Multi Digit Multiplication Strategies

Look at the problem below and think about how your students would respond to the two questions:

• What is the value of the 2?
• Why should we place a 0 in this space? 

If your students answer the questions by saying, "the 2 is worth 2," or "I placed the 0 in that area because I was always told to move it down," consider the idea that the student(s) do not fully understand the concept of multiplying multi digit numbers.

According to John Van De Walle, "For multiplication, the ability to break numbers apart in flexible ways is even more important than in addition or subtraction.  Your goal (as an educator) might be that each of your children has at least one or two methods that are reasonably efficient, mathematically correct, and useful with lots of different numbers."

In addition, the Standards of Mathematical Practice state that we should provide students opportunities to make choices and try out potential solution paths to answer problems.

When teaching, let's first question students to see how they solve a problem (student invented strategies).  If a limited number of strategies arise do not be afraid to introduce one of the strategies below.  These strategies develop deeper conceptual understanding while reinforcing the use of mental math.

 Another strategy that reinforces mental math and base ten understanding is partial products.

Click on the link below to see a Number Talks video in which students use various multiplication strategies:

Multiplication Number Talk Video

For additional multiplication strategies, download the FREE multiplication strategies anchor chart by clicking on the picture below.

P.S. Let's revisit the answers to the two questions at the beginning of the post:

• What is the value of the 2?  
• Answer: The 2 is worth 2 tens or 20.

• Why should we place a 0 in this space? 
• Answer: We have a 0 in the second row because any multiple of ten or one hundred ends in a zero.  With our base 10 number system a zero serves as a place holder.    Using the example, 20 x 3 is 60 and 20 x 10 is 200.  Combining both 60 and 200 yields 260.  The 0 represents a place holder in the ones place and ultimately showing there are no ones in the 200 or 60.