When Dividing, Zero Is No Hero - Why We Can't Divide by Zero

Have you ever wondered why we can't divide by zero?  I remember asking that long ago in a math class, and the teacher's response was, "Because we just can't!"  I just love it when things are so clearly explained to me. So instead of a rote answer, let's investigate the question step-by-step.

The first question we need to answer is what does a does division mean?  Let's use the example problem on the right.

1. The 6 inside the box means we have six items such as balls. (dividend) 
2. The number 2 outside the box (divisor) tells us we want to put or separate the six balls into two groups. 
3. The question is, “How many balls will be in each group?” 
4. The answer is, “Three balls will be in each of the two groups.” (quotient)

                                      

Using the sequence above, let's look at another problem, only this time let's divide by zero.

1. The 6 inside the box means we have six items like balls. (dividend) 
2. The number 0 outside the box (divisor) tells us we want to put or separate the balls into groups into no groups. 
3. The question is, “How many balls can we put into no groups?” 
4. The answer is, “If there are no groups, we cannot put the balls into a group.” 
5. Therefore, we cannot divide by zero because we will always have zero groups (or nothing) in which to put things. You can’t put something into nothing.

Let’s look at dividing by zero a different way. We know that division is the inverse (opposite) of multiplication; so………..

1. In the problem 12 ÷ 3 = 4.  This means we can divide 12 into three equal groups with four in each group.
2. Accordingly, 4 × 3 = 12.  Four groups with three in each group equals 12 things.

So returning to our problem of six divided by zero..... 

1. If 6 ÷ 0 = 0....... 
2. Then 0 × 0 should equal 6, but it doesn’t; it equals 0. So in this situation, we cannot divide by zero and get the answer of six.

We also know multiplication is repeated addition; so in the first problem of 12 ÷ 3, if we add three groups of 4 together, we should get a sum of 12. 4 + 4 + 4 = 12

As a result, in the second example of 6 ÷ 0, if six zeros are added together, we should get the answer of 6. 0 + 0 + 0 + 0 + 0 + 0 = 0 However we don’t. We get 0 as the answer; so, again our answer is wrong.

FREE

It is apparent that how many groups of zero we have is not important because they will never add up to equal the right answer. We could have as many as one billion groups of zero, and the sum would still equal zero. So, it doesn't make sense to divide by zero since there will never be a good answer. As a result, in the Algebraic world, we say that when we divide by zero, the answer is undefined. I guess that is the same as saying, "You can't divide by zero," but now at least you know why.

If you would like a free resource about this very topic, just click under the resource title page on your right.

Conducting Effective Parent/Teacher Conferences

If you are like most teachers, you are preparing for your first round of parent/teacher conferences. Now that I teach on the college level, this is one activity I currently don't have to do, but when I did, I really did enjoy them. Why? Because I was prepared with more than just the student's grades. Here are some of the ways I got ready.

First, in preparing for parent/teacher conferences, what can you do on a daily basis? Is the conference based on simply talking about grades or are there additional items that need discussing? How can an observation be specific without offending the parent or guardian? How is it possible to remember everything?

I kept a clipboard in my classroom on which were taped five 6” x 8” file cards so they overlapped - something like you see in the two pictures above. Each week, I tired to evaluate five students, writing at least two observations for each child on the cards. At the end of the week, the file cards were removed and placed into the children's folders. The next week, four different students were chosen to be evaluated. In this way, I did not feel overwhelmed, and had time to really concentrate on a small group of children. By the end of 4-5 weeks, each child in the class had been observed at least twice. By the end of the year, every child had been observed at least eight different times.

Below are sample observations which might appear on the cards.

Student	Date	Observation	IEP	ESL
Mary Kay	8/20   8/28	Likes to work alone; shy and withdrawn;  wears a great deal of make-up. She has a good self concept and is friendly. Her preferred learning style is  visual based on the modality survey.	X
Donald	9/19   9/21	Leader, at times domineering, likes to  play games where money is involved. His preferred learning style is auditory  (from the modality survey). He can be a  “bully,” especially in competitive games. He tends to use aggressive language with  those who are not considered athletic.


By the time the first parent/teacher conferences rolled around, I had at least two observations for each child. This allowed me to share specific things (besides grades) with the parents/guardians. As the year progressed, more observations were added; so, that a parent/guardian as well as myself could readily see progress in not only grades, but in a student's behavior and social skills. The cards were also an easy reference for filling out the paperwork for a 504 plan or an IEP (Individual Education Plan). As a result of utilizing the cards, I learned pertinent and important facts related to the whole child which in turn created an effective and relevant parent/teacher conference.

$1.95

To keep the conference on the right track, I also created a checklist to use during parent/teacher conferences.  It featured nine characteristics listed in a brief, succinct checklist form. During conferences, this guide allowed me to have specific items to talk about besides grades. Some of the characteristics included were study skills and organization, response to assignments, class attitude, inquiry skills, etc. Since other teachers at my school were always asking to use it, I rewrote it and placed it in my TPT store. It is available for only $1.95, and I guarantee it will keep your conferences flowing and your parents focused! When you have time, check it out!