What happens if you flip a fraction

We know what positive exponents do, can we extend that to zero? To fractions? To negative numbers? To complex numbers? That means, can we figure out what they do, if our rules stay true.

We want exponents to add when multiplying like bases, so what does that mean? Your CT cares about the skill issue, which is also important. But research Skemp, etc seems to show that retention and skill performance is better if it arises from understanding. Relational understanding, Skemp called it. Another way to think about this is patterns.

It fits. I struggle with this kind of dilemma a lot too. I wanted to have students explore why the log properties work. I agree that if you just tell them that they flip the fraction, your students may be able to memorize but not really know why. That confuses them. I believe you should not be looking for an universal answer that would fit all students. Your CT might have been right, given the specific student audience.

You know that. A teacher must be allowed more flexibility to adapt the materials and the teaching process to the student audience and individual student abilities.

Not impossible, just harder. There are probably all sorts of reasons why this is a bad idea, but: I draw a number line and then pick a number powers of 2 are simple to use , and go along the number line adding in the positive powers. Easy to get them to see that a number raised to the power of zero is 1, and then you continue the pattern ie keep on halving it.

I ask them how else you could show that and they generally get there on their own. So the question becomes why are we wasting resources teaching algebra to folks who will never us it except on a test? Almost none of them know anything about what math and science are. They are not memorization. I bought some fraction circles over Christmas to explain work problems to my top students. Struggling kids see exponents as utterly alien anyway.

Reblogged this on Reflections of a Second-career Math Teacher. If that leaves an empty space in the numerator, fill it with a 1. Flip the fraction inside the brackets first and then distribute the exponent to numerator and denominator. Thank you. In my experience, a lot of people seem to care more about the how than the why, which seems weird to me, because I understand better when I know why.

This is an old thread, but i just wanted to say as an adult university student i have always deplored shallow explanations and rote learning approaches. Far too few teachers take the time to provide comprehensive explanations; explanations I often require to really grip a concept and secure it in memory. I love your method and I hope that my teacher did the same. You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account.

You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. Email Address:. RSS - Posts. RSS - Comments. Show 2 more comments. Active Oldest Votes. Zubin Mukerjee Zubin Mukerjee Add a comment. Nick Nick 6, 9 9 gold badges 39 39 silver badges 67 67 bronze badges. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Related 0. Hot Network Questions. Question feed. Dividing fractions follows similar logic to multiplying fractions.

It involves working with the numerators and denominators separately. Once you have done your initial calculations, you put it all together to get your answer. Take a look at the math here. Do you see a pattern? What did you come up with? Did you notice that, when you take your original amount in this case, 20 and divide it by a number that continues to get smaller 10, then 5, then 2 , we end up with an answer that gets larger. Follow this logic into fractions, keeping in mind that fractions are not only less than 10, 5, and 2, but 1.

Using this pattern, we determine that dividing the 20 screwdrivers by a number less than 1 would get us a larger answer than if we divided the 20 by 10, 5, or 2. This does not mean that we end up with 40 screwdrivers, though. What it means is that we end up with 40 parts of screwdrivers. You have to imagine that each of the screwdrivers were split into 2.

Twenty screwdrivers split in half would give us 40 pieces in the end. The question now becomes, how do we do this mathematically? The answer lies in using what is known as a reciprocal.