Dear Rob,
As much fun of a place that the Study Hut is, it is not really the place I want to
be during the summer. Although I realize the importance of maintaining some sort of
intelligence over the summer break, thinking is not appealing at all. After focusing
almost all of my brain capacity on school work for 9 months, I think 3 months is a fair
break from all learning whatsoever.
Yes, it is true that many students are enrolled in summer school and therefore
you might say it is necessary to continue tutoring throughout at least the duration of
the course. However, the way that summer school is set up, we cover around 2 to 3
chapters a day and may have a test that day. In that case, I would be coming to
tutoring to go over something I have already been tested on making it a waste of forty
dollars. Also, the content, due to the lack of allotted time is very watered down causing
the difficulty, at least for me, rather easy. If I do not need to be at tutoring I am simply
not only my time, but yours as well.
Adding to the lack of need for tutoring, there is also the fact that I simply do not
want to be there. I wake up at 6:30 am to go to summer school for 5 ½ hours then
have to go to football for 3 hours. By the time I would be available to come to tutoring,
my brain is absolutely fried and I would not be able to concentrate at all, which would
once again be a complete waste of time. I want to use the few free hours I have to
just relax and take my mind off anything that is making summer not seem like summer,
especially school work.
Sincerely,
Donovan Ward

Mental Math

Nowadays, kids rely heavily upon their calculator for simple arithmetic. Most of us know our multiplication tables and how to multiple or divide some easier numbers. When the numbers start to get more complex thought, people get very frustrated and don’t even attempt to figure it out without a calculator. Here are some tips for doing mental math:

Say we wanted to multiply 12 by 23. Not too hard to do by hand or calculator, but when most are asked what the answer is without a calculator, their response is without thought, “I do not know”. You can always break these numbers down into problems that are much easier to do in your head:

First let’s look at something like 12×20. 20 is 2×10, so 12×20 is just 12x(2×10). Since 12×2 is 24 and 24×10 is 240, 12×20=240.

Now, let’s look at 12×23. The trick here is to rewrite one of the numbers as the sum of two numbers we can easily multiply, then use distributive property to make the one multiplication the sum of two easier multiplications. We can write 23 at 20+3. So, 12(23) = 12(20+3) which by the distributive property is 12(20) +12(3) = 240 +36 = 276. Since 12×20 and 12×3 are easy to do in the head, multiplying 12×23 can be just as easy if you can keep track of a few extra numbers.

Similarly 12 = 10+2, so (12)23= (10+2)23 = 10(23) +2(23) = 230+46 = 276. Either way, it isn’t as hard as most people think it is.

The next trick is to change the numbers we are multiplying. What is 15×18? Well, 18=2×9, so 15×18 = 15x(2×9) = (15×2)x9 = 30×9. Again, 30 = 3×10, so 30×9 is 10x(3×9) = 10×27 = 270. While this may seem like a lot of steps, once you get the hang of it, you can do this really quickly in your head.

These tricks work well for numbers under 100. When you get above 100, the tricks work the same, there are just more numbers to keep track of. Once you get the hang of keeping track of all the numbers, bigger numbers will become just as easy to multiply.

Try these in your head:

18×32 [18=20-2 so 18x32 = (20-2)x32 = 20(32)-2(32)= 640-64=576]

22×35 [22=2x11 so 22x35 = 11x2x35 = 11x70 = 770]

A lot of students from Palos Verdes and Peninsula High School come into our Redondo office despising math, and I don’t blame them. Mathematics is a tough subject that takes a lot of time to understand, and students often try to get by by memorizing the rules, proofs, and theorems without ever perceiving how they work. After all, it’s a nasty subject that I’ll never really need. Who cares about the directrix of a parabola? When do I need to know how to calculate the area of a n-sided polygon? What’s the point of being able to do basic arithmetic in my head? I can just use my iPhone calculator to get the answer, or Google search it. That’s good enough.

It’s tough to argue against these points, but I believe that putting your best foot forward when tackling math builds a solid foundation, not only in regards to academics but to life as well. If a child is willing to put in the time to genuinely understand how trigonometric identities work, they’ll be more likely to work for things in life, whether it be a job, sport, or relationship in the future. If a student understands that they need to address their poor grades in math head-on instead of ignoring it, they won’t run when life gets tough. On the other hand, if that student resorts to taking short cuts in math or gives up after trying only once, they’re likely to throw their hands up in the air whenever they face adversity. Just like there are no short cuts to becoming a great Sea King or Panther athlete, there are no short cuts in academics, especially math.

So please, help your child develop good life habits by spending some extra time one or two nights a week helping them with their math. Make sure they show their work and don’t just guess the answer. Ask them questions to see how well they really grasp the material. Tell them, “Good job!” or “Nice work!” when they’re trying their best. Teach them the joy of hard work. As a math tutor, there are no secrets to help these students. I help them first understand the basics and then build on those basics. I teach them how to systematically analyze a problem and try various approaches instead of looking in the back of the book for the answer. I encourage them to ask questions when they don’t understand something. These are all good habits that people need to succeed in life, and mathematics is a great place for children to start developing them.