6.3+Selecting+Delegates+0910

MMS January 18/2010 Math 7B

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?
 * Investigation 6: Choosing Strategies**

Find a method to find how many delegates should be fairly chosen from 9 geograhic regions, 5 races and 2 areas.
 * Problem 6.3

A. How many of the 1000 delegates should be chosen from each of the nine geographic regions?** There are 2 methods to find a fair amount of delegates from each region (I will use both). 1. Divide the region population by the total (U.S.) population, then multiply your answer by 1000 ((because all of the numbers that we use for the populations have 3 more 0's at the end) 2. Make a proportion. The region population divided by the total (U.S.) population which equals to delegates from region (X) divided by total # of delegates. 13,207 people (Population of New England) divided by 248,710 people (Population of the U.S.) = 0.053 0.053 multiplied by 1000 = 53.1 rounded(because you cant have 1/10 of a person)= 53 delegates from New England.
 * Note: Both methods will have same answer**
 * New England (method #1):

(method #2): Top Right - (people) Population of region (New England) Bottom Right - (people) Population of the U.S. Top Left - (people) # of delegates from New England Bottom Left - (people) Total # of delegates
 * Legend:**

You have to cross multiply: 13,207*1000=248,710*X 13,207,000=248,710*X

To leave X alone, you have to divide 248,710*X by 248,710 to cancel it out and leave X alone, and to do this, since 13,207,000 equals 248,710*X, you have to do anything that you did to one side to the other. Therefore, you have to divide 13,207,000 and 248,710*X by 248,710.

This equals to 13,207,000 divided by 248,710 = 53.1 (rounded)= 53 delegates from New England.


 * Note: * stands for multiplication**

Both methods have the same result and always will.

37,602 people (Population of Middle Atlantic) divided by 248,710 people (Population of the U.S.) = 0.151 0.151 multiplied by 1000 = 151.1 (rounded)= 151 delegates from Middle Atlantic.
 * Middle Atlantic (method #1):


 * East North Central (method #2):



Top Right - (people) Population of region (East North Central) Bottom Right - (people) Population of the U.S. Top Left - (people) # of delegates from East North Central Bottom Left - (people) Total # of delegates
 * Legend:**

You have to cross multiply: 42,009*1000=248,710*X 42,009,000=248,710*X

To leave X alone, you have to divide 248,710*X by 248,710 to cancel it out and leave X alone, and to do this, since 42,009,000 equals 248,710*X, you have to do anything that you did to one side to the other. Therefore, you have to divide 42,009,000 and 248,710*X by 248,710.

This equals to 42,009,000 divided by 248,710 = 168.9 (rounded)= 169 delegates from East North Central

> 0.071 multiplied by 1000 = 71.0 delegates from West North Central.
 * West North Central (method #1):17,660 people (Population of West North Central) divided by 248,710 people (Population of the U.S.) = 0.071

>
 * South Atlantic (method #2):

Top Right - (people) Population of region (South Atlantic) Bottom Right - (people) Population of the U.S. Top Left - (people) # of delegates from South Atlantic Bottom Left - (people) Total # of delegates
 * Legend:**

You have to cross multiply: 43,567*1000=248,710*X 43,567,000=248,710*X

To leave X alone, you have to divide 248,710*X by 248,710 to cancel it out and leave X alone, and to do this, since 43,567,000 equals 248,710*X, you have to do anything that you did to one side to the other. Therefore, you have to divide 43,567,000 and 248,710*X by 248,710.

This equals to 43,567,000 divided by 248,710 = 175.1 (rounded)= 175 delegates from South Atlantic

> 0.061 multiplied by 1000 = 61.0 delegates from East South Central.
 * East South Central (method #1):15,176 people (Population of East South Central) divided by 248,710 people (Population of the U.S.) = 0.061

26,703 people (Population of West South Central) divided by 248,710 (Population of the U.S.) = 0.093 0.093 multiplied by 1000 = 93.7 (rounded)= 94 delegates from West South Central.
 * West South Central (method #1):

Mountain (method #1):13,659 people (Population of Mountain) divided by 248,710 people (Population of the U.S.) = 0.054 0.054 multiplied by 1000 = 54.9 (rounded)= 55 delegates from the Mountains.

38,127 people (Population of Pacific) divided by 248,710 people (Population of the U.S.) = 0.153 0.153 multiplied by 1000 = 153.2 (rounded)= 153 delegates from the Pacific.
 * Pacific (method #1):

(Same methods as A.) ** 192,726 people (Population of people living in the metropolitan area in the U.S.) divided by 248,710 people (Population of the U.S.) = 0.77 0.77 multiplied by 1000 = 774.9 (rounded)= 775 delegates from the metropolitan area. 0.225 multiplied by 1000 = 225.0 delegates from the rural area. **
 * B. How many of the 1000 delegates should be from metropolitan areas, and how many should be from rural areas?
 * Metropolitan Area (method #1):
 * ** Rural Area (method #1): **
 * 55,984 people (Population of people living in the rural area in the U.S.) divided by 248,710 people (Population of the U.S.) = 0.225

