Multiplication Steps Graphic Organizer TEKS 4.4(D) Aligned Math Blueprint
Multiplication Steps Graphic Organizer
Standard Algorithm: 2-Digit by 2-Digit Multiplication
Name:
Date: Class:
1 Multiply Ones
Multiply top number by bottom ones digit. Regroup above tens place if needed.
2 Placeholder Zero
Keyphrase: “Placeholder”
Write the Placeholder 0 in the ones place of line 2 before multiplying by tens!
3 Multiply Tens
Cross out old regrouped digits. Multiply top by bottom tens digit.
4 Add Products
Add both partial products together carefully to get the final answer.
Modeled Example: \( 36 \times 24 \)
Follow the colored arrows and notes
STEP 1: \( 36 \times 4 \) ones
\( ^{+2} \)
3 6
× 2 4
1 4 4
4 × 6 = 24 (regroup 2).
STEP 2: “Placeholder” 0
\( ^{+2} \)
3 6
× 2 4
1 4 4
_ 0
Cross out old regrouping.Placeholder 0 in ones!
STEP 3: \( 36 \times 2 \) tens
\( ^{+1} \)
3 6
× 2 4
1 4 4
7 2 0
2 × 6 = 12 (regroup 1).
STEP 4: Add Partials
3 6 × 24
1 4 4
+ 7 2 0
8 6 4
144 + 720 = 864 .
Guided Practice: Complete the Steps
Fill in place-value boxes and calculate
Problem A: \( 43 \times 28 \) Estimate: \( 40 \times 30 = 1,200 \)
1 \( 43 \times 8 \) ones = _____
2 Write Placeholder 0
3 \( 43 \times 2 \) tens = _____
4 Add partial products
Th H T O
4 3
× 2 8
Problem B: \( 57 \times 36 \) Estimate: \( 60 \times 40 = 2,400 \)
1 \( 57 \times 6 \) ones = _____
2 Write Placeholder 0
3 \( 57 \times 3 \) tens = _____
4 Add partial products
Th H T O
5 7
× 3 6
Remember the Keyphrase “Placeholder”: Always write the Placeholder 0 in the ones column of Line 2 before multiplying! It holds the ones place because you are multiplying by tens.
Expansion Level Math Blueprint
Multiplication Steps Graphic Organizer
Standard Algorithm: 3-Digit by 2-Digit Multiplication
Name:
Date:
What Changes When You Multiply 3 Digits by 2 Digits?
1. Extra Place Value
You must multiply the bottom digit by the top ones, tens, AND hundreds place (3 multiplications per line).
2. “Placeholder” Zero Rule
Step 2 does not change ! Still write the Placeholder 0 in the ones place of Line 2 before multiplying by tens.
3. Larger Product Sum
Your final answer will often reach the thousands or ten-thousands place. Keep your columns strictly aligned!
Modeled Walkthrough: \( 248 \times 35 \)
Estimate: \( 250 \times 40 = 10,000 \)
TTh Th H T O
\( ^{+2}\ \ ^{+4} \) (Step 1)
\( ^{+1}\ \ ^{+2} \) (Step 3)
2 4 8
× 3 5
1 2 4 0 (\( 248 \times 5 \))
+ 7 4 4 0 (\( 248 \times 30 \))
8, 6 8 0
Line 1 (\( \times 5 \) ones): \( 5 \times 8 = 40 \) (write 0, regroup 4). \( 5 \times 4 = 20 + 4 = 24 \) (write 4, regroup 2). \( 5 \times 2 = 10 + 2 = 12 \). Line 1 = 1,240 .
Line 2 “Placeholder”: Cross out old regroup marks (+4, +2). Write the Placeholder 0 in the ones column because 3 represents 30!
Line 2 (\( \times 3 \) tens): \( 3 \times 8 = 24 \) (regroup 2). \( 3 \times 4 = 12 + 2 = 14 \) (regroup 1). \( 3 \times 2 = 6 + 1 = 7 \). Line 2 = 7,440 .
Sum Partial Products: Add \( 1,240 + 7,440 = \mathbf{8,680} \). Check against estimate (\( 10,000 \)) — reasonable!
