Quick, what is 88% of 25? (Don’t reach for your calculator, pen, phone or friend – we’ll show you below how easy it is to get the correct answer quickly, if you know the right shortcuts).
Adults call upon their mental math abilities every day – often without realizing it. When they need mental math capabilities and don’t have them, they might look to Google, or resort to lengthy hand calculations to find answers to questions. Since adults are generally not under time pressure to come up with answers to math questions and are not often graded on their math work, it does not usually hurt them to take the slow route to finding answers to math questions. Math students, who take timed classroom quizzes and exams and standardized tests and more, do not have the luxury to take the long road to answering math questions. Beyond testing situations, most of the math students we know would certainly prefer to get through their math homework faster, so they can focus on other things.
There are countless examples of mental math shortcuts that can speed up students’ work on homework, classroom quizzes and tests, on standardized tests, on placement tests and on admissions tests. The math shortcuts are not just nice to have, they are a key skill for math students to succeed in class and on tests. The math students with high scores, high confidence and minimal math anxiety are often those students who have a working knowledge of the mental math skills and shortcuts that help them work efficiently, to arrive at the right answer as quickly as possible. Those students are the ones who have extra time at the end of a test to check over the work, or to go back and work on a problem, or problems, that they found challenging. At MATH 1-2-3®, we do believe strongly that academics are about more than high scores, but we know that students, parents and teachers often measure success in terms of grades and achievement on tests. The good news is mental math shortcuts not only tend to raise grades and scores, but also increase confidence and decrease math anxiety, which is a great combination of benefits!
Math shortcuts can be as fun as they are helpful. Yes, there are some cool (well, we think they are cool!) math tricks that make for good fun at parties (OK, maybe not!), but more importantly, math shortcuts just make exams, quizzes, homework and life easier.
We also love to see our tutoring students’ improvement on practice tests for the SAT, ACT, and other standardized tests and on test day. Oftentimes, that increase is not solely because they have learned new materials (which, of course they have), but because they have developed a new relationship with old material, learning how to solve those problems faster. Since standardized tests are as much a test of time management and the ability to work efficiently as they are of the skills and material being tested, mental math skills and math shortcuts can have great impact on not only students’ test-taking confidence, but on their scores.
We also love that look of wonder on our tutoring students’ faces as they learn key relationships between numbers and between concepts which allow them to look at math problems – and solve them – in a new way.
Since we love to share tips and tricks for working faster and more efficiently, and avoiding getting stuck on questions designed to be time wasters, we thought we’d discuss a few simple examples here.
So, what is 88% of 25? Well, we know that 88% of 25 is the same as 25% of 88. We also know that 25% equals ¼. So, all we need to do is divide 88 by 4 and we get 22. Yes, it’s true. You can check our work. We will wait…. If that were a math exam question, or a component of a question, simply knowing how to calculate percentages backwards and memorizing common percentages and their fraction equivalents would speed up the math student’s work. It also reduces the question to a very basic principle, dividing by 4, which lessens the chance of calculation errors and makes arriving at the answer much quicker.
Mental math shortcuts allow students to perform subtraction without borrowing digits. Subtraction is certainly an elementary school-level skill (and an important one at that), but subtraction comes up as a component in much more advanced math subjects. The ability to perform subtraction mentally, without borrowing digits, speeds up calculations and makes students more efficient. Subtraction which does not require borrowing from the next place up is often simple to perform mentally. If the second number has some larger digits that the first, for example in the tens place, then the calculation can be trickier to do mentally, because it appears to require borrowing. Math students who can mentally eliminate those larger digits have an easier time getting to the correct answer quickly. For example, if a math student is presented with 719-552, either as a problem, or as a component of a problem, the tens place can complicate mental math. It is much simpler to calculate 719-502 mentally and then mentally subtract the extra 50 separately. 719-502=217 and 217-50=167. Some students may find it easier to ask: “How much do I need to get to an even 100?” The question 719 – 552 is the same as (719 + 48) – (552 + 48) = 767 – 600 = 167. Students may be able to mentally use their knowledge of subtraction from 100 (for the above example, think of a survey with 52% responding “yes” and the other 48% responding “no”).
Yes, there are lots and lots more mental math tips. Combining mental math shortcuts increases a students’ ability to dissect and attack problems, and arrive at the correct answers as quickly and efficiently as possible.
The bottom line is that with the right training, a math student can take less time to solve a problem than it does to explain the solution.