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U02 • Lesson 20 of 105

Multi-Digit Multiplication Strategies

Builds on the multiplication concept to multiply multi-digit numbers using area models, partial products, and the standard algorithm. Students decompose factors by place value, compute partial products, and combine results, progressing from 2-digit x 1-digit to 2-digit x 2-digit multiplication.

Upper Elementary • 3-5

Prerequisites: E04, U01

Key Concepts

  • area model for multiplication
  • partial products strategy
  • standard multiplication algorithm
  • estimating products for reasonableness

Multi-Digit Multiplication Strategies

Multiplying big numbers might look scary at first, but we have powerful strategies to break the problem into smaller, easier pieces. We will explore three approaches: the area model, partial products, and the standard algorithm.

Strategy 1: The Area Model

The area model uses a rectangle divided into sections. We break each factor into its place-value parts and multiply each part separately.

Worked Example 1: Area Model for 24 x 3

Break 24 into 20 + 4. Draw a rectangle split into two parts:

204
33 x 20 = 603 x 4 = 12

Add the partial products: 60 + 12 = 72

24 x 3 = 72

Strategy 2: Partial Products

This is the area model written as a list. Multiply each part of one number by each part of the other, then add all the results.

Worked Example 2: Partial Products for 36 x 27

Break apart: 36 = 30 + 6 and 27 = 20 + 7.

  1. 30 x 20 = 600
  2. 30 x 7 = 210
  3. 6 x 20 = 120
  4. 6 x 7 = 42

Add all partial products:

600 + 210 + 120 + 42 = 972

So 36 x 27 = 972.

Strategy 3: The Standard Algorithm

This is the traditional method, which is really just a shortcut for partial products.

Worked Example 3: Standard Algorithm for 46 x 53

  1. Multiply by the ones digit (3): 3 x 46 = 138. Write 138.
  2. Multiply by the tens digit (5, which is really 50): 50 x 46 = 2,300. Write 2300 below, shifted one place left (or write 2300).
  3. Add: 138 + 2,300 = 2,438.
   4 6
x  5 3
------
  1 3 8    (46 x 3)
2 3 0 0    (46 x 50)
------
2 4 3 8

Estimating Products

Before multiplying, round each factor to estimate the answer. This helps you catch mistakes.

46 x 53 is about 50 x 50 = 2,500 (actual: 2,438 -- reasonable!)

Which Strategy to Use?

The area model helps you see why multiplication works. Partial products organizes the work clearly. The standard algorithm is fastest once you master it. All three give the same answer!

Common Mistake

When using the standard algorithm for 2-digit x 2-digit, do not forget to shift the second row one place to the left (or add a zero). The tens digit represents tens, not ones!

Real-World Connection

A movie theater has 28 rows with 34 seats in each row. How many seats total? 28 x 34 = 952 seats. Multiplication counts equal groups!

Practice Problems

1. Use the area model to find 32 x 4.

Show Answer

30 x 4 = 120 and 2 x 4 = 8. Total: 120 + 8 = 128.

2. Use partial products to find 15 x 23.

Show Answer

10x20=200, 10x3=30, 5x20=100, 5x3=15. Sum: 200+30+100+15 = 345.

3. Use the standard algorithm to find 67 x 8.

Show Answer

8x7=56, write 6 carry 5. 8x6=48, plus 5=53. Answer: 536.

4. Estimate 48 x 62, then find the exact answer.

Show Answer

Estimate: 50 x 60 = 3,000. Exact: 48 x 62 = 2,976. The estimate is close.

5. A school orders 37 boxes of pencils with 24 pencils in each box. How many pencils total?

Show Answer

37 x 24 = 888 pencils. (30x24=720, 7x24=168, 720+168=888)

Lesson Summary

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