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A student claims that division always makes things smaller so 5 divided by .5 cannot be ten because ten is greater than the number 5 she started with. How do you respond?
Division does not always make things smaller.
Is it true that points are smaller than dots but bigger than specks?
Being strictly mathematical about it ... -- A point has a definition, but 'dots' and 'specks' don't, so it's kind of hard to compare them. -- A point is only a location. It has no dimensions ... no length, width, height, thickness, diameter, area, volume, etc. No measurements at all. -- So nothing can be smaller than a point. -- If a dot or a speck have any size at all ... and maybe they do because you're talking about things that are bigger or smaller than other things ... then a point must be the smallest one of all, because it has no size at all and I dare you to get any smaller than that.
What is Dimunition?
You probably mean diminution - making things smaller, or simply the action of becoming smaller.
Is it for a mirror to make things look larger or smaller?
No
Does multiplication always make things bigger?
This is a pretty technical question. The answer will vary depending on your grade level.If you are talking about magnitude (i.e., ignore the negative) than the answer is sort of (I'll explain further down).If you are allowing negative numbers,Start with 2, and multiply it by -1. 2 x -1 = -2 which is smaller than 2.Now, what about multiplying by a number between 0 and 1 (0.5 for example).Start with 4 and multiply by .5 to get 2. 2 is smaller than 4.However, you could argue that by multiplying by a decimal, you are in addition to multiplying, dividing which is why the number is reduced. By the same logic, division would always result in a number of lower magnitude. That would be the side I would tend to take as well, so:Multiplication always increases the magnitude of a number, but does notnecessarilymake it bigger. Division always reduces the magnitude of a number, but does not necessarily make it larger.I should also mention, this is controversial. People can make the argument either way (in regards to multiplication vs division).
