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Area Model Architects • Sequence • Lenny.com

Math Numbers & Counting Counting Objects Number Names Comparing Numbers Number Operations Counting Sequence Numbers 0-10 Place Value Understanding and System Add and Subtract Within 20 Addition and Subtraction Concepts Addition and Subtraction Equations Addition and Subtraction Problems Foundations for Multiplication Multiplication and Division Properties Multiply and Divide Within 100 Multiplication and Division Problems Factors and Multiples Properties of Operations Patterns and Relationships Generate and Analyze Patterns Multi-Digit Arithmetic Place Value Operations Multi-Digit and Decimal Operations Numerical Expressions Four Operations and Patterns Four Operations Problem Solving Measurement & Data Measurable Attributes Measuring Lengths Measure and Estimate Lengths in Standard Units Relate Addition and Subtraction to Length Classifying and Counting Objects Time and Money Area Concepts and Measurement Perimeter and Area Measures Angle Concepts and Measurement Time, Volume, and Mass Measurement Unit Conversions Geometry Identifying Shapes Shapes and Attributes Shape Attributes and Reasoning Shapes and Composition Classifying 2D Figures Geometric Figures and Relationships Lines, Angles, and Shapes Angle, Area, and Volume Geometric Measurement Volume of 3D Shapes Coordinate Plane Applications Transformations in the Plane Congruence and Similarity Understand congruence in terms of rigid motions Similarity and Transformations Prove Theorems Involving Similarity Pythagorean Theorem Trigonometry for General Triangles Make Geometric Constructions Prove Geometric Theorems Theorems About Circles Find Arc Lengths And Areas of Sectors of Circles Volume Formulas Relationships Between Two-Dimensional and Three-Dimensional Objects Prove Simple Geometric Theorems Algebraically Translate Between Geometric Description and Equation for Conic Section Apply Geometric Concepts in Modeling Situations Fractions & Decimals Fractions as Numbers Building Fractions Fraction Equivalence and Ordering Adding and Subtracting Fractions Multiplying and Dividing Fractions Dividing Fractions Decimal Fractions Multi-Digit Computation and Factors Add, Subtract, Multiply, and Divide Rational Numbers Rational Number System Irrational Numbers and Approximations Ratios Ratios and Proportions Proportional Relationships Unit Rate Algebra Algebraic Expressions Generate Equivalent Expressions Quantitative Relationships Proportional Relationships and Linear Equations Equations and Inequalities Equation Solving and Reasoning Linear Equations and Systems Graph Equations and Inequalities Systems of Equations Real-World Algebraic Problems Quantitative Reasoning with Units Expression Structure Equivalent Expression Forms Radicals and Integer Exponents Rational Exponents Rational and Irrational Numbers Polynomial Operations Polynomial Identities Polynomial Zeros and Factors Rational Expressions Complex Number Operations Complex Numbers in Polynomials Complex Numbers on Plane Statistics & Probability Represent and Interpret Data Data Distributions Statistical Variability Probability Models Compound Event Probabilities Statistical Sampling Interpret Categorical and Quantitative Data Bivariate Data Patterns Interpret Linear Models Comparing Two Populations Random Processes in Statistics Independence and Conditional Probability Expected Values Probability-Based Decision Making Statistical Inference and Conclusions Functions Function Concepts and Notation Define and Compare Functions Interpret Functions in Context Analyze Function Representations Model Relationships with Functions Identify Linear vs Exponential Growth Distinguish Between Function Types Compare Growth Rates Interpret Function Expressions Build Functions from Relationships Construct and Model Functions Transform and Combine Functions Model Comparison and Selection Solve Exponential Equations Trigonometry Trigonometric Ratios Involving Right Triangles Trigonometric Functions and Unit Circle Model with Trigonometric Functions Trigonometric Identities Vectors & Matrices Introduction to Vectors and Matrices Vector Quantities Vector Operations Matrix Operations Calculus Limits and Continuity Derivative Concepts and Notation Derivative Rules and Techniques Applications of Derivatives Optimization Problems Related Rates Curve Sketching and Analysis Integration Concepts and Notation Antiderivatives and Indefinite Integrals Definite Integrals and Area Fundamental Theorem of Calculus Integration Techniques Applications of Integration Differential Equations Sequences and Series Parametric and Polar Functions Vector-Valued Functions

