Math Background

Lesson: Multidigit by One-Digit Multiplication
Developing the Concept

In this lesson, students use the expanded form of numbers to multiply with two- and three-digit factors. Be sure to provide enough practice with multiplication facts and multiplying with multiples of 10 and 100 before covering this topic.

Materials: none

Preparation: none

Prerequisite Skills and Background: Students should know the basic multiplication facts and how to use mental math to multiply with multiples of 10 and 100. They should also know how to write numbers in expanded form.

  • Write3 x 45 in vertical form on the board.
    vertical equation
  • Ask: What is 45 in expanded form?
    Lead students to see that there are 4 tens 5 ones in 45, 4 tens equal 40, and 5 ones equal 5, so the expanded form of 45 is 40 + 5.
  • Write3 x 45 in expanded form on the board, as shown below.
    vertical equation
  • Say: We'll multiply the ones first. What is 3 x 5?
    Students should know their multiplication facts well enough to promptly say 15.
    Write15 below the ones.
    vertical equation
  • Say: Multiply the tens next. What is 3 x 40?
    Students should have sufficient experience with multiplying by multiples of ten to know the answer is 120. Write120 + below the tens.
    vertical equation
  • Say: Now we just have to find the sum of 120 and 15. What is 120 + 15? (135)
    What is the product of 3 and 45? (135)
    Write135 = on the board, as shown below.
    vertical equation
  • Say: Let's multiply with a three-digit factor.
  • Write4 x 156 in vertical form on the board.
    vertical equation
  • Ask: What is 156 in expanded form?
    Lead students to see that there are 1 hundred 5 tens 6 ones in 156. 1 hundred equals 100, 5 tens equal 50, and 6 ones equal 6, so the expanded form of 156 is 100 + 50 + 6.
  • Write4 x 156 in expanded form on the board.
    vertical equation
  • Say: Multiply the ones first. What is 4 x 6? (24)
    Write24 below the ones.
    vertical equation
  • Say: Multiply the tens next. What is 4 x 50? (200)
    Write200 + below the tens.
    vertical equation
  • Say: Now multiply the hundreds. What is 4 x 100? (400)
    Write400 + below the hundreds.
    vertical equation
  • Ask: What is 400 + 200 + 24? (624)
    What is the product of 4 and 156? (624)
    Write624 = on the board, as shown below.
    vertical equation
  • Continue with additional examples that emphasize the connection between place value and multiplication.

Wrap-Up and Assessment Hints
Students need time to develop confidence and understanding of multidigit multiplication. When you assess students' progress, take extra time to ensure that students understand the importance of place value in multiplication.


Houghton Mifflin Math Grade 3