Lesson 6: The Standard Multiplication Algorithm

Getting Started

Questions to Explore

  • What are some strategies we can use to multiply large numbers?

Facts and Definitions

  • algorithm: a set of steps that can be used to solve a particular type of problem
  • The standard algorithm for multiplication is a common approach to solving multiplication problems where factors are stacked vertically and a series of steps are followed to find the product
  • When using the standard algorithm for multiplication, it is important to line up the places of the two factors correctly (for example, the ones place of the first factor directly on top of the ones place of the second factor)

Skills

  • 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

Materials

  • calculator
  • fine point dry-erase markers (kit)
  • glue or glue stick
  • Interactive Notebook (kit)
  • laminated grid (kit)
  • scissors
  • whiteboard (kit)

Introduction

Materials: fine point dry-erase markers (kit), whiteboard (kit)
Explain to your child that now that she's practiced multiplying multi-digit numbers using arrays and the area model, it's time to move on to a more challenging approach. Say, "This approach is called the standard algorithm for multiplication. An algorithm is a set of steps that we can use to solve a particular type of problem. This approach is the one that most people use when multiplying big numbers."

Write 12×4=48 vertically on the whiteboard, and ask, "What do you see happening here?" Lead your child to see that the top number (12) is being multiplied by the bottom number (4) one digit at a time. Remind your child that, as with multi-digit addition and subtraction problems, it's important to line up the places correctly. That means that bottom number must line up right under the ones place of the top number.

As needed, say, "First, we multiply 2 times 4 and write 8 in the ones place and below the 2 and 4. Next, we multiply 1 times 4 and write 4 in the tens place and below the 1."
Now, write 13x5=65 vertically on the whiteboard, and explain that we always begin multiplying on the right and move to the left. Ask, "What is 3 times 5?" (15) Show your child that the 5 is written in the ones place and the 1 in 15 is then carried over the tens place (above the 1 in 13) and added to the product of 1 and 5 to make 6.
Next, provide time for your child to watch the video at the following web link.
Web Link