Area Model Architects

A progressive math sequence developing deep conceptual understanding of the area model for multiplication. Students master place-value decomposition and blueprint modeling from 2-digit to multi-digit factors without computational overload.

TGTyonna Gunter

Area Model Architects

A targeted 3rd and 4th grade math lesson focusing on conceptual understanding of the area model for single-digit by two-digit multiplication. Students master decomposing factors into tens and ones and labeling dimensions and partial product expressions without performing multi-digit computation.

Three Digit Architects

Lesson 2 expands the area model blueprint to 3-digit by 1-digit multiplication. Students master decomposing numbers into hundreds, tens, and ones, setting up 3-compartment area models with explicit outside dimensions and inside factor expressions.

Area Model Architects

A progressive math sequence developing deep conceptual understanding of the area model for multiplication. Students master place-value decomposition and blueprint modeling from 2-digit to multi-digit factors without computational overload.

TGTyonna Gunter

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

Three Digit Practice Worksheet

Math Blueprint Series • 3×1 Multiplication

Three-Digit 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!

\( 2 \times 134 \) →

2

100 30 4

2×100

2×30

2×4

1 Problem: \( 2 \times 134 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 134 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

2 Problem: \( 3 \times 123 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 123 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

Three-Digit Architects • Decomposing & Setting Up Area Models Page 1 of 5

Three-Digit Architects Practice Packet

Name:

Date:

3 Problem: \( 4 \times 112 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 112 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Three Digit Exit Ticket

Math Blueprint Series • Quick Formative Check

Three-Digit Architects Exit Ticket

Name:

Date:

Class:

Exit Mission: Decompose the 3-digit factor into Hundreds + Tens + Ones. Fill all outside dimensions and inside factor expressions. Setup only—do not compute final products!

2 Problems

1 Problem: \( 2 \times 342 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 342 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

2 Problem: \( 3 \times 213 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 213 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

Confidence Check:

😃 Got it! 😐 Need practice 🙁 Need help

Exit Score: ___ / 2

Three-Digit Architects • Exit Ticket • Setup Only Page 1 of 1

Three Digit Homework Sheet

Math Blueprint Series • Practice at Home

Three-Digit Architects Homework Sheet

Name:

Date:

Due:

Family / Helper Note: Students decompose the 3-digit number into Hundreds + Tens + Ones. Then label the 4 outside dimensions and inside factor expressions. Setup only—do not calculate final products!

4 Problems Total

1 Problem: \( 2 \times 234 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 234 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

2 Problem: \( 3 \times 142 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 142 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

Three-Digit Architects • Homework Sheet • Setup Only Page 1 of 2

Three-Digit Architects Homework Sheet

Name:

Date:

3 Problem: \( 4 \times 212 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 212 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Three Digit Answer Key

Teacher Resource • Answer Key

Three-Digit Architects Answer Key

Practice Packet (Part 1) Problems 1 – 5

Grading Focus: Full credit requires (1) correct H + T + O decomposition, (2) all 4 outside dimensions, and (3) accurate factor expressions inside all 3 rectangles. Products are intentionally NOT computed.

