Mathematical+Reflections,+p.+64+-+2010-2011

= = =**AC ** = =**7H ** = =**January 11th, 2010 ** =

Mathematical Reflection 5 = =

= **__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.

=1) For each situation, explain how you could use the given information to estimate the total population of fish in the pond. Be sure to include any assumptions you make. =

A. **Biologists caught 25 fish in a net, tagged them, and returned them back into the pond. In a later catch of 20 fish, 3 had tags. ** To estimate the total number of fish in the living in the pond, I would multiply 25 by 3 and then I would need to divide the result by 20, then I would add the 25 fish I am sure are in the pond, in order to get an accurate answer. I assumed that the fish were distributed evenly among the area of the pond

B. **Park officials tagged and released 40 fish. They kept records of the fish caught over the next month and found the 30% had tags. ** In order to estimate the total population of fish in the pond I have to divide 40 by 30% and then I need to multiply the result by a 100 so that I get the total. I assumed that some of the tagged fish may have died, also I assumed that the tagged fish were distributed evenly among the pond.

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-family: 'Comic Sans MS',cursive; font-size: 22px;">2) In the problems you did in <span style="font-family: 'Comic Sans MS',cursive; font-size: 22px; line-height: 33px;">this investigation, what data did you need to find the densities of populations? ** =

<span style="font-family: 'Comic Sans MS',cursive; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">To find the population density, you need to have the total land area in squared units and the total population of the area.

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-family: 'Comic Sans MS',cursive; font-size: 22px;">3) ** =

<span style="font-family: 'Comic Sans MS',cursive; font-size: 16px;">A. **<span style="font-family: 'Comic Sans MS',cursive;">Wha ** **<span style="font-family: 'Comic Sans MS',cursive;">t da ****<span style="font-family: 'Comic Sans MS',cursive;">ta would you need to estimate the density of deer in a wildlife area? ** **<span style="font-family: 'Comic Sans MS',cursive; font-weight: normal;">I would need the total deer population of the forest and the total land area in the forest. **

<span style="font-family: 'Comic Sans MS',cursive; font-size: 16px; margin: 0px; padding: 0px;">B. **<span style="font-family: 'Comic Sans MS',cursive;">What data would you need to estimate the density of trees in a forest? ** <span style="font-family: 'Comic Sans MS',cursive; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">I wound need the total number of trees in the forest and I would need the total land are of the forest.

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-family: 'Comic Sans MS',cursive; font-size: 22px;">3) Which of the following comparisons statements is most like the population density comparisons? Explain your reasoning. ** = = = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"> //<span style="font-family: 'Comic Sans MS',cursive; font-size: 16px; line-height: 24px;">I. People prefer Bolda Cola to Cola Nola by a ratio of 3 to 2. // = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"> //<span style="font-family: 'Comic Sans MS',cursive; font-size: 16px; line-height: 24px;">II. Mary's car gets 30.5 miles per gallon of gas. //  = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"> //<span style="font-family: 'Comic Sans MS',cursive; font-size: 16px; line-height: 24px;">III. The population of California is 28,156,00 greater than the population of Connec <span style="font-family: 'Comic Sans MS',cursive; font-size: 16px; line-height: 24px;">t <span style="font-family: 'Comic Sans MS',cursive; font-size: 16px; line-height: 24px;">icut. // =

>
 * 1) //<span style="font-family: 'Comic Sans MS',cursive; font-weight: normal;">The first one is a ration and doesn't really relate to the population density comparisons. //
 * 1) I think that this one relates the most to the population density comparisons because it uses the same type of words and the same formatting but substitutes people with miles and gas with land area.
 * 2) Even though this statement is about population it doesn't relate to to the population density comparisons because it's a difference.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 430%; font-style: normal; font-weight: normal;">﻿ <span style="font-family: 'Comic Sans MS',cursive; font-size: 100px; font-style: normal; line-height: 58px;">**Summary** <span style="font-family: 'Comic Sans MS',cursive; font-size: 700%; font-style: normal; font-weight: normal;">

<span style="font-family: 'Comic Sans MS',cursive; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this investigation I learnt many many helpful skills that I know will prove to be helpful later in life. Such as knowing how to calculate population density. Before I used to have a vague idea on how to, but know I know the process and I know how and where to use the information. While taking the unit test problems like the ones I completed in this Investigation were the one which gave me a hard time. I found this investigation helpful and I think it taught me a lot of skills that may come in handy in the future.