When working with fractions, I find it effective to require students to convert each fraction that we work with to its decimal equivalent, to convert that decimal equivalent back into the original fraction, to convert that decimal into its percentage equivalent, to work a simple percentage problem using that percentage and finally to work the same problem using the initial fraction. This comprehensive method helps students to see the relationships between fractions, decimals and percentages in a holistic way and to promote the necessary skills in each element.
While working on quadratic equations with students I have discovered a few techniques that are particularly effective. By far the most effective is to require the students to solve each one by all three methods ( factoring, completing the square and quadratic formula ) for each and every problem rather than solving it only by the easiest way and to require the graph for each and every one. Of course, most quadratics are more easily solved by one particular method rather than the other two so I allow them to do the easiest first and simply prove the result with the other two. This technique assures that the student can do it in each way and that they develop the skill of determining which is the “best” way for any particular problem. Another is to require students to show each and every quadratic in both standard form ( ax^2+bx+c ) and in vertex form (a(x-h)+k). Still another is to explain and require students to be able to explain the derivation of the quadratic... read more