Verona High SchoolAlgebra CP 1 2014 Summer

Assignment

All VHS incoming freshmen who are taking Algebra CP 1 must complete this summer assignment. The completed assignment is due on the first day of school, Thursday, September 4 th. There are three multi-part problems that are based on work you have done at HBW. All work is to be done on your own—no parents, siblings or friends. You may use textbooks or internet

resources to help you understand the problems but you cannot use any solutions to the problems in this packet you may find online.

If you need any help with these problems, Mr. Cashill of the VHS Math Department will be happy to assist you. He can be reached via email at rcashill@veronaschools.org. A link to this packet will be posted on MR. Cashill’s school website at www.veronaschools.org/cashill.

Please print your name and sign the Academic Integrity pledge below. If you are not sure of what constitutes “unauthorized aid” please contact Mr. Cashill.

Student Name: ______________________________________

“On my honor, I have neither given nor received any unauthorized aid on this assignment.”

Student Signature: ______________________________________

Summer Problem #1: Are You Ready for Some Football?

(6.EE.1, 6.EE.2, 6.EE.9, 7.NS.1, 7.NS.2, 7.EE.3, 7.EE.4, A-CED.4)

We will soon be in the midst of another exciting NFL season just as we come back to school in September. Aside from the actual football games being played, a “fantasy” game based on the National football League (NFL) is becoming more and more popular. Fantasy football is played by an estimated 25 to 30 million people each year. To play, contestants join or form a league and have a draft to form their own teams comprised of NFL players. Each person in the league typically drafts an NFL quarterback, running backs, wide receivers, etc. The more offensive production out of your players, the more points you get, the more games your team wins

League scoring systems vary, but players usually earn points for touchdown passes, passing yard, rushing yards, receiving yards and receptions with interceptions and fumbles earning negative points.

Websites such as ESPN.com and Yahoo Sports who host fantasy leagues use formulas to compute the number of points each player and team totals in an NFL weekend.

Quarterbacks

Let’s look at an example with quarterback scoring:

Touchdown Passes = 6 points Passing Yards = 0.05 points Interceptions = -2 points

1. In week one of the 2013 – 2014 season Tom Brady threw four touchdown passes, had 510 passing yards and t h r e w one interception. Find the number of fantasy points Tom Brady scored this week. Show your work below.

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2. In week two, Cam Newton threw one touchdown pass, had 420 passing yards and three interceptions. Find the number of fantasy points Cam Newton scored this week. Show your work below.

3. Look back at your method for finding total points in the previous two problems. Write a formula or rule that gives the points (p) a s a f u n c ti o n o f t h e number of touchdowns (t), passing yards (y), and interceptions (n).

4. Drew Brees threw for 180 yards, had three interceptions and ended with 15 total points. Use your rule from above to find the number of touchdown passes he threw for. Show your work below.

5. Geno Smith had a total of 35 fantasy points. He had four touchdowns, one interception. Use your rule to find the number of passing yards he threw for. Show your work below.

6. Robert Griffin III had 18 total fantasy points. He had one touchdown pass and 320 passing yards. Use your rule to determine how many interceptions he threw. Show your work below.

Wide Receivers and Tight Ends

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Some leagues use the following scoring system for wide receivers and tight ends:

Receptions = 0.2 points Receiving Yards = 0.1 point Touchdowns = 6 points Fumbles = -2 points

7. Write a rule that calculates the number of fantasy points for a wide receiver. Explain what each term in your rule represents. Show your work below.

8. Use your rule to find the number of fantasy points earned by LeSean McCoy who had seven receptions, 100 yards, two touchdowns and no fumbles in week seven. Show your work below.

9. The wide receiver on my fantasy team scored 24 fantasy points on Sunday. There are numerous combinations of receptions, receiving yards, touch downs and fumbles that would total 24 fantasy points. Show two different combinations using all four methods of scoring to total 24 fantasy league points.

Running Backs

Some leagues use the following scoring system for running back:

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Receptions = 0.2 points Receiving Yards = 0.1 point Rushing Yards = 0.1 point Touchdowns = 6 points Fumbles = -2 points

10. In week seven of the NFL season, which running back scored more fantasy football points? Show all work.

• Reggie Bush who had 120 yards receiving, 5 receptions and 2 touchdowns and 115 rushing yards OR

• Marshawn Lynch who had 253 rushing yards, zero fumbles, zero receiving yards, zero passing yards and one touchdown.

11. Write an algebra expression that gives the total points scored by any player for any number of p passing yards, r rushing yards, v receiving yards, c receptions, t touchdowns and f fumbles or interceptions.

12. Bonus Points for correctly naming the three old time players whose pictures are shown. You can use your father’s or grandfather’s help on this one.

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Summer Problem #2: Who is Going Back to School?

(6.RP, 6.EE, 6.SP, 7.RP, 7.SP, 7.EE)

According to the U.S. Census Bureau’s 2010 data, 78 million students are projected to be enrolled in the nation's elementary an d s eco ndar y sch oo ls (Kindergarten—12 t h Grade ).

(Source: U.S. National Center for Education Statistics as cited in the Statistical Abstract of the United States: 2010, Table 214

http://www.census.gov/hhes/school/data/cps/historical/index.html )

Use the table below to answer the questions on school enrollment.

