Mathematical+Reflections,+p.+25+0910

V.H Nov. 10, 2009 Math 7D Essential Question: //What methods are there for comparing things?//  **Vocabulary:** Percent: A fraction with the replaced ‘out of 100’ shown in this symbol: %.
 * 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. **

If you want to convert a part-to-part ratio to a percent, first you change the ratio to part to whole (by adding both parts for the fraction denominator, and taking the first part for the numerator), converting this to a decimal, and then to a percent.
 * Notes:**

Ms. Andrea wants to separate her students in 3 groups: beginners, intermediates, and advanced. She has 50 students in total. 6 students ar at the beginner level, 29 are in the intermediate, and 15 students are in advanced. (Very easy to turn these fractions into percents)
 * 1. Give an Example of a situation in which it makes sense to use percents to make comparisons.**

58% of the students are in Ms. Andrea’s intermediate group and 42% are not.
 * 2. Using your example from part 1, show how to make a comparison using percents. **


 * 3. Explain why percents are useful for making comparisons.**

Percents are good for making comparisons because they show part to whole instead comparisons of part to part like in a ratio. Percents are easy to convert and help you understand a more complex fraction.

Luis tested 5 people for his science experiment. His experiment was testing whether people when asked a math question would change answers when a variable was added (but the other variables may not match what they’re told to be). 3 people did not change their answer, and 2 didn’t. Therefore, the ratio of who did and who didn’t is 3:5
 * 4. Give an example of a situation in which you think another form of comparison is better than percents. Explain your reasoning. **

Ratios are better to use here because you are dealing with small numbers without drastic differences. Percents would just enlarge the numbers.


 * 5. Can you find a percent comparison from a ratio comparison? Explain how, or tell what additional information you would need.**

You //can// find a percent comparison from a ratio comparison by making a fraction out of the ratio, changing it to a decimal, and then changing it to a percent.


 * Summary:**

Percents are very simple ways of writing complex fractions. I have mostly mastered percents even before this sub-unit, and hope I will be able to use more ratios (which I have not ‘mastered’ yet) in the next unit.  I may want to practice the skill of finding whole percents without using a calculator, and hopefully the next ACE problems will involve some percents that will allow me to use my mental math but still check my work on a calculator.


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