Stretching+and+Shrinking

=Variables and Patterns/Stretching and Shrinking=

HW
2.2 and 2.3 Complete with follow - up ACE 3: 5, 7, 9 MR page 27

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Journal 5.2
A.1-Think about the equation and make a table. Equation: y=3x 2.X 0 1 2 3 4 5 6 7 Y 0 3 6 9 12 15 18 21 3. If x= 5,y= 15 B.1.Equation: y= 0.5x+2 2.X 0 1 2 3 4 5 6 7 Y 2 2.5 3 3.5 4 4.5 ll5 5.5 3. If x=5,y=4.5

A 1. Set 1 - y=3x - 4 and y=3x + 2 have graphs that are similar. Set 2 - y=3x and y=1x have graphs that are similar. Set 3 - y=2x + 3 and y=2x - 5 have graphs that are similar. Set 4 - y=2/x and y=2x A 2. Set 1 - the graphs slant the same way. Set 2 - the graphs both cross each other. Set 3 - the graphs both meet at some point. Set 4 - the graphs will eventually meet. A 3. Set 1 - the equations both have 'y=3x'. Set 2 - The equations both have 'x' numbers that are close to each other. Set 3 - They both have 'y=2x'. Set 4 - they both have 'y=2' B 1. Set 1 - y=x². Set 2 - y=5. Set 3 - y=0.5x + 2. Set 4 - y=x + 5. B 2. Set 1 - the graph curves differently. Set 2 - The graph is a straight horizontal line. Set 3 - the graph is at a different angle. Set 4 - the graph curves in a different direction. B 3. Set 1 - y=x² has an exponent. Set 2 - y=5 doesn't have an independent variable. Set 3 - y=0.5x + 2 has a decimal which is added with 2. Set 4 - y=x + 5 doesn't have a number which is multiplied or divided by the dependent variable. Follow Up: a. y=4 b. y=1 ⅓ c. y=13 d. the equation is y=2x
 * x || 0 || 1 || 2 || 3 || 4 || 5 || 6 ||
 * y || 0 || 2 || 4 || 6 || 8 || 10 || 12 ||

Homework
Remember, we have a quiz next class, September 18, 2007!

Please type your name below to show that you are a member and you know how to click the  button and how to click the  button:

Mr. Cooper (example) Sneha mathew Avita Streatfield Akbar Sattar Pailin Rinfret Mee Ae Yu Ice Manityakul

Please log into the class wiki, add your name to the "name" list (above) and the "things we'd like to see" list. Remember, we have a quiz next class, September 18, 2007! please bring 3 or more suggestions for improving our Learning Environment (due sept 24) Complete 4.3 with follow-up Complete Mathematical Reflections page 60 ACE 4:3, 5, 7, 11

Journal
A- Make table of time and distance data,similar to the table you made in 4.1. A- On the table of 4.1. B- How are the tables for the 3 speeds similar? How are they different? B- Yes, the tables are similare because the numbers are very close together they are just a little ahead or they are behind.Like for 1 hour the distance for 55mph is 55,50mph the distance is 50 and for 65mph the distance is 65. C- How are the graphs similar ?How are they different? C- Yes, the graphs are similar because they are very close to each other. D-1- Look at the table and graph for 65mph.what pattern do you see? In words,write a rulethat explains how to calculate the distance. D-1- I can see that you can ho much farther in 65mph than in 50 or 55 mph.I think that the rule should be distance is 65thimes the hour. D-2- Use symbols to write your rule as an equation. D-2- D=65xh E-1- Write a rule in words that explains how to calculate the distance traveled for any given time. E-1- I thind taht the rule should be the same as before because they are like the same things. Distance is 50 times the hour E-2- Use symbols to write your equations. E-2- D= 50xh F- How are the rules for calculating distance for the three speeds similar? how are they different? F- I think that to find the distance was the same on all three of them because in them you are suposed to multiply it by the hour.

1- I think that this equation is distance is 60times time. 2-it would take us 6hours for 50mph, 5 1/10
 * Follow up-**

Homework
ACE4# :1, 8, 9, 13

10 150 25 382 40 600
 * A.** __Customers=>__ __Profit__

200 14 500 34 600 40
 * B.** __Customers=>__ __Profit__


 * C.** As the customers increase, obviously the profit will also increase. This shows on the graph by just a diagonal line going right.
 * D.** The profit will be different because they would get more money or profit if they reduce their expenses.

