- Why should I bother learning this?
Division allows you to share things. Without the ability to divide, you could get uneven amounts. Without division, you wouldn't be able to decide how to share 20 baseball cards fairly among your friends or how to decide how many tables are needed to seat students in the cafeteria.
- Why is division by zero not equal to zero?
Since 0 4 = 0, many students are convinced that 4 0 = 0 as well. Remind students that when solving a division expression such as 0 4, you have 0 items and are trying to find out how many groups of 4 items you can make. Obviously, you will have 0 groups if there are 0 items to begin with. If you had 4 0, you would have 4 items and would be trying to find out how many groups you will need if you wanted 0 items in each group. The problem is that if you have 0 items in each group, you would never get to divide or share the 4 items among the groups. As a matter of fact, in this case, you could make an infinite number of groups that contain zero objects in each group. Therefore, the answer is undefined.
- Why do I need to check my answer?
It is common for students to not want to take the extra time to check their work. Although it is often difficult to convince students of the merit to checking their work, once students find a few of their mistakes, they will be more likely to see the worth in this extra effort. Students need to know that checking your work is not simply busy work.