"In this session, the student and I continued to look at content-based skills and shortcuts for the Math test of the ACT. Specifically, we explored:
* recognizing when a question lends itself either to working with longer, more time-consuming numbers or calculations or with shorter numbers or operations that can be done mentally in less time than it would take to use a calculator;
* using the properties of factors and multiples to solve equations for 2x, 3x, etc. without doing the extra work of solving for x and then multiplying;
* quickly determining whether 2-digit or longer numbers are divisible by 3 (by a choice of 2 different methods);
* calculating the area of trapezoids and the volume of non-rectangular 3-dimensional shapes;
* using logarithms and their properties; and
* reducing the amount of work necessary to calculate the total items involved by the end of a sequence that includes a constant increase or decrease in items across each interval for a given number of intervals, with or without a starting ("base") number of items by working from the two outermost ends of the sequence toward the middle thusly:
-- 1. finding the total items for the last entry in the sequence by multiplying the increase per interval by the total number of intervals remaining after the first entry;
-- 2. adding the starting base to the total items for the last entry in the sequence; and
-- 3. multiplying the resulting sum by the total number of *pairs* of entries in the sequence (i.e. the number of entries divided by 2).
Although this last technique seemed time-consuming and counter-intuitive to the student when I first presented it, she was open-minded enough to try it on a fresh problem of the structure described above. Upon using the shortcut, she expressed that it was indeed much faster than the method she had been using to solve problems of this type.
We also reviewed the value of solving only for 1 or 2 digits and checking those digits against the corresponding digits of the answer choices, as opposed to solving the entire problem first and comparing the complete solution to the answer choices only afterward."