I have always taught how to identify if functions are even or odd by substituting in -x for x and then multiplying the original function by -1. For my honor students this is still the way I approach it but I tried a different approach for my on-level students this year.
I started the class by each student reading an article from the BBC released in December 2012 about Superstorm Sandy and if '0' is even or odd. New York residents were limited to the days they could pump gas based on the last number of their licence plate number. Odds went one day and the evens (add those ending with '0' as the mayor said) could pump gas the next day. The article is easy to read and shows why zero is indeed zero. As a class we discussed the major points of the article.
Then each student received notes and we went went over it together. The approach is if all exponents of the function is even (and a constant has an even exponent of zero) then the function is even, if all exponents are odd then the function is odd, and if the exponents are a mixture of even and odd then the function is neither even or odd.
I 'borrowed' the powerpoint from a teacher in Georgia and then added in a few polleverywhere.com polls at the back end. I had each student send their response to the question asked by texting on their phone. The program is free (up to 40 responses) and you can choice how people can respond. There is an option to embed the poll in your powerpoint and the poll will automatically update as answers are submitted. My students LOVED this. I did have to reset it after each class and make sure you have internet connection! You can answer my questions by selecting the following links below:
I only use the free options provided by the site but the paid options look fabulous. I honestly know I would not use them to the fullness of their abilities and it would be waste to spend that money.
I ended the class by having students answer 5 questions for a ticket-out-the door. I graded that sheet for correctness and that was entered in my gradebook as their homework grade for that objective.
Educator who loves math and working with students.