Your Turn: 3-Digit by 2-Digit Practice
Show all regrouping numbers clearly
Problem C: \( 316 \times 24 \) Est: \( 300 \times 20 = 6,000 \)
• Line 1: \( 316 \times 4 \)
• Write Placeholder 0
• Line 2: \( 316 \times 20 \)
• Add both lines
Final Product:
Th H T O
3 1 6
× 2 4
Problem D: \( 425 \times 38 \) Est: \( 400 \times 40 = 16,000 \)
• Line 1: \( 425 \times 8 \)
• Write Placeholder 0
• Line 2: \( 425 \times 30 \)
• Add both lines
Final Product:
TTh Th H T O
4 2 5
× 3 8
5-Point Algorithm Accuracy Checklist
Multiplied top by bottom ones Wrote “Placeholder” 0 Crossed out old regroup marks Multiplied top by bottom tens Added partial products correctly
Product Quest Review Activity TEKS 4.4(D) Review Multiplication Mission
Product Quest Review Activity
Phase 1: Algorithm Error Analysis & Conceptual Connections
Student Name:
Date: Partner:
Mission Objective
Identify breakdowns in multi-digit standard algorithm steps, connect area models to partial products, and prove computation mastery.
Goal: 100% Accuracy
Station 1: Spot the Algorithm Glitch (Error Analysis)
Find the step breakdown, explain it, and correct it
Glitch Case #1: \( 48 \times 26 \) Student Work
\( ^{+4} \)
4 8
× 2 6
2 8 8
+ 9 6
3 8 4
Which step failed?
Step 1: Ones Step 2: Zero Step 3: Tens Step 4: Add
Explain the error:
Corrected Solution (\( 48 \times 26 \)):
Glitch Case #2: \( 324 \times 15 \) Student Work
\( ^{+1}\ \ ^{+2} \)
3 2 4
× 1 5
1 6 2 0
+ 4 4 4 0
6 0 6 0
Which step failed?
Step 1: Ones Step 2: Zero Step 3: Tens Step 4: Add
Explain the error:
Corrected Solution (\( 324 \times 15 \)):
Station 2: Connect the Models (Area Model to Algorithm Bridge)
Connect partial products to algorithm lines
Look at the expanded area model for \( 54 \times 32 \). Connect the sections of the area model to the two partial product lines of the standard algorithm.
Area Model: \( (50 + 4) \times (30 + 2) \)
50
4
30
\( 50 \times 30 = \) 1,500
\( 4 \times 30 = \) 120
2
\( 50 \times 2 = \) 100
\( 4 \times 2 = \) 8
Algorithm Line 1: \( 54 \times 2 \)
Sum of blue boxes: \( 100 + 8 = \) ______
This equals standard algorithm Line 1: ______
Algorithm Line 2: \( 54 \times 30 \)
Sum of green boxes: \( 1,500 + 120 = \) ______
This equals standard algorithm Line 2: ______
Total Product: Line 1 + Line 2 = ______
TEKS 4.4(D) Review Multiplication Mission
Product Quest Review Activity
Phase 2: Target Computation Showdown & Code Breaker
Student Name:
Date:
Station 3: Target Product Showdown (Standard Algorithm)
Estimate first, then execute with place-value precision
Task 1: 2D × 2D Standard
\( 64 \times 37 \)
Est: \( 60 \times 40 = \) ______
Th H T O
6 4
× 3 7
Product:
Task 2: 3D × 2D Advanced
\( 518 \times 42 \)
Est: \( 500 \times 40 = \) ______
TTh Th H T O
5 1 8
× 4 2
Product:
Task 3: Word Problem Applied
A Texas elementary school ordered 325 packages of math manipulatives. Each package has 24 counters . How many counters are there in all?
Set up and solve:
Total Counters:
Station 4: Product Code Breaker Riddle
Calculate the products to unlock the letters of the answer
Riddle: “Why did the student multiply their math problems sitting on the classroom floor?”
Letter T \( 23 \times 14 \)
Product: _____
Letter A \( 45 \times 22 \)
Product: _____
Letter B \( 132 \times 16 \)
Product: _____
Letter S \( 215 \times 31 \)
Product: _____
322 = T 990 = A 2,112 = B 1,260 = L 480 = E 6,665 = S
Punchline: “Because their teacher told them not to use 322 990 2,112 1,260 480 6,665 !”
Write the matching letter above each product to solve the riddle!
Multiplication Blueprint Answer Key Teacher Key & Guide TEKS 4.4(D) Solutions
Multiplication Blueprint Answer Key
Part 1: Graphic Organizer Step-by-Step Solutions & Pedagogical Notes
Master Answer Key
TEKS 4.4(D) Core Teaching Focus: The “Placeholder” Zero
Students must transition from concrete/representational models (area models, partial products) to the standard algorithm. Emphasize that the keyphrase “Placeholder” in Step 2 is not a trick —it represents multiplying by a group of tens (e.g., \( 43 \times 20 \)).
Graphic Organizer Page 1: 2-Digit by 2-Digit Guided Practice Solutions
Problem A: \( 43 \times 28 \) Product: 1,204
\( ^{+2} \)
4 3
× 2 8
3 4 4
+ 8 6 0
1, 2 0 4
Line 1: \( 43 \times 8 = \mathbf{344} \)
Line 2 Zero: Write Placeholder 0 in ones.
