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What Does the Zero Mean in Multi-Digit Multiplication?

For the past two weeks I have been requiring my students complete a Computation Check Up everyday because even though they may have learned the skill they are not fluent with any of the 4 operations. Each day the students complete 4 computation problems  that addresses one of the 4 operations. The first problem is always subtraction with zeros, the second problem  2 digit by 2 digit  multiplication, the third problem is  division, and the last problem is subtraction with a zero in the middle. I grade the problems daily so that the students can have immediate feedback which encourages them to do better the next day.

Since I have implemented the Computation Check Up everyday, I have noticed that some of my higher level students who problem solve very well have been struggling with the computation. This has been a real eye opener for me as well as these students because I tend not to pay as close attention to these students because they do not require as much attention as the other students.  Well, this one particular student has been struggling with the computation to the point that he was constantly making 50’s everyday. So, I decided to bring him to my class along with the other students for tutoring. When I teach 2 digit by 2 digit multiplication I  teach my students to see the problem as two separate problems because it’s easier for them see it this way; it helps them to compartmentalize the problem instead of seeing it as one gigantic  problem with many parts. While we were working on the problem below the student asked, “Do I move the 2 over ?” I responded, ” You can move the 2 but you have to add a zero because the 2 is in the tens place and you are actually multiplying by 2 tens which is 20.”

2digit multiplication

This question made me realize why he was so confused because I had taught every  skill within the context of place value, but when I taught this skill I did not make the connection for the students by explicitly saying  that the 2 in the tens place is 2 tens which is actually 20.

The next day in class I asked the students why do we put the zero in ones place when multiply in tens place? Hands began to raise, but before I called on a student I told the class that the answer was not the zero was a place holder. All around the room you could see hands slowly go down. This made me realize that many of my students had been taught that zero is a place holder and therefore has NO value in the number system.  I don’t think elementary teachers realize when a student is taught that zero is a place holder  it sends the message to students that zero always holds the place and does not reinforce the understanding that if a zero is in a number there is nothing in that place.

My approach to teaching operations with numbers that have a zero has changed because I now understand that many of my students have to learn that a zero has meaning even though the value of zero is nothing.

4 thoughts on “What Does the Zero Mean in Multi-Digit Multiplication?”

  1. your flaw is that you are not teaching a algorithm and not a concept. try using the grid method to teach that 20 is 2 x 10 and we are not adding a zero but multiplying by ten. Using small numbers multiplied by 10 or even a hundred to see the pattern. math is about patterns and not about algorithms or i was taught ” tricks” .

    1. Thank you for your comment. The the blog post is not about teaching algorithms or concepts it is about students’understanding of place value and multiplying by multiples of 10 and 100. Yes, your statement about teaching an algorithm is correct. The standard or expectation is for 4th grade math students to be fluent with the standard algorithm. Also, I dedicated a previous blog post to teaching patterns to students

  2. When I taught 3rd and 4th grade, I would use the exercise of holding out a handful of actual money to a student, and then say, “Now I’m going to give you this zero times. What do you get?”

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