Mathematical+Reflections,+p.+81+1011

= = A.L (Alex Lampell) January 25, 2011 Math 7B = = = **__ 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.
**__ Investigation 6 Essential Question: __**

Which comparing strategies work best in which situations?

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** In this investigation you used ratios, rates, percents, fractions, and proportions to solve problems. You thought about which methods of making comparisons would be helpful in solving particular types of problems. These questions will help you summarize what you have learned: ** =====

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** Rates are good to use when you are comparing two different things which have different units of measure. In the situation below you will be able to see how you can use rates to compare different sets of data. ** =====

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**__ Situation: __**** There are two options for taking a test. One is a 8 page essay test were you get 2 hours to finish it. The other test is a 11 page essay were you get 3 hours to finish it. Bob wants to know which test would give him the most time for each page he does. So which test gives him that? ** =====

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**__ Answer: __**** The best option for Bob to take would be the 11 page essay with 3 hours because Bob will be able to do 3.6 pages in one hour while in the other one he would do 4 pages per one hour. ** =====

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** In this situation using a rate was good because I was able to compare two sets of information and then by making the rate I was able to make them from being different units to one unit which makes it very easy to compare. ** =====

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__ Situation: __ You want to buy a car that is good fuel economically. The salesman shows you two very nice cars which you end up liking a lot. The Duck car goes for 300 miles with 10 gallons of gas while the Dog car goes for 500 miles with 15 gallons of gas. =====

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For this problem it was the best choice to use the unit rate so that then you could know how many miles the car goes per gallon because if you know that then it is really easy to compare the two cars. =====

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1) Rodrigo drove 200 miles and used 6 gallons of gas. This shows that when the car has droven 200 miles then it has already used 6 gallons, so if it rode 600 miles then it would use 18 gallons of gas. =====

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2.) Rodrigo drove 33.33 miles and used 1 gallon. This is the same as the one above, but it is telling you how many miles Rodrigo has to drive to use up a gallon of gas. =====

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160 cans of chili would feed 240 people. I know this because since 4 cans of chili feed 6 people and 240 people is 40 times more than 6 people, so then to find how many cans I need to feed 240 people I just have to multiply 4 times 40 and get 160. So 160 cans would feed 240 people. =====

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You can feed 67.5 people with 45 cans of chili. I know this because since 2 cans of chili feed 3 people, then that equals 2/3. Then all I have to do to find out how many people you can feed with 45 is find its half and then add it by itself. So 45 divided by 2=22.5 and 22.5 is half of the cans a third of the people, so then 22.5+45=67.5. =====

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I would recognize if the situation needed to use a ratio comparison rather than simply finding differences because if it already asked me about comparisons then I would already know that I should use a ratio since a ratio already compares and the differences just gives you a plain number =====

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In this unit I specifically learned how to choose what strategy to use in a given situation. This is really helpful because this relates with the world since in the world you have to decide which of the strategies that you have learned the best to use in each situation is. Throughout the whole unit of Comparing and Scaling I discovered many different ways which I can use to compare data. This will help me in the future since in any job you have to compare numbers and the more ways you know to compare the better. =====