Line 2: \( 43 \times 20 = \mathbf{860} \)
Sum: \( 344 + 860 = \mathbf{1,204} \)
Estimate check: Close to 1,200.
Problem B: \( 57 \times 36 \) Product: 2,052
\( ^{+4}\ \ ^{+2} \)
5 7
× 3 6
3 4 2
+ 1 7 1 0
2, 0 5 2
Line 1: \( 57 \times 6 = \mathbf{342} \)
Line 2 Zero: Write Placeholder 0 in ones.
Line 2: \( 57 \times 30 = \mathbf{1,710} \)
Sum: \( 342 + 1,710 = \mathbf{2,052} \)
Estimate check: Close to 2,400.
Graphic Organizer Page 2: 3-Digit by 2-Digit Practice Solutions
Problem C: \( 316 \times 24 \) Product: 7,584
\( ^{+2} \)
3 1 6
× 2 4
1 2 6 4
+ 6 3 2 0
7, 5 8 4
Line 1: \( 316 \times 4 = \mathbf{1,264} \)
Placeholder: Place 0 in ones.
Line 2: \( 316 \times 20 = \mathbf{6,320} \)
Sum: \( 1,264 + 6,320 = \mathbf{7,584} \)
Problem D: \( 425 \times 38 \) Product: 16,150
\( ^{+2}\ \ ^{+4} \)
4 2 5
× 3 8
3 4 0 0
+ 1 2 7 5 0
1 6, 1 5 0
Line 1: \( 425 \times 8 = \mathbf{3,400} \)
Placeholder: Place 0 in ones.
Line 2: \( 425 \times 30 = \mathbf{12,750} \)
Sum: \( 3,400 + 12,750 = \mathbf{16,150} \)
Teacher Alert (Regrouping Confusion): In Problem D, students must regroup twice on Line 1. Remind students to cross out the 4 and 2 before calculating Line 2.
Teacher Key & Guide TEKS 4.4(D) Solutions
Multiplication Blueprint Answer Key
Part 2: Product Quest Review Activity Full Solutions & Grading Guide
Master Answer Key
Station 1: Spot the Glitch (Error Analysis) Solutions
Glitch #1 (\( 48 \times 26 \)):
Failed Step: Step 2 (Placeholder Zero)
Explanation: The student multiplied by 2 instead of 20. They wrote 96 instead of 960 (they forgot to write the placeholder zero in the ones place on Line 2).
Line 1: 288 • Line 2: 960 • Correct Product = 1,248
Glitch #2 (\( 324 \times 15 \)):
Failed Step: Step 3 (Multiplying by Tens)
Explanation: The student failed to cross out the old regrouped numbers from Line 1 (+1, +2). When multiplying \( 1 \times 2 \), they added the old 2 to get 4; when multiplying \( 1 \times 3 \), they added the old 1 to get 4.
Line 1: 1,620 • Line 2: 3,240 • Correct Product = 4,860
Station 2: Connect the Models (Area Model to Algorithm Bridge)
Algorithm Line 1: Blue boxes: \( 100 + 8 = \mathbf{108} \)
(\( 54 \times 2 \) ones)
Algorithm Line 2: Green boxes: \( 1,500 + 120 = \mathbf{1,620} \)
(\( 54 \times 30 \) tens with placeholder 0)
Total Product: \( 108 + 1,620 = \mathbf{1,728} \)
Sum of all 4 partial areas
Station 3: Target Product Showdown Solutions
Task 1: \( 64 \times 37 \) Estimate: \( 60 \times 40 = 2,400 \)
6 4 × 3 7
Line 1: 448
+ Line 2: 1,920
= 2,368
Task 2: \( 518 \times 42 \) Estimate: \( 500 \times 40 = 20,000 \)
5 1 8 × 4 2
Line 1: 1,036
+ Line 2: 20,720
= 21,756
Task 3: Word Problem \( 325 \times 24 \) markers
3 2 5 × 2 4
Line 1: 1,300
+ Line 2: 6,500
= 7,800 markers
Station 4: Code Breaker Computation & Riddle Solution
Letter T \( 23 \times 14 = \) 322
Letter A \( 45 \times 22 = \) 990
Letter B \( 132 \times 16 = \) 2,112
Letter S \( 215 \times 31 = \) 6,665
Riddle Punchline: “Because their teacher told them not to use TABLES !” (multiplication tables)
Multiplication Blueprint Teacher Resource • TEKS 4.4(D) Master Key • Page 2 of 3
Teacher Key & Guide TEKS 4.4(D) Solutions
Multiplication Blueprint Answer Key
Part 3: Homework Practice Full Worked Solutions & Grading Guidance
Homework Key
Homework Page 1: 2-Digit by 2-Digit Computation Solutions
1. \( 53 \times 24 \)
L1: 212
+ L2: 1,060
= 1,272
2. \( 68 \times 35 \)
L1: 340
+ L2: 2,040
= 2,380
3. \( 47 \times 62 \)
L1: 94
+ L2: 2,820
= 2,914
4. \( 84 \times 29 \)
L1: 756
+ L2: 1,680
= 2,436
Placeholder Check: On problems 1–4, ensure students placed exactly one 0 in the ones column of Line 2. Notice that \( 53 \times 20 = 1,060 \), \( 68 \times 30 = 2,040 \), \( 47 \times 60 = 2,820 \), and \( 84 \times 20 = 1,680 \).