__**Problem 3.3 Follow-up**__
1 person- $15 (profit) 1,000 person- $5,000 (profit) 10 person- $150 (profit)

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Notes:
//This Problem/Investigation is called "Renting Bicycles." A company called Ocean and History Bike Tours needed rented bicycles for customers. They surveyed the rental fees of two companies called "Rocky's Cycle Center" and "Adrian's Bike Shop". Rocky's sent a table of their fees and Adrian sent a graph. Then we made a table for Adrian's and a graph with both companies' fees on it.//

Journal 3.1 - Renting Bicycles
Adrian's Rental Fees:
 * Number of Bikes || 5 || 10 || 15 || 20 || 25 || 30 || 35 || 40 || 45 || 50 ||
 * Rental Fee ($) || 180 || 300 || 440 || 600 || 780 || 900 || 1020 || 1200 || 1380 || 150 ||

Rocky's Rental Fees:
 * Number of Bikes || 5 || 10 || 15 || 20 || 25 || 30 || 35 || 40 || 45 || 50 ||
 * Rental Fee ($) || 400 || 535 || 655 || 770 || 875 || 975 || 1070 || 1140 || 1180 || 1200 ||

Coordinate Graph:

1. After looking at the tables and graphs I decided that Adrian's Bike Shop was a wiser chose for the customers because it was way cheaper. I also noticed that when you rent __less__ than 37 bikes you should rent the bikes at Adrian's, but when you rent __more__ than 37 bikes you should rent it at Rocky's Cycle Shop.

2. I noticed that in Rocky's graph, that when you finish connecting all the dots when the pattern reaches onto 35 bikes they start to drop down from that point on. 3. After connecting all the point on Adrian's graph i noticed that the points stay the same, it doesn't decrease or drop down.

4. On Rocky's Table, the patterns appear the same as on Problem 2, no differences in between.

5. On Adrian's Table, the patterns appear the same as on Problem 3, no differences in between.

Homework
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A. Theo's fastest speed was 20 mph which occured in 90 minutes. B. His slowest recorded speed was 0. But during his ride he got a record of 0 which occured in 40 minutes. C. Every 10 minute, his speed was increasing and decreasing very often. D.1)The speed just increases in a constant rate. 2)In the begging he rushed but as time passed he slowed down. 3)He slowed down in the begging but speeded up later. 4)He didn't move for quite a time and then speeded up really fast as time passed. 5)He shooted up in the beggining and slowed down later.

FOLLOW - UP 1) I think its impossible because his speed is rising up but he is not traveling anywhere and just stay in the same place. 2) From 40~50 minute Theo's speed changed most rapidly.

Homework = =

Homework
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REPORT: The seven students Sidney, liz, Celia, Malcom, Theo, Sara, and Tony all started thier bike tour at 8:00am in the morning near the Liberty Bell and the Independence hall in Philidelphia Pensylvania. They started thier bike tour. The first hour was a great start with a slight breeze to thier back on a flat path. The next hour the wind was in their face while going up a slanted hill about a 20 degree angle. They finally got over the hill and were starting to go down. The hill didn't last that long but now the wind was on thier back giving them a nice push on the bumpy trail. At 11:00am they got a flat tire by a lake. They fixed it but they dicided to say and have lunch thier and take a swim. At noon they decided to hit the road so they left the lake. They also stopped to look at landsapes and nice views. At 1:00pm they saw the time and decided to pick up the pace. They did stop a couple more times to use the bathroom. From 2:00pm to 4:00pm they were pedalling up and down hills until they finally reached thier destination. It took them 8 hours to travel 89 miles.

( graph attached)
 * A.** **Make a graph of your jumping jack data**


 * B.** **What does your graph show about jumping jack rate as time passes? (Another way to say this is, What does your graph show about the relationship between the number of jumping jacks and time?)**

As the seconds went by, the jumping jacks increased, some seconds had more jumping jacks the others but they always increased. I think the table is better for seeing the numbers, but for the relationships you can see on the graph that as the time goes by the number of jumping jacks increased.
 * Follow up:**

Journal

 * Problem 1.2**

A. On the graph

B.What does your graph show about jumping jack rate as time passes B. My jumping jack graph shows that the relationship between jumping jacks and time is that jumping jack needs something to be measured in and time is one of them.

1. Is the relationship you found between the jumping jack and time easier to see in table or the graph? Explain your answer. 1. the relationship between the jumping jack and time is easier to see in a table because it gives the exact information and dosent make you look all over the page to find out.
 * Problem 1.2 follow up**

Homework
ACE 1, 3, 5