Comparing+and+Scaling

=Comparing and Scaling=

=Comparing and Scaling=

What we already know: Working with Fractions - simplifying mathematical similarity - comparing figures Estimating populations working with percentages - scaling figures using percents scale factors Ratios for comparison making tables different ways of organizing data

What we want to know: scaling numbers estimating populations fractions to percent conversions unit rates probability (odds) scale factor conversion to percentages choosing strategies for comparison Anders

5.5 Predicting traffic Jams
A.) Question: The city of Ole has 450,237 registered vehicles foe 3000 miles of road. What is the traffic density of Ole? Calculate the number of vehicles per mile of road and the number of feet of road per vehicle. 1 mile = 5,280 feet

Answer: 450,237 vehicles ÷ 3000 miles = 150 vehicles/mile. 5,280 feet ÷ 150 vehicles = 35.2 feet/vehicle

B.) Question: The city of Driftwood Bay has 396 registered vehicles for 10 miles of road. What is the traffic density of Driftwood bay? Calculate the number of vehicles per mile of road and the number of feet of road per vehicle.

Answer: 396 vehicles ÷ 10 miles = 39.6 vehicles/mile 5,280 feet ÷ 39.6 vehicles = 133.33 feet/vehicle

C.) Question: Which of the three cities-Hong Kong, Ole or Driftwood Bay-do you think is most likely to have traffic jams? Explain your answer.

Answer: Hong Kong is most likely to have traffic jams, because already in 1992 the vehicles only had 12.63 feet each. Now it is even worse.

D.) Question: Which of the three cities do you think is least likely to have traffic jams? Explain your answer.

Answer: Driftwood Bay is the city that is least likely to have traffic jams, because the vehicles have 133.33 feet each and that is a lot of space.

Follow Up 1. Question: Other than traffic density, what factors might affect the likelihood of traffic jams? Answer: Accidents, weather conditions, road works, end and start of holidays if all people take of at the same day and rush hour traffic when people get of at work.

2. Question: A typical four-passenger car is about 13 feet long. Compare this statistics to the amount of road per mile in Hong Kong. What does this say about the traffic in Hong Kong? What might Hong Kong do if this situation gets worse? Answer: That means that there is more vehicles than space in Hong Kong. If this situation gets worse then they maybe have to stop the registered of new vehicles.

Homework:
Mathematical Reflections 5 page 64 Finish 5.5 Study for partner quiz

Collected: ACE5# 3*** and 10**

=Esther= December-8-07, Day 3.1:Mixing Juice What methods are there to compare things? Ratios** Journal 3.1 Mix A 2 cups concentrate 3 cups cold water
 * Notes:
 * Marvin and Arvind tested four orange juice mixes for the class in the camping trip to see which mix tested better.

Mix B 1 cup of concentrate 4 cups cold water

Mix c 4 cups concentrate 8 cups cold water

Mix D 3 cups concentrate 5 cups coldwater** A**: Which recipe will make the juice more orangey? Explain you answer.** A**: The recipe that will make the mix more “orangey” will be mix A because the concentrate is just one cup less than the water and it is closest to a hole.** B**: What recipe will make the juice less orangey? Explain you answer.** B**: The recipe that will make the mix less orangey and more watery is Mix B because the quantity of the concentrate is 3 cups below it and since there is more water the water is dominate; taking over the flavor a little bit.** C**: Assume that each camper will get ½ cup of juice. For each recipe, how much concentrate and how much water is need to make juice for 240 campers? Explain you answer.** C**: They will need 2,400 cups of water, and 4,800 cups of concentrate because, first we had to multiply 240 by all the water for each recipe then add that all up to see how much they needed; I did the same way for the concentrate as well.** =Follow up= 1**.How did you use ratios in solving problem 3.1?** 1**: we used the ratios to compare the different ingredients to make the orange juice.** 2**: For each recipe, how much concentrate and how much water is needed to make I cup of juice.** 2**: Mix a: 2 cups concentrate divide by 1 = .5 cups 3 cups water divided by 1 = .3 cups Mix b: 1 cup concentrate divide by 1 = 1cups 4cup water divide by 1 = .25 cups Mix c: 4 cups of concentrate divided by 1 = .25 cups 8 cups water divide by 1 = .125 cups Mix d: 3 cups concentrate divide by 1 = .3 cups 5 cups water divide by 1 = .2 cups
 * 1) A~C and Follow up

