Verona High School

Algebra 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 4th.  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. 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.

Student Name: ______

VHS Algebra CP 1 Summer Assignment Page 1 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.

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 t i o n o f t h e number of touchdowns (t), passing yards (y), and interceptions (n).

VHS Algebra CP 1 Summer Assignment Page 2 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.

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 and secondary schools (Kindergarten—12 t h Grade).

VHS Algebra CP 1 Summer Assignment Page 3 (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 78,519,000 72,214,000 60,588,000 46,260,000 Enrolled % of Population Enrolled in School

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

2. Using the 2010 Census statistics, what percent of the US population was enrolled in K-12 schools in 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.)

VHS Algebra CP 1 Summer Assignment Page 4 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.

VHS Algebra CP 1 Summer Assignment Page 5 Problem #3: Predicting the Future

(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.

VHS Algebra CP 1 Summer Assignment Page 6 Selected Movie Grosses

Title Seen/Not Opening Gross Total Gross Opening Date Seen Marvel'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 $169,189,427 $381,011,219 7/15/11 Hallows Part 2 The Hunger Games: Catching $158,074,286 $424,668,047 11/22/13 Fire

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 $138,122,261 $281,287,133 11/18/11 Dawn Part 1 Pirates of the Caribbean: Dead $135,634,554 $423,315,812 7/7/06 Man's Chest Harry Potter and the Deathly $125,017,372 $295,983,305 11/19/10 Hallows Part 1 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

VHS Algebra CP 1 Summer Assignment Page 7 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?

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?

VHS Algebra CP 1 Summer Assignment Page 8 7. 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?

8. 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.

VHS Algebra CP 1 Summer Assignment Page 9