
1
Multiples of 10 & Mental Math Patterns
When multiplying tens by tens, multiply the basic facts first, then count and attach the total number of zeros.
Fact + 1 Zero \(6 \times 40 = 240\) \(24 \text{ tens} = 240\)
Fact + 2 Zeros \(60 \times 40 = 2,400\) \(24 \text{ hundreds} = 2,400\)
Watch Out Fact! \(50 \times 60 = 3,000\) \(5 \times 6 = 30\) (has its own zero!)
2
Estimating Products: Rounding vs. Compatible Numbers
Method A: Round to Nearest 10
Round both factors to the nearest ten to get a close estimate:
\(48 \times 32 \approx ?\)
\(48 \rightarrow 50\)
\(32 \rightarrow 30\)
\(50 \times 30 = 1,500\)
Method B: Compatible Numbers
Change numbers to friendly values that are easy to compute:
\(26 \times 39 \approx ?\)
Think: \(25 \times 40\)
\(25 \times 4 = 100\)
\(25 \times 40 = 1,000\)
Underestimate: Both numbers rounded DOWN \(\rightarrow\) estimate is LESS than exact. Overestimate: Both numbers rounded UP \(\rightarrow\) estimate is MORE than exact.
3
Area Model & Partial Products (The "Box" Method)
Example: Solve \(43 \times 28\) by expanding each factor: \(43 = 40 + 3\) and \(28 = 20 + 8\).
40 3
20 8
\(20 \times 40\) 800
\(20 \times 3\) 60
\(8 \times 40\) 320
\(8 \times 3\) 24
Sum the 4 Partial Products:
800
320
60
+ 24
1,204
Check: \(40 \times 30 = 1,200\) ✓
Topic 4 Study Guide • Strategies & Foundations Page 1 of 2
SG
Double Digit Study Guide
Topic 4 Test Preparation • Algorithms, Pitfalls & Self-Check
Topic 4 Test Ready
Grade 4 Mathematics
4
Vertical Partial Products Algorithm (Step-by-Step)
56
× 34
24
200
180
1500
1,904
1 Multiply ones: \(4 \times 6 = 24\)
2 Multiply ones by tens: \(4 \times 50 = 200\)
Double Digit Answer Key
AK
Double Digit Answer Key
Complete Solutions • Nights 1 & 2
Educator & Parent Reference
Night 1: Multiples of 10 & Place Value Models (4-1 & 4-2) Pages 1 of Practice Packet
Part A: Multiplication Patterns
- 1. \(50 \times 30 = \mathbf{1,500}\) • \((5 \times 3) \times 100 = 15 \times 100 = 1,500\)
- 2. \(70 \times 80 = \mathbf{5,600}\) • \(7 \times 8 = 56\) plus 2 zeros
- 3. \(90 \times 40 = \mathbf{3,600}\) • \(9 \times 4 = 36\) plus 2 zeros
- 4. \(50 \times 60 = \mathbf{3,000}\) • \(5 \times 6 = 30\) plus 2 zeros \(= 3,000\)
Part B: Place Value Breakdown
5. \(24 \times 30 = \mathbf{720}\)
• \(20 \times 30 = 600\); \(4 \times 30 = 120\); \(600 + 120 = 720\)
6. \(36 \times 20 = \mathbf{720}\)
• \(30 \times 20 = 600\); \(6 \times 20 = 120\); \(600 + 120 = 720\)
Part C: Word Problem Challenge
7. \(30 \times 48 = 30 \times (40 + 8) = (30 \times 40) + (30 \times 8) = 1,200 + 240 = \mathbf{1,440}\text{ apples}\).
Parent Tip: Remind students that counting zeros only works after finding the product of non-zero digits.
Night 2: Estimation with Rounding & Compatible Numbers (4-3) Page 2 of Practice Packet
Part A: Round to Nearest Ten
- 1. \(38 \times 52 \approx 40 \times 50 = \mathbf{2,000}\)
- 2. \(79 \times 41 \approx 80 \times 40 = \mathbf{3,200}\)
- 3. \(63 \times 28 \approx 60 \times 30 = \mathbf{1,800}\)
- 4. \(91 \times 69 \approx 90 \times 70 = \mathbf{6,300}\)
Part B: Reasoning & Justification
5. It is an underestimate.
Reasoning: Both factors were rounded down (\(53 \rightarrow 50\) and \(74 \rightarrow 70\)). Because both numbers were decreased, the estimated product (\(3,500\)) must be less than the exact product (\(3,922\)).
Part C: Estimation in Action
6. Round \(26 \rightarrow 30\) and \(48 \rightarrow 50\). Estimate: \(30 \times 50 = \mathbf{1,500}\text{ spectators}\). (Compatible numbers method: \(25 \times 50 = 1,250\) is also acceptable. Exact is \(1,248\).)
Quick Parent Check: If a student gets stuck on estimation, have them place the number on a number line to see which ten it is closer to.