Esther**

Notes-
3.2 Helping the Cook A.)Q **How many cans of tomatoes would you advise the cook to buy to make spaghetti for 240 campers? A- 1 can = 5-6 campers 240 divide by 5 = 48 240 divide by 6 = 40 The cook would need to buy 40 - 48 cans of tomatoes to make spaghetti for 240 campers because for 5-6 students its only 1 can therefore I needed to how many times 5 and 6 enter 240. B.)Q How much would these cans cost together? A- Number of cans: 40-48 cans** 4 dollars for 1 can 48 x 4 = 192 The cost of all the cans together in $ 160-192. Follow up** 1.) Q **At the EatMore grocery store, you can buy seven cans of tomatoes for $6.00. the cans are the same size as the cans for CannedStuff. Are the tomatoes at EatMore a better buy than the tomatoes in CannedStuff? Explain your answer. A- Seven cans-$6.00 EatMore is not a better buy because for 7 cans in CannedStuff for 5 it would be $5.06 and for 6 it would be $4.06, because I divide $4.00 by 5 and 6, then taking that answer I multiplied that by 2 for 5 because the difference between 5 and 7 is two, then I multiplied the answer for 6 by 1 because the difference between 6 and 7 is 1. Then taking those answers then add it to $4.00 to know how much 7 is and the price is lower then prices for 7 cans in EatMore.** 2.) Q **Gus was trying to figure out how to think about the EatMore price of the seven cans of tomatoes for $6.00. HE divided 7 by 6 and got 1.16666667. HE then divided 6 by 7 and got 0.85714286. What does each of these numbers mean in the context of seven cans of tomatoes for $6.00?** A**-** These means about how many tomatoes there is in a can.
 * The camp cook must buy enough ingredients for all the meals he intends to prepare during the week. One of the cook’s most popular meals is spaghetti. The spaghetti recipe he uses call for canned tomatoes. The CannedStuff store has large cans of tomatoes on sale, five cans for $4.00. The cook says he can make sauce for five to six campers from each can of tomatoes.**
 * 40 x 4 = 160

Sreerag
=15 January 2008= Sreerag Rajan January 15, 2008 Math 7 F Day 41 4.1 Comparing Fuel Efficiency

Notes Luis car used: 15.5 gallons for 452 miles / 2= 226 Madeline’s car used: 19 gallons for 490 miles / 2 = 245 Miles till Trinidad: 190 miles

Problem 4.1

Which car do you think is more fuel-efficient on the highway? Explain how you decide and why you think you are correct? (use the understanding steps)

Understand: The firs part of the question is asking which car saves more fuel while going long distances. The second part is asking how did you decide that and how do you know that is correct.

Plan: The plan to solve this question is by first to finding the total amount of fuel each used which is for Madeline 19 gallons and for Luis 15.5 gallons. Then you find the total amount of miles each went which for Madeline is 490 miles and for Luis 15.5. next step is to divide both their totals of miles by a half. Which for Madeline will be 245 and for Luis will be 226.

Solve Madeline’s: 580/19 = 30 So, her car goes 30 miles per gallon.

Luis’s: 452/ 15.5= 29 So, his car goes 29 miles per gallon.

This shows that Madeline’s car I s more fuel efficient.

Check

Madelines: 30*19= 608 (that is the closest it is going to get.

Luis’s: 15.5 * 29= 449.5 (that is the closest it will get)

HOMEWORK collected: Noting Assinged: 3.3 and follow up, Mathemathical reflection 3, 4.1(no follow up) Ace 3: 3-7 odds, 13-23 odds.

=__Avita__=

Date: Jan. 18, 2008/Day 41 Notes: none

Problem 4.2 Using Unit Rates
Madeline's car went 580 miles with 19 gallons of gasoline. Luis's car went 452 miles with 15.5 gallons of gasoline.

A) Q: For each car, find a unit rate describing the mileage. Which car got better gas mileage? In other words, which car went more miles per gallon of gas? Madeline: 580 divided by 19 = 31 miles per gallon of gas Luis: 452 divided by 15.5 = 29 miles per gallon of gas So Madeline got better gas mileage.

B)
 * Gallons of gas || 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 ||
 * Miles in Madeline's car || 0 || 31 || 62 || 93 || 124 || 156 || 187 || 218 || 249 ||
 * Miles in Luis's car || 0 || 29 || 58 || 87 || 116 || 145 || 174 || 203 || 232 ||

C) Equations: miles driven (m) and gallons of gas used (g). Madeline: 31(g) = m Luis: 29(g) = m

D) Madeline: 9.5 g x 31 =294.5 miles. 15.5 x 31= 480.5 miles. 19 x 31 =589 miles. 23.8 x 31= 737.8 miles. 100 x 31 =3100 miles. 125 x 31= 3875 miles. 150 x 31 = 4650 miles. Luis: 9.5 g x 29 =275.5 miles. 15.5 x 29= 449.5 miles. 19 x 29 =551 miles. 23.8 x 29= 690.2 miles. 100 x 29 =2900 miles. 125 x 29= 3625 miles. 150 x 29 = 4350 miles.