2010 2000 1990 1960

Population of United States 308,745,538 281,421,906 248,709,873 179,323,175

Number of Students Enrolled 78,519,000 72,214,000 60,588,000 46,260,000

% of Population Enrolled in School

1. Write two different mathematical statements comparing any of the data in the table.

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2. Using the 2010 Census statistics, what percent of the US population was enrolled in K-12 schools i n September, 2010? (Please show your work.)

3. Using the 2000 Census statistics, what percent of the US population was enrolled in K-12 schools in 2000? (Please show your work.)

4. Using the 1990 Census statistics, what percent of the US population was enrolled in K-12 schools in 1990? (Please show your work.)

5. Using the 1960 Census statistics, what percent of the US population was enrolled in K-12 schools in 1960? (Please show your work.)

6. Does this imply that the US population is getting older, younger, less educated, more educated, or something else? Explain your reasoning.

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7. There are approximately 14.8 million computers for use in the classroom in the United States according to the 2010 Census. On average, how many students would one computer serve?

2010 2000 1990Population of Massachusetts 6,547,629 6,349,097 6,016,425

8. What percent of the people who live in the United States in 2010 live in Massachusetts today?

9. Based on the 2010 census, how many students would you guess will be enrolled in K-12 schools in Massachusetts in 2010?

According to the 2010 Census the average annual earnings based on the highest level of education attained are as follows:

Highest Education Level Annual Earnings

$ Difference Between High School Diploma

Income & Others

Percent Change from High School Diploma

Income & OthersNo High School Diploma $21,023

High School Diploma $31,283 0 0.00%

Bachelor’s Degree From College $58,613

Advanced College Degree $83,144

10. Use the table above to help you calculate the difference in earnings between people with various education VHS Algebra CP 1 Summer Assignment Page 7

levels. Show your work here.

11. Why did I ask you to calculate all of these income differences?

Problem #3: Predicting the Future

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(CCSS: 8.SP.1 , 8.SP.2 , 8.SP.3 , HSF-IF.B.6 , HSS-ID.B.6)

On opening weekends, a movie’s opening gross income is often used as a way of measuring the movie’s eventual success. Can you predict a movie’s total gross income from its opening weekend count?

The table on the next page has data on 15 movies that you might have seen. We’ve included the gross amount that they earned on their opening weekend and the gross amount that they have earned since they came out. We also included Godzilla but did not give its long-term gross income since it just opened in May.

I’ve also left a few blank lines in the chart above for you to add your favorite movies. You can find the opening weekend and final gross data at http://boxofficemojo.com/.

1. Check off whether or not you have seen the movies.

2. I am wondering if you can predict what this movie’s total gross income will be from studying the opening weekend data. Maybe there is a pattern between the opening weekend data and the final gross total income of the movie. Let’s see if that is true.

3. On the page following the table I’ve created a graph for you to use to create a scatter plot. The horizontal axis will represent the Opening Weekend Income of each film. The vertical axis will be the Final Gross Income of the movie. Plot the data from the table on the chart.

Selected Movie Grosses

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Title Seen/Not Seen Opening Gross Total Gross Opening DateMarvel's The Avengers $207,438,708 $623,279,547 5/4/12

Wreck-It Ralph $188,440,226 $189,180,082 11/2/12

Iron Man 3 $174,144,585 $409,013,994 5/3/13

Harry Potter and the Deathly Hallows Part 2

$169,189,427 $381,011,219 7/15/11

The Hunger Games: Catching Fire $158,074,286 $424,668,047 11/22/13

The Hunger Games $152,535,747 $396,022,168 3/23/12

Spider-Man 3 $151,116,516 $336,530,303 5/4/07

The Twilight Saga: New Moon $142,839,137 $296,623,634 11/20/09

The Twilight Saga: Breaking Dawn Part 1

$138,122,261 $281,287,133 11/18/11

Pirates of the Caribbean: Dead Man's Chest

$135,634,554 $423,315,812 7/7/06

Harry Potter and the Deathly Hallows Part 1

$125,017,372 $295,983,305 11/19/10

Toy Story 3 $110,307,189 $415,004,880 6/18/10

Godzilla 2014 $93,188,384 5/16/14

Dr. Seuss' The Lorax $70,217,070 $177,412,055 3/2/12

Frozen $67,391,326 $400,523,079 11/22/13

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4. Is the relationship between Opening Weekend Income and the film’s Final Income a linear association or something else? How can you tell? Describe the association between the two variables.

5. Draw a Line of Best Fit (A straight line that balances the vertical distance of all of the points and the line itself) that best models the data. How do you decide where to draw your line?

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6. Using your Line of Best Fit predict what Godzilla will finally earn? Do the same for any additional movies that you plotted? What are your predictions based on?

7. Describe your confidence in your prediction(s).

8. Based on the data you graphed above, how much would you expect movies to make in gross that had opening weekends of:

$60 million

$80 million

$100 million

$180 million?

How did you determine your estimates?

9. Write the linear equation for your line of best fit (y = mx + b). This equation should give a reasonable (yet rough) prediction of the amount of money a movie will gross for any opening weekend total. Please show or explain how you came to your rule.

10. When the data becomes available go and check the actual domestic gross for Godzilla (and any other movies that you plotted. You can get this data from boxofficemojo.com. Describe how accurate your predictions for lifetime domestic gross were.

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