For the students taking Professor Snyder's class...

Let us start with the verb あがる, since the the vowel before the る is あ the verb must be a consonant verb. Therefore, the ます form is あがります. Also, the て and た forms, which are always the same (minus the え and あ), must have a small つ to replace the dropped consonant. So we have, あがって and あがった. The vowels before the る for a consonant verb are あ and お, if the verb ends in う its て and た conjugations are the same as a consonant verb. For example, take the word かう, which becomes かって and かった. However, the う becomes い for the ます form,かいます.
For verbs that don't end in る, such as う、く、ぐ、す、む、つ、ぶ、ぬ.
く　ー＞　いて／いた
　　　　　ぐ　ー＞　いで／いだ　
　　　　　す　ー＞　して／した
　　　　　む　ー＞　んで／んだ
　　　　　ぶ　ー＞　んで／んだ
　　　　　ぬ　ー＞　んで／んだ
　　　　　つ　ー＞　って／った

If the verb is ーえる or ーいる as たべる or みる then the verb is a vowel verb and conjugates like this...
たべて／たべた
　　　みて／みた

Hope this helps, good-luck!