I really enjoy teaching my students the quadratic formula, because I think I've found a great blend of pedagogy and gimmickry to get them to apply it. Here are a few things I do:
1) Instead of using the phrasing "minus b", I use the phrasing "the opposite of b." This really helps my students to understand that the notation "-b" does not always make the number negative; it just flips it to its opposite.
2) Traditionally, we ask our students to write down the values of a, b, and c before substituting it into the quadratic formula. I have them write down four values instead of three: a, b, -b, and c, so that when they reach the "-b" portion of the formula, they already have that figured out.
3) I have a quadratic equations song, which is not sung to the tune of "pop goes the weasel." Instead, it goes to the tune of "Jingle Bells," and kids really love to hear it. The song lyrics are included on this worksheet.
**You may also download the free 30-second video of me singing this song, which is listed as a free product named "Quadratic Formula 2012 - Song to the tune of "Jingle Bells"
4) Instead of having them write down the formula and laboriously lecturing them, I simply provide each student with a half-page of the notes to simply tape into their notebooks. We go over a few examples and I set them to task working on this assignment.
I still admit defeat when it comes to the b^2-4ac portion (the discriminant); they often use incorrect notation such as -3^2, instead of (-3)^2, and they often seem to get flustered with whether to multiply by -4, or whether to subtract. Try as I might, I have to admit that this step is the most difficult for my students and always has been. I've tried to remedy this problem by having them substitute values for a, b, and c into the expression b^2-4ac throughout the year before we get to the quadratic formula, and doing so has helped.
If any of you have a suggestion for how to best get over this hurdle, please send it along!
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The second page of the file is for student notes: please run off one half-sheet per student.
This worksheet is intended for students to show their work on a separate sheet of paper.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.