Problem 4.2 Follow up 2. Both of the graphs increase by a pattern. But Luis's points on the graph increase less so they are lower than Madeline's. 3. Since Luis's car goes 29 miles per gallon of gas and Madeline's car goes 31 miles per gallon of gas, Luis's points on the graph are lower than Madeline's.**
 * 1.

=M.J= January 14, 2007 Day 41 Notes: None __Journal 4.4:"Buying Beads"__ Cubes: c=0.8 cents (x) 12 cents divided by 15. Cylinders: c=0.8 cents (x) 8 cents divided by 10.** Follow-Up: 2.) You would need the cost for each beed.**
 * Spheres: c=0.6 cents (x) 12 cents divided by 20.
 * 1.) For each cost you will need the number of beeds for each unit.

Homework
Collected: MR p. 36 Assigned: Problem 4.2 and 4.3, ACE 4: 1, 4-6, 10, 11 and Mathematical reflections p. 51

=__Sneha__=

Notes-
How can we use percentages to compare different steps of data?
 * We con compare population estimates between your class and other countries or classes.
 * It makes comaring easirt because we know that it is out of a 100%

2.2 comparing your class to the Nation
Yow conducted a class survey at the beginning og this investigation. now, organize the results for bicycle ridingm campimg, exercise walking, fishing, and swimming into a table similar to the one on page 17. Your table should have separate columns for males and females. A-**Look back at the three statements you wrote in part B of Problem 2.1 comparing the numbers of males and female paricipandts in the various activities. now, make the same conparisons for boys and girls in your class.** A- **In biking males are 34% more than the females. In exercise walking females and males are the same 87% females run and 87% males run, the difference is of 0%.for swimming boys are 2 times less than the girls.** B-**Compare the statements about your class data to the sstatements about the national data.** B-**The only difference is that they have the numbers of the whole U.S while ours is of a small class.** C-**Write theree statements comparing sports activities of all students in your class to those of** C-1- 2- Follow up- 1- **Write a paragraph telling how your class data is like the national data and how it is different. For any ways in which your class data appears to be different from the national data, give reasons why your think your class is differents.** 1- **I think that it is very different because the total kids in our class ae 15 while the surbey as millions of people. The way that we compare is the same and ecerything is different.** 2- **In your class survey, you added several acticities to the five listed in the national survey. Write at least three statements comparing the munbers of boys and girls in your class who participate in these activities.** 2- **1. Boys have a 100% for running while the girls have 1% less. 2. for soccer girls are 87% while for boys it is 85% which has the difference of 2%. 3. In handball girls are 2 times more than the boys.**
 * 1) 12-17 year olds in the national survey.
 * 2) 55-64 year olds inthe national survey.
 * 1) 53% bike in our class while41% bike in the survey.
 * 2) for camping the difference is 12%.
 * 3) 40%of our class does ecercise walking 13% for the survey.
 * 1) Only 13% camp in our class while camping in the survey os only 11%.
 * 2) 80% of our class swim while 13% of people swim in the survey the difference is of 67%.
 * 3) for exercise walking only 6/15*100 walk which is 40% while in the survey for ecercise walinf 7,782,000/20,922,000*100 which is 37%

Homework:ACE 2,1-8(1&2), 17-22
Collected: none Assigned: mathematical Reflections,p25;ACE 2, 9-15,16;Study for check-up