1 \( 2 \times 134 \) 134 = 100 + 30 + 4

Side

2

100 30 4

2×100

2×30

2×4

Partial Products: 200 + 60 + 8 = 268

2 \( 3 \times 123 \) 123 = 100 + 20 + 3

Side

3

100 20 3

3×100

3×20

3×3

Partial Products: 300 + 60 + 9 = 369

3 \( 4 \times 112 \) 112 = 100 + 10 + 2

Side

4

100 10 2

4×100

4×10

4×2

Partial Products: 400 + 40 + 8 = 448

4 \( 2 \times 243 \) 243 = 200 + 40 + 3

Side

2

200 40 3

2×200

2×40

2×3

Partial Products: 400 + 80 + 6 = 486

5 \( 3 \times 214 \) 214 = 200 + 10 + 4

Side

3

200 10 4

3×200

3×10

3×4

Partial Products: 600 + 30 + 12 = 642

3-Digit Common Misconceptions

Digit vs Value: Watch for students writing single digits like 2 + 1 + 4 instead of values 200 + 10 + 4.
Distributing Side Factor: The side factor must appear in all three compartments.
Premature Addition: Emphasize that setup means writing factor expressions, not adding products.

Pacing Tip: Have students check that all 4 outside dimensions are labeled before filling inside expressions.

Three-Digit Architects • Teacher Answer Key Page 1 of 3

Three-Digit Architects Answer Key • Practice Packet (Part 2)

Problems 6 – 10

6 \( 2 \times 321 \) 321 = 300 + 20 + 1

Side

2

300 20 1

2×300

2×20

2×1

Partial Products: 600 + 40 + 2 = 642

7 \( 4 \times 221 \) 221 = 200 + 20 + 1

Side

4

200 20 1

4×200

4×20

4×1

Partial Products: 800 + 80 + 4 = 884

Break 44 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.

Master Architect Challenge

An area model has side length 4 and top labels 20 and 1. What was the original problem?

×

Model Architects • Homework Sheet • Setup Only Page 2 of 2

Partial Products: 80 + 4 = 84

10 \( 2 \times 43 \) 43 = 40 + 3

Side

2

40 3

2×40

2×3

Partial Products: 80 + 6 = 86

Packet Rubric (10 Points Total)

Decomposition (Tens + Ones): 3 pts

Outside Dimensions (Side & Top): 3 pts

Inside Box Setup Expressions: 4 pts

Target Standard: CCSS 3.OA.B.5 / 4.NBT.B.5 (Conceptual Base)

Model Architects • Teacher Answer Key Page 2 of 3

Model Architects Answer Key • Exit Ticket & Homework

Assessment Keys

Exit Ticket Answer Key (2 Problems) 2 Points

Problem 1: \( 2 \times 42 \) 42 = 40 + 2

Side 2

40 2

2×40

2×2

Partial Products: 80 + 4 = 84

Problem 2: \( 3 \times 22 \) 22 = 20 + 2

Side 3

20 2

3×20

3×2

Partial Products: 60 + 6 = 66

Homework Sheet Answer Key (4 Problems + Challenge) 4 Problems + Challenge

Problem 1: \( 2 \times 32 \) 32 = 30 + 2

Side 2

30 2

2×30

2×2

Partial Products: 60 + 4 = 64

Problem 2: \( 3 \times 13 \) 13 = 10 + 3

Side 3

10 3

3×10

3×3

Partial Products: 30 + 9 = 39

Problem 3: \( 4 \times 11 \) 11 = 10 + 1

Side 4

10 1

4×10

4×1

Partial Products: 40 + 4 = 44

Problem 4: \( 2 \times 44 \) 44 = 40 + 4

Side 2

40 4

2×40

2×4

Partial Products: 80 + 8 = 88

Challenge Answer: Side = 4, Top = 20 & 1 → Recombined factor is \( 20 + 1 = 21 \)

\( 4 \times 21 \)

Model Architects • Teacher Answer Key Page 3 of 3

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

4 Problem: \( 2 \times 243 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 243 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

Three-Digit Architects • Decomposing & Setting Up Area Models Page 2 of 5

Three-Digit Architects Practice Packet

Name:

Date:

5 Problem: \( 3 \times 214 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 214 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

