5.4+Comparing+the+Dakotas+0910

V.H December 13, 2009  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? // //** Notes from Class: **// //Remember to isolate the variable and keep your labels on so that you don’t get confused at the end of your problem**;** if your answer is per mi^2, than you should be dividing per the mile. Remember to use **unit rates**, and to solve the problem as a **proportion.** // //**Unit rate – **////A rate in which the denominator is always 1. // //**Proportion – **////2 ratios that are equal to each other. // //__(Extra) __////**Population Density - **////Population density is a unit rate that compares the amount of people to area, labeled in square units. People/unit^2. // A. Which state, North Dakota, or South Dakota, has the greater population density? ** South Dakota: 721,000 people/75,896 mi^2 = 9.5 people/mi^2 North Dakota: 638,000 people/68,994 mi^2 = 9.2 people/mi^2 South Dakota has the larger population density. B. How many citizens of one state would have to move to the other state to make the population densities in the two states equal? Explain how you arrived at your answer. **  75,896 mi^2 (1) mi^2 Cross multiply. 75,896 * 9.4 = 713422.4 713422.4 = 1x 713422.4/1 = 713422.4 – this is the amount of people who will stay in South Dakota. __ 721,000 people (who live in South Dakota) __ _- 713,422.4___ = 7,577.6 people who will have to move from South Dakota to North Dakota. Problem 5.4 Follow-Up: ** <span style="font-family: 'Georgia','serif'; font-size: 12pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-font-family: 'Times New Roman'; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">In my state, Washington D.C. (District of Columbia), which is really a federal district, the population density is 9,378 people/mi^2. This is much bigger than the population density of both Dakotas. This is probably because D.C. is more of a city-like area, and the Dakotas are not. And also this may be because the textbook holding this problem is a bit old, so time has passed and the human population has grown, exponentially.
 * <span style="color: black; font-family: 'Georgia','serif'; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Arial;">The Big Idea: **
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 * <span style="font-family: 'Georgia','serif'; font-size: 12pt; line-height: 115%;">Find the population density of your state. How does it compare to the population densities of North and South Dakota? **

Here's some more information about my home state:


 * ~ ||||||~ Historical Populations[|[e]] ||
 * **Year** || **Population** || **Change** ||
 * [|1800] || 8,144 || - ||
 * [|1810] || 15,471 || 90.0% ||
 * [|1820] || 23,336 || 50.8% ||
 * [|1830] || 30,261 || 29.7% ||
 * [|1840] || 33,745 || 11.5% ||
 * [|1850] || 51,687 || 53.2% ||
 * [|1860] || 75,080 || 45.3% ||
 * [|1870] || 131,700 || 75.4% ||
 * [|1880] || 177,624 || 34.9% ||
 * [|1890] || 230,392 || 29.7% ||
 * [|1900] || 278,718 || 21.0% ||
 * [|1910] || 331,069 || 18.8% ||
 * [|1920] || 437,571 || 32.2% ||
 * [|1930] || 486,869 || 11.3% ||
 * [|1940] || 663,091 || 36.2% ||
 * [|1950] || 802,178 || 21.0% ||
 * [|1960] || 763,956 || -4.8% ||
 * [|1970] || 756,510 || -1.0% ||
 * [|1980] || 638,333 || -15.6% ||
 * [|1990] || 606,900 || -4.9% ||
 * [|2000] || 572,059 || -5.7% ||
 * **2008** || **591,833**[|[1]] || **3.5%** ||

Weather data for Washington, District of Columbia || (26) ||= 84 (29) ||= 93 (34) ||= 95 (35) ||= 99 (37) ||= 102 (39) ||= 106 (41) ||= 106 (41) ||= 104 (40) ||= 96 (36) ||= 86 (30) ||= 79 (26) ||= 106 (41) || (6) ||= 47 (8) ||= 56 (13) ||= 66 (19) ||= 75 (24) ||= 84 (29) ||= 88 (31) ||= 86 (30) ||= 79 (26) ||= 68 (20) ||= 57 (14) ||= 47 (8) ||= 66 (19) || (-3) ||= 30 (-1) ||= 37 (3) ||= 46 (8) ||= 56 (13) ||= 65 (18) ||= 70 (21) ||= 69 (21) ||= 62 (17) ||= 50 (10) ||= 40 (4) ||= 32 (0) ||= 49 (9) || (-26) ||= -15 (-26) ||= 4 (-16) ||= 15 (-9) ||= 33 (1) ||= 43 (6) ||= 52 (11) ||= 49 (9) ||= 36 (2) ||= 26 (-3) ||= 11 (-12) ||= -13 (-25) ||= -15 (-26) || (81.3) ||= 2.6 (66) ||= 3.6 (91.4) ||= 2.8 (71.1) ||= 3.8 (96.5) ||= 3.1 (78.7) ||= 3.6 (91.4) ||= 3.4 (86.4) ||= 3.8 (96.5) ||= 3.2 (81.3) ||= 3.0 (76.2) ||= 3.0 (76.2) ||= 39.1 (993.1) || (134.6) ||= 5.3 (134.6) ||= 2.1 (53.3) ||= 0.0 (0) ||= 0.0 (0) ||= 0.0 (0) ||= 0.0 (0) ||= 0.0 (0) ||= 0.0 (0) ||= 0.0 (0) ||= 0.8 (20.3) ||= 3.1 (78.7) ||= 16.6 (421.6) ||
 * ~ Month ||~ Jan ||~ Feb ||~ Mar ||~ Apr ||~ May ||~ Jun ||~ Jul ||~ Aug ||~ Sep ||~ Oct ||~ Nov ||~ Dec ||~ Year ||
 * ~ Record high °F (°C) ||= 79
 * ~ Average high °F (°C) ||= 42
 * ~ Average low °F (°C) ||= 27
 * ~ Record low °F (°C) ||= -14
 * ~ [|Precipitation] inches (mm) ||= 3.2
 * ~ [|Snowfall] inches (mm) ||= 5.3
 * ~ Avg. rainy days ||= 10 ||= 9 ||= 11 ||= 10 ||= 11 ||= 9 ||= 13 ||= 9 ||= 8 ||= 7 ||= 9 ||= 9 ||= 115 ||
 * = //Source: The Weather Channel[|[52]] Weatherbase.com[|[53]] August 2009// ||