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Identifying things that make you feel capable and inspired should be the things that you hold with high regards. Most people would consider those things their source of empowerment; and should be dedicating time to it daily. This is one way to ensure you have the fuel you need to be as productive as you desire.
Offering to be of assistance to help another person with their maths tuition is a powerful way to wake up the community action levels in the world. There is such a strong need for tutors and other academically savvy persons to reach out to others. There is always enough room at the table for people who are intellectually driven to make a contribution.
Knowing how to create a space to learn begins with the initial outlook you have about yourself – like a student with their maths tutor. This is where your closest relationships might be put to good use; their insight as to how they experience you can be useful when you want to examine their information to your own. What you might discover are areas for improvement and attributes on which you should be placing more time into.
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One of the best ways to get the most out of things that inspire you is to have someone that you trust to share them with. Everyone needs a sounding board to weight out the pros and cons of their ventures; you should not be any different. The positive thoughts and ideas one has needs to be appreciated; and there is no better way to do that than putting them into action.
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I had my own math shortcuts when I was a child. Using these meant that I didn’t “show my work” in math class, as was required. This annoyed many of the teachers, and lowered my grades. I did get the correct solutions to my math problems, however. I was simply using different algorithms, ones which I had a hard time expressing on paper.
In my thinking, for example, 97 x 16 became 100 x 16 (1600) minus 3 x 16 (48). It was easier that way, and thinking this way became almost automatic. As a result, I might just write down 1552 even though I couldn’t explain very well how I arrived at the answer. My teachers called that a problem, but many years later such math shortcuts were being sold in seminars and books.
Making Your Own Math Shortcuts
You can make your own math shortcuts. The following may give you some ideas on how to do that. Alternately, you can try any of the shortcuts and algorithms you read about and adopt the ones that are best suited to you. There are no perfect techniques for all people, because our minds work in slightly different ways.
For example, suppose you want to multiply 68 x 6. My mind immediately thinks “60 x 6 = 360 and 8 x 6 = 48, and 360 + 48 is 408.” That is one way to quickly arrive at a solution without pen and paper. It is essentially this: (60 x 6) + (8 x 6) = 408.
Want another way? Think of it as (70 x 6) – (2 x 6). The “internal dialog” might be something like this: “70 x 6 = 420, but that is two “sixes” too many, so take away two sixes (12) and I have 408.” The point is that there is often more than one way, and you can use whichever math shortcut is easier for you.
If the problem was 68 x 9, by the way, my mind immediately focuses on the 9. Why? Because it is close to 10, and multiplying by 10 is easy. 68 x 10 is 680, from which I just have subtract the extra 68 to arrive at the solution of 612. Always look for the numbers that are close to 10 or 100 or 1000, and you’ll find the easier way to do the math, especially if you are trying to do it in your head.
Percentages can be trickier to do as mental math, but there are ways. Suppose, for example, that you want to figure what the 4.6% sales tax will amount to on your $29 book. One quick way to estimate it is to take 10%, or $2.90, cut that in half to arrive at 5%, or $1.45, and then just guess at around $1.35, because you know 4.6% is a little less than 5%. Alternately, you could think of 5% as a 20th of the price – if this is easier – and then round that figure down a bit.
What if you want a more precise solution? 1% of $29 is easy to arrive at (.29), so multiply that by 4 to arrive at $1.16. (You might think of this as (4 x 30) – 4.) Now you just need to add .6% to that. Think 6 x 29 = 174, and then put the decimal in the right place: .174. Add that .18 (round it up as the store will likely do) to the 1.16 and you have $1.34 in sale’s tax, pretty close to our quick estimate. This is not as difficult as it might seem once you practice these shortcuts a bit.
These simple methods do require a basic understanding of math. If you don’t understand that 123 multiplied by 199 is just adding 123 to itself 199 times – that multiplication is just another way to do addition – you will have problems with these math shortcuts. In that case, you may want to simply use the easiest of the math shortcuts – a calculator.
