Mathematical+Reflections,+p.+64+0910

01/12/10   AB     Comparing and Scaling ** 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? //

I can change 3 to 25, and then divide 25 by 3 and multiply that by 20. I will add that number with 25 and then finally get the total. I assumed they distributed easily. I can divide 40 by 30% and then multiply that by 100 and I will get the total. I assume the tagged fish were distributed equally.
 * 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.**
 * b. Park officials tagged and released 40 fish. They kept records of the fish caught over the next month and found that 30% had tags.**

You need the area of the space and you need the total population.
 * 1) **In the problems you did in this investigation, what data did you need to find the densities of populations?**

I need the total amount of deer’s and the amount the amount of land. Just like the question above, I need the amount of trees and the size of the forest.
 * 1) **a. What data would you need to estimate the the density of deer in a wildlife area?**
 * b. What data would you need to estimate the density of trees in the forest?**

B is the most like a population density comparison, because it’s like a unit rate and most like a population density. A is comparing a ratio and C is a difference comparison.
 * 1) **Which of the following comparisons statements is most like the population-density comparisons? Explain your reasoning.**
 * 2) **People prefer Bolda Cola to Cola Nola by a ratio of 3 to 2.**
 * 3) **Mary’s car gets 30.5 miles per gallon of gas.**
 * 4) **The population of California is 28,156,000 greater than the population of Connecticut.**

In this investigation I used sampling and ratios to estimate the size of a population density, to describe and compare the crowd of geographic regions and roads. This investigation is good for scientists who deal with population. We also learned how they find their information.
 * Think about your answers to these questions, discuss your ideas with other students and your teacher, and then write a summary of your findings in your journal.**