Home›Lesson Plans›Mathematics›Number & Operations in Base Ten · Grade 4

Multi-Digit Multiplication: Break It Apart to Build It Up

Students split a big multiplication into place-value chunks with the area model — turning a scary problem like 4 × 23 into two easy ones they add back together.

Grade 4Multiplication45 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Break a two-digit number into tens and ones to multiply.
  • ✓Use an area model to find partial products.
  • ✓Add partial products to get the total.
  • ✓Connect the area model to the distributive property.
Essential Question

4 × 23 looks hard all at once. What if you could break the 23 into pieces you already know how to multiply?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Area Model Builder

Project this and change the factors. Watch the two-digit number split into tens and ones, each becoming a partial product you add together.

✖️ Split the factor — build the area modelTry it
One-digit factor4
Two-digit factor23

The Lesson · Gradual Release (I Do · We Do · You Do)

45 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Too Big at Once

5 min

4 × 23 — can we make it easier?

👩‍🏫 Teacher Moves

  • Write 4 × 23.
  • Ask if there’s a way to break it up.
  • Set the goal: the area model.

🎒 Student Actions

  • React to the big product.
  • Suggest splitting the 23.
  • Predict an easier path.
2

I Do — Split and Multiply

10 min

Teacher models the area model.

👩‍🏫 Teacher Moves

  • Split 23 into 20 + 3.
  • Multiply each: 4×20=80, 4×3=12.
  • Add partial products: 80+12=92.

🎒 Student Actions

  • Copy the split.
  • Find each partial product.
  • Add them to get 92.
3

We Do — Build Together

12 min

Class drives the Area Model Builder.

👩‍🏫 Teacher Moves

  • Use the Builder with new factors.
  • Read the two partial products.
  • Connect to the distributive property.

🎒 Student Actions

  • Call out factors to build.
  • Name each partial product.
  • Add to find the total.
4

You Do — On Your Own

13 min

Students multiply with the model.

👩‍🏫 Teacher Moves

  • Assign 2-digit × 1-digit problems.
  • Include a word problem.
  • Check the split-and-add steps.

🎒 Student Actions

  • Draw area models and solve.
  • Solve a multiplication word problem.
  • Show partial products added.
5

Close — Prove It

5 min

Solve the opener with the model.

👩‍🏫 Teacher Moves

  • Return to 4 × 23.
  • Have students show the full model.
  • Hand out the exit ticket.

🎒 Student Actions

  • Show 4 × 23 = 92 with the model.
  • Explain the two pieces.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
4.NBT.B.5

Multiply a whole number of up to four digits by a one-digit whole number using strategies based on place value.

CCSS
3.OA.B.5

Apply properties of operations as strategies to multiply, including the distributive property.

CCSS
4.OA.A.3

Solve multistep word problems using the four operations.

SMP
MP.7

Look for and make use of structure — decomposing by place value.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Base-ten blocks to build each partial product.
  • Sentence frame: “___ × ___ plus ___ × ___.”
  • Color the tens part and the ones part differently.

Support & Access

IEP / 504
  • Pre-split the two-digit number for them.
  • Focus on ×2 and ×5 before harder facts.
  • Provide a labeled area-model template.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Multiply 2-digit × 2-digit (four partial products).
  • Compare the area model to the standard algorithm.
  • Estimate the product first, then check.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Area Model Builder
  • 🧱Base-ten blocks
  • 📐Grid paper
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

factora number being multipliedproductthe answer to a multiplicationpartial productpart of the answer from one piecearea modela rectangle split to multiplydistributive propertybreak a factor apart to multiplytensthe tens placeonesthe ones placedecomposebreak a number into parts
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Break 6 × 34 into two partial products and add them.
6 × 30 = 180 and 6 × 4 = 24; 180 + 24 = 204.
QUESTION 2
Why does splitting 23 into 20 + 3 make 4 × 23 easier?
Because 4 × 20 and 4 × 3 are easy facts; you multiply each piece and add — that’s the distributive property.
QUESTION 3
Find 5 × 48 using the area model.
5 × 40 = 200 and 5 × 8 = 40; 200 + 40 = 240.

Going deeper? Multiply two-by-two.

Challenge students to use a four-box area model for problems like 23 × 14, splitting both factors. A printable area-model grid is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Multi-Digit MultiplicationFlip
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Term
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Multi-Digit MultiplicationQuiz
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Multi-Digit MultiplicationPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: area model, decompose, distributive property, factor, ones, partial product, product, tens
  1. part of the answer from one piece
  2. the ones place
  3. a number being multiplied
  4. break a factor apart to multiply
  5. the answer to a multiplication
  6. break a number into parts
  7. a rectangle split to multiply
  8. the tens place

Part B · Show what you learned

  1. Break 6 × 34 into two partial products and add them.
  2. Why does splitting 23 into 20 + 3 make 4 × 23 easier?
  3. Find 5 × 48 using the area model.
Answer key — Part A: 1) partial product · 2) ones · 3) factor · 4) distributive property · 5) product · 6) decompose · 7) area model · 8) tens
Part B: 1) 6 × 30 = 180 and 6 × 4 = 24; 180 + 24 = 204. 2) Because 4 × 20 and 4 × 3 are easy facts; you multiply each piece and add — that’s the distributive property. 3) 5 × 40 = 200 and 5 × 8 = 40; 200 + 40 = 240.