Model Architects Practice Worksheet
Math Blueprint Series • 2×1 Multiplication
Model Architects Practice Packet
Name:
Date:
Class:
Blueprint Guide: Fill Every Box
Fill in each box: decompose the factor, label outside dimensions, and write the factors inside each rectangle. Setup only—do not calculate final products!
\( 2 \times 14 \) →
2
10 4
2×10
2×4
1 Problem: \( 2 \times 14 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 14 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
2 Problem: \( 3 \times 12 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 12 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
Model Architects • Decomposing & Setting Up Area Models Page 1 of 5
Model Architects Practice Packet
Name:
Date:
3 Problem: \( 2 \times 23 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 23 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
4 Problem: \( 4 \times 12 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 12 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
Model Architects • Decomposing & Setting Up Area Models Page 2 of 5
Model Architects Practice Packet
Name:
Date:
5 Problem: \( 2 \times 31 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 31 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
6 Problem: \( 3 \times 21 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 21 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
Model Architects • Decomposing & Setting Up Area Models Page 3 of 5
Model Architects Practice Packet
Name:
Date:
7 Problem: \( 2 \times 34 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 34 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
8 Problem: \( 3 \times 23 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 23 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
Model Architects • Decomposing & Setting Up Area Models Page 4 of 5
Model Architects Practice Packet
Name:
Date:
9 Problem: \( 4 \times 21 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 21 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
10 Problem: \( 2 \times 43 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 43 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
Packet Complete! You have set up all 10 area models.
Score: ___ / 10
Model Architects • Decomposing & Setting Up Area Models Page 5 of 5
Model Architects Exit Ticket
Math Blueprint Series • Quick Formative Check
Model Architects Exit Ticket
Name:
Date:
Class:
Exit Mission: Show what you learned! Decompose each 2-digit number and fill all outside and inside boxes of the area model. Setup only—do not compute final products!
2 Problems
1 Problem: \( 2 \times 42 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 42 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
2 Problem: \( 3 \times 22 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 22 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
Confidence Check:
😃 Got it! 😐 Need practice 🙁 Need help
Exit Score: ___ / 2
Model Architects • Exit Ticket • Setup Only Page 1 of 1
Model Architects Homework Sheet
Math Blueprint Series • Practice at Home
Model Architects Homework Sheet
Name:
Date:
Due:
Family / Helper Note: Students are mastering area model setup! Decompose the 2-digit number into Tens and Ones, fill the outside dimension boxes, and write the factors inside each rectangle. Setup only—do not calculate final products!
4 Problems Total
1 Problem: \( 2 \times 32 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 32 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
2 Problem: \( 3 \times 13 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 13 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
Model Architects • Homework Sheet • Setup Only Page 1 of 2
Model Architects Homework Sheet
Name:
Date:
3 Problem: \( 4 \times 11 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Break 11 into Tens + Ones:
= +
Architect Checklist
Decomposed into Tens + Ones
Outside dimension boxes filled
Inside expression boxes filled
Step 2 & 3: Set Up Area Model Fill in all boxes on the outside and inside the model.
Factor
Tens
Ones
Tens Expression
×
Ones Expression
×
Do not compute final product.
4 Problem: \( 2 \times 44 \)
Setup Only
Step 1: Decompose 2-Digit Factor
Model Architects Answer Key
Teacher Resource • Answer Key
Model Architects Answer Key
Practice Packet (Part 1) Problems 1 – 5
Grading Focus: Full credit requires (1) correct tens and ones decomposition, (2) correct outside dimensions, and (3) accurate factor multiplication expressions inside both rectangles. Products are intentionally NOT computed.
1 \( 2 \times 14 \) 14 = 10 + 4
Side
2
10 4
2×10
2×4
Partial Products: 20 + 8 = 28
2 \( 3 \times 12 \) 12 = 10 + 2
Side
3
10 2
3×10
3×2
Partial Products: 30 + 6 = 36
3 \( 2 \times 23 \) 23 = 20 + 3
Side
2
20 3
2×20
2×3
Partial Products: 40 + 6 = 46
4 \( 4 \times 12 \) 12 = 10 + 2
Side
4
10 2
4×10
4×2
Partial Products: 40 + 8 = 48
5 \( 2 \times 31 \) 31 = 30 + 1
Side
2
30 1
2×30
2×1
Partial Products: 60 + 2 = 62
Common Misconceptions
- Single Digit on Top: Watch for students writing the 1-digit factor on top instead of the side.
- Digit vs Value: Ensure students decompose 23 as 20 + 3, not 2 + 3.
- Partial Products: Inside the tens box, it must be 2 × 20, not just 40.
Pacing Tip: Have students self-check using the Architect Checklist.
Model Architects • Teacher Answer Key Page 1 of 3
Model Architects Answer Key • Practice Packet (Part 2)
Problems 6 – 10
6 \( 3 \times 21 \) 21 = 20 + 1
Side
3
20 1
3×20
3×1
Partial Products: 60 + 3 = 63
7 \( 2 \times 34 \) 34 = 30 + 4
Side
2
30 4
2×30
2×4
Partial Products: 60 + 8 = 68
8 \( 3 \times 23 \) 23 = 20 + 3
Side
3
20 3
3×20
3×3
Partial Products: 60 + 9 = 69
9 \( 4 \times 21 \) 21 = 20 + 1
Side
4
20 1
4×20
4×1