22,354 people (Population of Hispanic people in the U.S.) divided by 248,710 people (Population of the U.S.) = 0.089 0.089 multiplied by 1000 = 89.8 (rounded)= 90 delegates from Hispanic origin.
 * C. How many of the delegates should be of Hispanic origin?**


 * D.** **Four racial groups are named in the data: White; Black; Native American--Eskimo--Aleut; and Asian--Pacific Islander. How many of the 1000 delegates should represent each of these races (a)? How many should represent the category "all other races" (which is not mentioned in the data) (b)? (a) **

(a) 0.802 multiplied by 1000 = 802.8 (rounded)= 803 delegates from White people 0.12 multiplied by 1000 = 120.5 (rounded)= 121 delegates from Black people 0.007 multiplied by 1000 = 7.8 (rounded)= 8 delegates from the Native American/Eskimo/Aleut people 0.029 multiplied by 1000 = 29.2 (rounded)= 29 Asian/Pacific Islander delegates
 * White (method #1) - 199,686 people (Population of the White people in the U.S.) divided by 248,710 (Population of the U.S.) = 0.802
 * Black (method #1) - 29,986 people (Population of the Black people in the U.S.) divided by 248,710 (Population of the U.S.) = 0.12
 * Native American/Eskimo/Aleut - 1,959 (Population of the Native American/Eskimo/Aleut) divided by 248,710 (Population of the U.S.) = 0.007.
 * Asian/Pacific Islander - 7,274 (Population of Asian/Pacific Islander) divided by 248,710 (Population of the U.S.) = 0.029

(b)

All other races would be determined by adding all the races listed, then subtracting them from the total population to see the # of people in the "other race". White - 199,686 Black - 29,986 N.A./Eskimo/Aleut - 1,959 Asian/Pacific Islander - 7,274+ TOTAL: 238,905 people (in races listed)

To find the remaining people, you would have to subtract the total by the U.S. population. 248,710 people-238,905 people = 9,805 people in the "other race".


 * E. Use your answers to A-D to help you develop a plan for selecting the delegates. Describe your plan in a report that you could submit to the conference organizers.**

 Dear the planners of the Environmental Studies Conference,  There are 9 regions, 5 races (including the race not included in the data) and 2 areas that the delegates have to be chosen from in the U.S. To make the # of delegates from each criterion fair, you must develop a formula (or method) to pick the right amount. I found 2 ways to find a fair amount of delegates out of 1000 from each criterion.  I have found 2 formulas (although I am sure there are many more) that I find easy to use. The first one is to divide the region population by the total (U.S.) population, then multiply your answer by 1000 (because all of the numbers that we use for the populations have 3 more 0's at the end). The second one is to make a proportion. The proportion is made up of the region/race/area population divided by the total (U.S.) population which equals to delegates from region/area/race (X) divided by total # of delegates. You also have to round the end number because you can’t have half or 1/10 of a delegate.  The formulas can also be known as method #1 (region/race/area population/U.S. population then multiply by 1000) or method #2 (the proportion). I have used these methods (they have the same results/answers) on different questions in this problem (6.3). They are very effective and the results that they find are accurate.  For example for New England, (method #1) would be: 13,207 (Population of New England) divided by 248,710 (Population of the U.S.) = 0.053 multiplied by 1000 equals 53 delegates chosen from New England. For New England (method #2) the proportion would look like this:                 Legend of Proportion: Left top quadrant: Population of region (13,207,000 people) <span style="color: black; font-family: 'Arial','sans-serif';">Left bottom quadrant: Population of the U.S. (248,710 people) <span style="color: black; font-family: 'Arial','sans-serif';">Right top quadrant: # of delegates from that region (X) <span style="color: black; font-family: 'Arial','sans-serif';">Right bottom quadrant: total # of delegates (1000 delegates) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: black; font-family: 'Arial','sans-serif';">The only flaw in these formulas is the fact that a person is part of a race, area and region, so you would need to get each person from a specific area, region and race to equal out the specifications (found by the formulas). What I am trying to explain is that one person does not just apply in 1 criterion—they are from 1 race, 1 area, and 1 region, which means that you have to choose the middle-schoolers very carefully to equal out the # of delegates needed for that criterion (chosen with the formulas). <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: black; font-family: 'Arial','sans-serif';">Other than that, the 2 formulas I think are very useful for any race/region/area in this problem. Therefore, I think that this committee should use these formulas to fairly choose the # of students from each ethnic/region/area. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> -MMS

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 * 6.3 Follow up**

I would add the grade-level as another criterion (6th grade-8th grade). This is because we need a blend of different grade-level not just all 6th graders or 8th graders. This balance might show that the different grade-levels think differently due to their lack of experience in Middle School (6th graders) or their more experience in Middle School (8th graders). This might show that they think differently. This is why I would add this criterion.
 * If you could choose another criterion to help choose the delegates to that representation would be fair, what criterion would you add and why?**