=Mee Ae= December 6,2007 Day 36 __2.1 Comparing Leisure Activities__ Notes: -Explaining how a number outnumbered another number and telling the percentages** Students: 15 people Boys: 7 people Girls: 8 people Problem 2.1 A) **The numbers in the columns don't add to the given totals because they scaled the original answer.** B) **Statement 1: 22% of th Males who bike ride outnumbered the females who bike ride (20%) <(24,562,000/ 111,851,000)X100=21.9=21% Male bike ride> <(23,357,000/ 118,555,000)X100=19.7=20% Female bike ride> Statement 2: 21% of the Males who did camping out numbered the females who did camping (16%). <(23,165,000/ 111,851,000)X100=20.7=21% Male camping> <(19,533,000/ 118,555,000)X100=16.4=16% Female camping> Statement 3: 37% of the female who did exercise walking outnumbered the males who did exercise walking (19%). <(43,373,000/ 118,555,000)X100=36.5=37% Female exercise walking> <(21,054,000/ 111,851,000)X100=18.8=19% Male exercise walking>** C) **Statement 1: 37% of the older-adults who did exercise walking outnumbered the teenagers who did the walking (13%) <(7,782,000/ 20,922,000)X100=37.1=37% older-adults excercise walking> <(2,816,000/ 21,304,000)X100=13.2=13% teenagers exercise walking> Statement 2: 23% of the teenagers who did fishing outnumbered the older-adults who did fishing (15%) <(4,945,000/ 21,304,000)X100=23.2=23% teenagers fishing> <(3,156,000/ 20,922,000)X100=15.0=15% older-adults fishing> Statment 3: 51% of the teenagers who did swimming outnumbered the older-adults who did swimming (13%) <(10,874,000/ 21,304,000)X100=51.0=51% teenagers swimming> <(2,756,000/ 20,922,000)X100=13.1=13% older-adults swimming>** D) **Statement 1: In the teenagers swimming, 51% is larger than the older-adults who was in the swimming activity (13%). Statement 2: In the Males exercise walking, 21% is larger than the teenagers exercise walking (13%). Statement 3: In the Females exercise walking, 37% is similar to the older-adults exercise walking (37%).** __Problem 2.1 Follow-up__ 1) **I think the percentages are the better way to explain the comparisons because if you use the percents like for example, 23% of the teenagers who did fishing outnumbered the older-adults who did fishing (15%). You can compare 23 and 15 to see which one is better.** 2)** You can compare the participation of teenage boys in these activities to the participation of older-adult women by using the data in the table because since the book only tells that from the age of 12 through17 are doin these activities, you can't figure out which of them are boys.
 * How can we use percentages to compare different steps of data?
 * Activities || Boys || Girls ||
 * Biking || 5 || 3 ||
 * Camping || 1 || 1 ||
 * Exercise Walking || 3 || 3 ||
 * Fishing || 2 || 1 ||
 * Swimming || 4 || 8 ||
 * Soccer || 6 || 7 ||
 * Running || 7 || 7 ||
 * Basketball || 6 || 5 ||
 * Dodgeball || 6 || 5 ||
 * Handball || 3 || 6 ||

Yoo Rin

Journal 1.3: Getting the message across
PROBLEM 1.3 A) Suppose you are writing a news story about the popularity of camping in the U.S. based on the data on the table. What headline would you use for your story? HEADLINE: "Camping a must for our soul!!" My first sentence might say, "Do you at least camp once or twice a year? "
 * 1) A~B and follow-up

B) Here are five statements that I might use in my newspaper article? 1. Almost 22,000,000 kids or teenagers go camping. 2. Almost 27,000,000 young adults go camping. 3. Almost 42,000,000 young adults go camping. 4. Almost twice as many adults go camping as kids. 5. 10,000,000 adults go camping at least twice a year. 6. A third of America's population goes camping. Follow-Up 1/3 of americas population goes camping=

HOMEWORK:
Collected: None Assigned: ACE 1: #7~11

Sneha 1.1 Writing Ads

Notes-
What methods are there for comparing things? Percentages

Ratio

Fraction

Decimal

Differences (subtraction)

__1.1 Writing Ads__
1.1 Writing ads A- Describe what you think each of the four statements means. Explain how each shows a comparison. Be sure to tell what is being compared and how it is being compared. A- The four statements mean that Bolda Cola is better than Cola Nola. The first one is a ration 2 out of 3 people liked Bolda cola better.The second one is a ratio showing the people's actual number in a ratio. The third one is how many people like it better in differences and the fourth one is a percent 60% out of a 100% like Bolda Cola better. B- Is it possible that all four advertising claims are on the same survey data? Explain our answer. B- Yes all of them are the same.because thy are all showing the same thing in a different format. C- Which comparison do you think is the most accurate way to report the survey data?Why? C- For me it is the percent because i know percents better than the ration and the others. and we also know that 30% likes Cola Nola but if you had the ratio you only know that 2:3 is better which was confusing for me at the beginning. D- Which comparison do you think would be the most effective advertisement for Bolda Cola? Why? D- I think that the percent one is the most effective one because for kids who are above third grade know percents but they usually don't know what ratios are. Follow up- Write two or more statements comparing the popularity of the two colas. Explain each statement you write. 1- Out of 200 people 160 prefer Bolda Cola This statement means that only 40 people like Cola Nola 2- From the age of 2-70 custome from2-60 like bolda cola. This statement means that only the people from 60-70 years like cola nola