6 Problem: \( 2 \times 321 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 321 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

Three-Digit Architects • Decomposing & Setting Up Area Models Page 3 of 5

Three-Digit Architects Practice Packet

Name:

Date:

7 Problem: \( 4 \times 221 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 221 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

8 Problem: \( 3 \times 312 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 312 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

Three-Digit Architects • Decomposing & Setting Up Area Models Page 4 of 5

Three-Digit Architects Practice Packet

Name:

Date:

9 Problem: \( 2 \times 413 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 413 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

10 Problem: \( 3 \times 232 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 232 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

Packet Complete! You have set up all 10 3-digit area models.

Score: ___ / 10

Three-Digit Architects • Decomposing & Setting Up Area Models Page 5 of 5

Ones

×

Do not compute final product.

4 Problem: \( 2 \times 423 \)

Setup Only

Step 1: Decompose 3-Digit Factor

Break 423 into Hundreds + Tens + Ones:

= + +

Architect Checklist

Decomposed into H + T + O

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

Hundreds

Tens

Ones

Hundreds

×

Tens

×

Ones

×

Do not compute final product.

Master Architect Challenge

An area model has side length 3 and top labels 200, 40, and 5. What was the original problem?

×

Three-Digit Architects • Homework Sheet • Setup Only Page 2 of 2

8 \( 3 \times 312 \) 312 = 300 + 10 + 2

Side

3

300 10 2

3×300

3×10

3×2

Partial Products: 900 + 30 + 6 = 936

9 \( 2 \times 413 \) 413 = 400 + 10 + 3

Side

2

400 10 3

2×400

2×10

2×3

Partial Products: 800 + 20 + 6 = 826

10 \( 3 \times 232 \) 232 = 200 + 30 + 2

Side

3

200 30 2

3×200

3×30

3×2

Partial Products: 600 + 90 + 6 = 696

Packet Rubric (10 Points Total)

Step 1 Decomposition (H + T + O): 3 pts

Outside Dimensions (Side & 3 Top): 3 pts

Inside 3-Box Setup Expressions: 4 pts

Target Standard: CCSS 4.NBT.B.5 (Multiplication Area Models)

Three-Digit Architects • Teacher Answer Key Page 2 of 3

Three-Digit Architects Answer Key • Exit Ticket & Homework

Assessment Keys

Exit Ticket Answer Key (2 Problems) 2 Points

Problem 1: \( 2 \times 342 \) 342 = 300 + 40 + 2

Side 2

300 40 2

2×300

2×40

2×2

Partial Products: 600 + 80 + 4 = 684

Problem 2: \( 3 \times 213 \) 213 = 200 + 10 + 3

Side 3

200 10 3

3×200

3×10

3×3

Partial Products: 600 + 30 + 9 = 639

Homework Sheet Answer Key (4 Problems + Challenge) 4 Problems + Challenge

Problem 1: \( 2 \times 234 \) 234 = 200 + 30 + 4

Side 2

200 30 4

2×200

2×30

2×4

Partial Products: 400 + 60 + 8 = 468

Problem 2: \( 3 \times 142 \) 142 = 100 + 40 + 2

Side 3

100 40 2

3×100

3×40

3×2

Partial Products: 300 + 120 + 6 = 426

Problem 3: \( 4 \times 212 \) 212 = 200 + 10 + 2

Side 4

200 10 2

4×200

4×10

4×2

Partial Products: 800 + 40 + 8 = 848

Problem 4: \( 2 \times 423 \) 423 = 400 + 20 + 3

Side 2

400 20 3

2×400

2×20

2×3

Partial Products: 800 + 40 + 6 = 846

Challenge Answer: Side = 3, Top = 200, 40, & 5 → Recombined factor is \( 200 + 40 + 5 = 245 \)

\( 3 \times 245 \)

Three-Digit Architects • Teacher Answer Key Page 3 of 3

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