Multi-Digit Multiplication with the Area Model

Multi-Digit Multiplication with the Area Model

Grade 4 · Math · NYS NY-4.NBT.5 · 55 Minutes

Math Teacher Review Pilot: This resource is eligible for review by a NYS-certified Mathematics teacher.

NYS-Aligned Standard

NY-4.NBT.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. NYS Next Generation Mathematics Learning Standards (2017)

Learning Objectives — “I Can” Statements

• I can break a multi-digit number into expanded form to make multiplication easier.
• I can use the area model to multiply a 3-digit number by a 1-digit number.
• I can use the area model to multiply two 2-digit numbers.
• I can explain how the area model connects to place value.

Essential Question

How does breaking a number into its place value parts make multiplication manageable?

Lesson Sequence

Hook / Warm-Up (8 minutes)

1. Area model warm-up: Draw a 10 × 4 rectangle on the board. “This rectangle has an area of ___?”
2. Draw a 13 × 4 rectangle. “What if I split it into 10 × 4 and 3 × 4? Does that make it easier?”
3. Students calculate both parts and add: 40 + 12 = 52. “Is that what 13 × 4 equals?”
4. Bridge: “Today we’ll use this strategy — the area model — to tackle even bigger multiplication.”

Direct Instruction (12 minutes)

1. Model 234 × 6 with area model:
   • Break 234 into 200 + 30 + 4
   • Draw three boxes: [200 × 6] [30 × 6] [4 × 6]
   • Calculate: 1200 + 180 + 24 = 1404
2. Connect to place value: “Each box is one PLACE VALUE position × 6.”
3. Model 23 × 14 with a 2×2 area model grid:
   • Top: 20 + 3 (columns)
   • Side: 10 + 4 (rows)
   • Four boxes: 200, 30, 80, 12
   • Sum: 200 + 30 + 80 + 12 = 322

Guided Practice (12 minutes)

1. Class works through 145 × 7 together:
   • Students draw their own area model on whiteboards
   • Teacher models on board; students check
   • Sum: 700 + 280 + 35 = 1015
2. Pairs try 32 × 21 using the 2×2 grid format.
3. Share out and compare; discuss: “Did anyone make a different area model that still works?”

Independent Practice (15 minutes)

1. Students complete 4 problems on the Area Model Practice Sheet.
2. Students must draw the model AND show the partial products AND the total.
3. Teacher circulates; look for: correct place value decomposition, accurate partial products, correct addition of partials.

Closure (8 minutes)

1. Connect area model to standard algorithm: “The area model shows us WHY the algorithm works.”
2. Exit ticket: “Use the area model to solve 36 × 25. Draw the grid, label the partial products, find the total.”

Area Model Practice Sheet

Name: __________________ Date: __________

Problem 1: 312 × 5
Area Model:  [300 × 5] [10 × 5] [2 × 5]
             = ______ + _____ + _____ = _______

Problem 2: 416 × 8
Area Model: Draw your own boxes below, then solve.
□ □ □
Partial products: ___ + ___ + ___ = _______

Problem 3: 24 × 13 (2-digit × 2-digit)
     20    4
10  [   ] [   ]
3   [   ] [   ]
Partial products: ___ + ___ + ___ + ___ = _______

Problem 4: 36 × 45 (challenge)
Draw your area model below:

Total: _______

SDI & Differentiation Block

Supports for MLLs/ELLs

Entering/Emerging (NYSESLAT Levels 1–2):

• Provide a bilingual vocabulary card: area model, partial product, expanded form, multiply, factor
• Begin with 2-digit × 1-digit area model only (2 boxes)
• Label each box with its calculation shown; student fills in the product
• Sentence frame: “I broke ___ into ___ and ___. I multiplied each part by ___. The total is ___.”

Transitioning/Expanding (NYSESLAT Levels 3–4):

• Provide an area model template with pre-drawn boxes
• Academic vocabulary review: partial product, expanded form, decompose
• Allow verbal explanation of process before writing

Supports for Students with IEPs

SDI Adaptation Dimensions: content, methodology, delivery

• Content: Limit to 2-digit × 1-digit area model (2 boxes); allow calculator for partial product calculations; focus on understanding the structure rather than computation fluency
• Methodology: Color-code each place value column (hundreds = yellow, tens = blue, ones = green) consistently across all representations; provide step-by-step checklist: (1) break apart, (2) draw boxes, (3) multiply each box, (4) add partials
• Delivery: Provide pre-drawn area model grids; provide graph paper for alignment; allow extended time per IEP

Suggested Placement: ICT, Resource Room

Suggested IEP Goal Reference (Teacher Reference Only — Not Legal Advice): Given a pre-drawn area model grid and a 3-digit × 1-digit multiplication problem, the student will correctly label the partial products and compute the total with 80% accuracy across 4 of 5 problems, supporting progress toward NY-4.NBT.5.

Extensions for Advanced Learners

• Connect area model to standard algorithm: label where each partial product appears in the algorithm
• Try 3-digit × 2-digit area models
• Explore the distributive property formally: a(b + c) = ab + ac

Answer Key

Problem 1: 312 × 5 = 1500 + 50 + 10 = 1,560 Problem 2: 416 × 8 = 3200 + 80 + 48 = 3,328 Problem 3: 24 × 13: 200 + 40 + 30 + 12 = 312 Problem 4: 36 × 45: 1200 + 150 + 240 + 30 = 1,620 Exit ticket: 36 × 25: 600 + 100 + 150 + 30 = 880 → Wait: 36 × 25 = 900. Let me verify: 30 × 20 = 600; 30 × 5 = 150; 6 × 20 = 120; 6 × 5 = 30; 600 + 150 + 120 + 30 = 900. ✓

Alignment Record