Homework Page 2: 3-Digit by 2-Digit Computation Solutions
5. \( 234 \times 26 \)
L1: 1,404
+ L2: 4,680
= 6,084
6. \( 418 \times 35 \)
L1: 2,090
+ L2: 12,540
= 14,630
7. \( 362 \times 48 \)
L1: 2,896
+ L2: 14,480
= 17,376
8. \( 527 \times 34 \)
L1: 2,108
+ L2: 15,810
= 17,918
Homework Page 2: Real-World Word Problem Solutions
9. Book Drive: \( 125 \times 48 \)
Line 1 (\( 125 \times 8 \)): 1,000
Line 2 (\( 125 \times 40 \)): 5,000 (Placeholder 0)
Total = 6,000 books
10. Bakery Batch: \( 245 \times 36 \)
Line 1 (\( 245 \times 6 \)): 1,470
Line 2 (\( 245 \times 30 \)): 7,350 (Placeholder 0)
Total = 8,820 cinnamon rolls
Fast Grading Check: Scan Line 2 of every problem for the ending zero. If the zero is missing, the student computed as single-digit multiplication. Total Points: 10 Problems (10 pts each)
Multiplication Homework Practice TEKS 4.4(D) Homework Independent Practice
Multiplication Homework Practice
Part 1: 2-Digit by 2-Digit Standard Algorithm
Name:
Date: Due:
Step 2 Keyphrase Check: “Placeholder” Zero
Before you multiply by the tens digit on Line 2, always write down your Placeholder 0 in the ones place!
Line 2 = __ 0
Solve Using the Standard Algorithm (Show Regrouping & Placeholder Zero)
Show all partial products
1. \( 53 \times 24 \) 2-Digit × 2-Digit
Th H T O
5 3
× 2 4
Placeholder 0 checked: □ Product:
2. \( 68 \times 35 \) 2-Digit × 2-Digit
Th H T O
6 8
× 3 5
Placeholder 0 checked: □ Product:
3. \( 47 \times 62 \) 2-Digit × 2-Digit
Th H T O
4 7
× 6 2
Placeholder 0 checked: □ Product:
4. \( 84 \times 29 \) 2-Digit × 2-Digit
Th H T O
8 4
× 2 9
Placeholder 0 checked: □ Product:
Algorithm Precision: Keep digits neatly aligned in their place-value columns (ones, tens, hundreds, thousands).
4th Grade TEKS 4.4(D)
TEKS 4.4(D) Homework Independent Practice
Multiplication Homework Practice
Part 2: 3-Digit by 2-Digit & Problem Solving
Name:
Date:
3-Digit by 2-Digit Standard Algorithm Practice
Remember: 3 multiplications per line + Placeholder 0!
5. \( 234 \times 26 \) 3-Digit × 2-Digit
TTh Th H T O
2 3 4
× 2 6
Placeholder 0: □ Product:
6. \( 418 \times 35 \) 3-Digit × 2-Digit
TTh Th H T O
4 1 8
× 3 5
Placeholder 0: □ Product:
7. \( 362 \times 48 \) 3-Digit × 2-Digit
TTh Th H T O
3 6 2
× 4 8
Placeholder 0: □ Product:
8. \( 527 \times 34 \) 3-Digit × 2-Digit
TTh Th H T O
5 2 7
× 3 4
Placeholder 0: □ Product:
Part 3: Real-World Word Problems
9. Book Drive: The 4th-grade team collected 48 boxes of books for the community library. Each box holds 125 books . How many total books did the 4th graders collect?
Answer: books
10. Bakery Batch: A Texas bakery prepared 245 sheet pans of cinnamon rolls for a school festival. If each sheet pan holds 36 rolls , how many rolls did they bake in all?
Answer: rolls
