Mathematical+Reflections,+p.+25+0910

11/20/09 Block 7E
 * MM
 * __Big Idea:__** Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
 * __Essential Question:__** What methods are there for comparing things?


 * __MR 2__**

When you're dealing with large numbers, or small numbers, and trying to sell something. A lot of people understand percents, because it gives you a lot of information, (part to whole, and part to part) and a lot of people understand percents because they are very simple. A good example is if you're comparing discounts, I bet you've seen many ads or posters that say "Now 20% off!" or something like that.
 * __1- Give an example of a situation in which it makes sense to use percents to make comparisons-__**

__**2- Using your example from part 1, show how to make a comparison using percents-**__ Numbers larger than 100- Let's say you took a survey to find out how much people enjoyed cola over juice. 1000 people took the survey, and 750 people out of those 1000 people preffered cola. You would find out how many times 100 goes in 1000. (100/1000=10) You would then divide 750 by 10 (the number of times 100 goes into 1000. 10 goes into 750, 75 times. You now have your percent of people who preffered cola: 75%. That means that the percent of people who preffered juice is 25%. (100-75=25) 75% of the people surveyed preffered cola, while only 25% of people surveyed preffered juice. When comparing numbers with percents, it's always more useful to use part to part.

__3- **Explain why percents are useful for making comparisons-**__ Percents are useful because as I stated before: People understand percents, and they're simple. Percents are also useful because they can be converted into other units of comparison, such as ratios, and fractions.

__**4- Give an example of a situation in which you think another form of comparison is better than percents. Explain your reasoning-**__ The only problem with percents is that they don't give the exact numbers that you're comparing. If someone wants to know exactly how much people you surveyed, or exactly how much more people preffered cola, they shouldn't use percents.

__**5- Can you find a percent comparison from a ratio comparison? Explain how, or tell what additional information you would need-**__ Yes, you can find a percent comparison from a ratio comparison. Let's say the ratio of people who prefer cola to juice is 7.5 to 2.5. Add 7.5 to 2.5 and see how many time that number goes into 100. (7.5+2.5=10 100/10=10). Multiply 10 by 7.5. (10*7.5=75) = 75%.

In this unit, I learned a lot more about converting raw data into comparison units, such as percents ratios, and fractions. I also learned that different situations call for different units. In problem 2.1 A: I learned to keep your eyes out for directions and info about the data because sometimes if you don't read some of them you could end up misunderstanding the data! ||
 * __Summary-__**