Estimation and powers of 10 notation may be the most powerful tools at your hand in a test. Multiplication techniques are always useful too, and always tested.
Estimation gives you a tool to quickly and smartly make an educated guess as to the right answer. In a multiple choice test this lets you discard stupid answers quickly. Powers of 10 notation lets you extend this to confidently deal with very large and very small numbers. Both of these techniques are likely to be tested because they are also incredibly useful in a work situation. When watching a presentation confident use of these skills will let you quickly check the plausibility of numbers you are being shown, and make sure the presenter isn't trying to pull the wool over your eyes.
Estimation
Estimation is an art form, rather than a science. It is about making good guesses to give you a reasonably close answer to the actual answer, whilst making the numbers easier to do. Let us consider a sum that we should all be able to do (but many people struggle with) 7 X 8. The answer, in case you are struggling, is 56. We could, quite happily estimate this as 5 X 10 = 50, which is pretty close. Slightly smarter we could estimate it as 5 X 11 = 55, which is obviously very close. Armed with the knowledge that 5 X 11 gives a very close answer, lets look at 7 X 16. This is actually 7 X (8 X 2). We could therefore estimate it as 5 X 22 and be sure we're pretty close. 5 X 22 = 110, the actual answer is 112. This illustrates the idea of proportional movement in a relatively simple form. When estimating for multiplication (or addition) you get better answers if you alter your values in opposite directions, and if you move them about proportionately. 7 is estimated down to 5, a change of 2/7. So, we estimate 8, or 16 up... so they go in opposite directions. 2/7 down and 2/8 up sounds about right... although we've seen 3/8 up actually gives us a closer answer. 2/7 down and 6/16 up gives us a good estimate as well (4/16 up, to 20 would give us 100 as our estimate, still not bad).
When estimating for division or subtraction the rule of thumb is you change both your numbers in the same direction. The idea of proportionate movement remains though. 121/11 = 11. Dividing by 10 is easy, so this will become x/10 1/11 at the 121 range, well 10 or 11 sounds good, it's about right. 121 - 11 = 110, and 110/10 = 11 - in this case exactly the right answer by happenstance.
One last thing. Many people confuse estimation with rounding. Estimation is an art with no hard or fast rules. Rounding is used with very strict rules and for very specific purposes. When rounding, you look at the number in the next place. If it is 0-4 you ignore it, if 5-9 you add one in the last place. Rounding is used to chop off values beyond reasonable, or usable limits. Your bank does this all the time: you can't get fractions of a penny from your account, so it is rounded off to the nearest penny.
Powers of 10 notation
We actually use powers of 10 notation a lot, without realising it. Prefixes such as kilo, mega, giga, tera, milli and micro use this concept to move things around by thousands (or 10
Let's look at the powers part first. 10 X 10 is 10
Now let's look at some more useful, if harder to handle numbers. How about 623,134. Well... this is 6.23134 X 10
So far, not that useful. But, this makes estimating in either multiplication or division with these numbers much easier.
What is 623,134 X 12, 543? Well it's about 78 X 10
What is 623,134 / 12, 543? Here we move the numbers the same way, and again stop to think. 60 X 10
Multiplication tools
You were probably only taught one method of multiplying at school. It is fast and efficient, but if you make a mistake it is hard to catch and correct. There are several other methods, which can be reviewed in the factsheets on the BBC Skillswise site. I am planning to develop interactive displays for these methods, but they are not currently ready.
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