Homework
Collected:None Assigned: Complete unit test project Due Thursday __and__ ACE1: 1-4

1.2 Targeting the audience A- Read the statements below about how Neilson students prefer to spend thier evenings. Tell whether each statement accurately reports the results of the survey. Explain your answers. 1. 6 out of 10 students prefer television to radio. Yes this is true because above it is 60 out of 100 and if you divide 60 by 10 it equeals 6 and then you have to divide 100 by 10 and it equeals 10. Then it becomes 6 out of 10. 2. Students prefer radio to television by a ratio of 4 to 6. Yes this is true because 40 divided by 10 equals 4 and then divide 60 by 10 and you get 6. Then you make it in to a ratio and it is 4 to 6. 3. Students who prefer televison outnumber those who prefer radio by 20. Yes this is true because 60 - 40 = 20. 4. Students who prefer televison outnumber those who prefer radio by a ratio of 3 to 2. Yes this is true because 40 divided 10 equals 4 and four divided 2 equals 2. 60 divided 10 equals 6, 6 divided by 2 equals 3 and therefore it makes a ratio of 3 to 2. 5. The number of students who prefer watching television is 1.5 times the number who prefer listening to radio. Yes this is true because 40 times 1.5 equals 60 6. 40% of the students prefer radio to television. Yes this is true because 40 people out of 100 is also the same as 40% out of 100%. 7. 3/5 of the students prefer television to radio. Yes this is true because 60 divided by 10 equals 6 and 6 divided by 2 equals 3. 100 divided by 10 equals 10 and 10 divided by 2 equals 5 therefoe it is 3/5.

B. If you were writing a paper to convince local merchants that they would reach more students by advertising on the radio than on television, which statement from above would you use? Why? I would use Statement 6 because 40% makes it a large number and all the other statemenst do not make it as large as this one.

C. Imagine that you are advertising director for a television station in the town where Lelson is located. You have been asked to prepare a report for a meeting between your ad department and a large local skateboard manufacturer. Which accurate statement from above would you use I to try to convince the manufacturer to advertise on your station? Why? I would use Statement 5 becasue it is saying that is multiplying 1.5 times any number. Thus, it makes any number larger 50% more than the number you are multiplying.

Problem 1.2 Follow-Up

1. For each statement in part A on page 7, write a similar statement about your class data. 1. 8 out of 15 students prefer television to internet 2. Students prefer internet to television by a ratio of 7 to 8. 3. Students who prefer television outnumber those who prefer internet by 10. 4. Students who prefer television outnumber those who prefer internet by a ratio of 8 to 7. 5. The number of students who prefer watching televison is 1.15 times the number who prefer using the internet. 6. 47% of the students prefer internet to television. 7. 8/15 of the students prefer television to internet. 2. In what ways is your class data similar to the Nelson data? In what ways is your data different? Both of our numbers are close together. The class data has diferent numbers, fractions and percent than the Nelson data. 3. You may have heard people talk about an interest group manipulating data to promote their cause. That doesn't mean they used incorrect data, but that they made careful decisions about which data to use and how to present the data to support their cause. How could you manipulate your class data to persude local merchants to advertise on internet rather than on television? Internet is quickly becoming a preference of studenst to television. Already nearly 50% of the students prefer internet to television

Zareen

Problem 3.3 + follow up:
A.) No they wouldn’t get an equal amount of pizza, because the people at the large table will get 3.2 pieces out of a total of 32, and the people at the small table will get 3.75 pieces out of 30. The larger table gets more pizza.

B.) There are sixteen large tables and ten small tables, because 16 x 10 is 160, and 8 x 10 = 80, together which is 240 which is the total number of campers needed.

Follow Up:

1. I used ratios on number one, turning the decimals into ratio’s for problem one and comparing them. 2. If he wants to feed that many people he will need 95 pizzas.

Pailin Rinfret

5.4 Comparing the Dakotas
A. North Dakota- 638,000(people) divided by 68,994(area) = 9.247 people per mile South Dakota- 721,000(people) divided by 75,896(area) = 9.49 (9.5) people per mile B. Find the mean of pop. densities - 9.2 + 9.5 = 9.35 p/m2 (target) 2 9.35 x area of S/N Dakota 68, 994 x 9.35 = 645,094 people in N.D 75,896 x 9.35 = 709628 people in S.D 11,372 people had to move from South D. to North. D

Follow-up: State- East South Central: (From problem 5.3) The density is 0.88 people/mile. Which is way smaller than both the Dakota's density.

Homework
= = Collected: None Assigned: 5.3, Ace 5: 8,9,11,12