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Zombies Game
Leo likes playing a video game where he has to zap Zombies and turns them into statues before they invade a town. In the game, Zombies hide everywhere. Leo’s goal is to clear all the Zombies to make the town safe again. To advance to the next level you have to zap all the Zombies in that level. Each level has the same number of Zombies and you get the same
number of points for each zapped Zombie. As you move through the levels, the Zombies get harder to zap. Leo made the table below to show a relationship between the number of Zombies zapped and
points earned.
Level 2 4 6 8 10 12
Maximum number of Zombies zapped
140 210 350
Points earned 7,700 23,100 30,800
1. Complete the table above. Look for relationships and patterns in the table. Describe at least three patterns.
2. Describe the ratios between the levels and the maximum number of Zombies zapped. How
are these ratios related?
Proportional Reasoning It’s All Connected
© 2011 Math Solutions, mathsolutions.com. Reproducible for one teacher’s classroom use only.
3. What are the ratios of the number of Zombies zapped to the number of points earned? How are these ratios related?
4. Name at least two different rates you can find in this game.
5. List the unit rates in this problem? How do you know the rates are unit rates?
6. Write an equation for each relationship described below. a. the level in the game and the number of Zombies zapped
b. the number of Zombies zapped and the points earned
Proportional Reasoning It’s All Connected © 2011 Math Solutions, mathsolutions.com. Reproducible for one teacher’s classroom use only.
c. the level in the game and the points earned
7. How did you use a unit rate to write each equation?
Proportional Reasoning It’s All Connected © 2011 Math Solutions, mathsolutions.com. Reproducible for one teacher’s classroom use only.
Reading Challenge
Andrew and Kelly were reading the same book in class. Andrew asked Kelly what page she was on. Kelly said that Andrew would have to figure it out using these clues:
• When she put down the book for lunch, she noticed that the product of the two facing page numbers was 32,580. • Kelly said that the last page she read was an odd number page.
What was the last page Kelly read before lunch?
CHALLENGE: Where must you open the book to make the product of the two facing pages
3660? Have you found a shortcut? Try to write about how you are doing these problems — how
you begin, what you do next, etc.
Bulldog Travel Agency
SITUATION: The Bulldog Travel Agency has been asked to evaluate three different rental car companies in order to recommend the best deals to its customers. Please examine the different rate schedules and make recommendations about which rental company to use for customers traveling to the Orlando, Florida area. ABC Rental Company charges $95 per week plus $0.18 per mile. Sunshine Car Rental charges $62.50 per week plus $0.27 a mile. Orange Rental charges a flat fee of $255 per week with no mileage charge. NOTE: All charges are for the same basic compact car. Please recommend the best deal for each of the following clients. Be sure to explain why it is best for their particular situation. 1. The Small family wants a car to tour the Orlando area. Since they are staying in the Disney Village, they will most likely put about 200 miles on the rental car in one week.
2. The Express family plans to see a lot of Florida. Their itinerary will mean putting about 1,500 miles on the rental car in a week’s time. 3. The Golf family wants to visit family and golf courses while in the Orlando area. They estimate their week’s travel to be between 500 and 700 miles.
4. The owner of Bulldog Travel Agency recognizes your mathematical expertise. She therefore asks you to write up a company policy regarding use of these three rental companies. Since she knows that some of the other agents do not have your mathematical prowess, she asks you to make it very easy to follow. She would like you to write a memo about this. How do you present the plan?
Memo
To: All travel agents From: Date: Re: car rental companies in the Orlando area Message:
Baby Olivia weighed 6 pounds at birth and gained
of a pound per week.
a. Make an in-out table showing Olivia’s weight for each of her first 10 weeks.
b. Find a formula that gives Olivia’s weight, y, in pounds as a function of her age, x, in weeks.
c. How many weeks until Olivia weighs 20 pounds?
Data for three babies is shown in the table below. Assume the rate of weight gain per week stays constant. Copy the table and fill in the missing blanks for each baby. Age in weeks x 0 1 2 3 4 5 6 7 8 9 10 Extra information Kalusha 7 Formula:
y = ½ x + 7
Annie 10 Gains
lb per
week Imani 8 11 NO other
information
a. Which baby weighs the most at 10 weeks?
b. Which baby has the fastest rate of growth?
c. How long will it take until all three babies weigh more than 20 pounds?
1975 During what is dubbed “The Storm of the Century,” the wind chill is between –50° and –80°Fahrenheit in Duluth, Minnesota. Weather information is available from many online sources. Investigate Keep a weather graph charting the temperature for a month. Then find the average temperature for the month. Check an almanac to find out whether this is above or below average.
1985 The Coca-Cola Company announces it is replacing its 99-year-old recipe with a new formula. Customers react so negatively that on July 10 the same year it reintroduces the old Coke under a new name, Coca-Cola Classic. Investigate Every minute, people around the world drink 311,111 Cokes. How many Cokes are consumed in one week?
Math Investigations 1998 Carl Gorman, a gentle Navajo artist and one of the 400 Navajo code talkers during World War II, dies. Gorman and 28 other Navajo volunteers turned their native language into a secret code that allowed Marine commanders to issue reports and orders and to coordinate complex operations. Although the highly respected Japanese code crackers broke U.S. Army, Navy, and Air Corps codes, they were never able to break the Marine Navajo code. As Gorman’s New York Times obituary notes, “Navajo is a language without an alphabet and with such a complex, irregular syntax that in 1942 it was estimated that outside of the 50,000 Navajos, no more than 30 other people in the world had any knowledge of it, none of them Japanese.” Online information from the Native American museum that is part of the Smithsonian Institution is available at http://www.si.edu/nmai/nav.htm. The Navajo Code Talkers’ Dictionary is available online at: http://www.history.navy.mil/faqs/faq61-4.htm. Investigate Team up with at least one other person and invent a code using numbers.
January 29, 1861 Kansas becomes the 34th state. The name Kansas comes from an Indian word meaning flat or spreading water. The state flower is the sunflower. The sunflower provides pioneer settlers in the Midwest with oil for their lamps and food for themselves and their stock. Native Americans roast sunflower seeds and ground them into flour for bread or pound them to release an oil for cooking and for making body paint. Investigate Look at a live sunflower or a detailed picture of one. A sunflower has two distinct parallel rows of seeds spiraling clockwise and counterclockwise. The seeds are Fibonacci numbers, typically 34 going one way and 55 going the other way, although sometimes they are 55 and 89. Find other natural examples of Fibonacci patterns. Good places to look include pinecones, pineapples, artichokes, and African daisies. For a terrific site on Fibonacci numbers, go to http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html.
Word Problems 1. I’m thinking of two numbers, 12 and another number. 12 and my other number
have a greatest common factor of 6 and their least common multiple is 36. What’s the other number I’m thinking of?
2. Tom had a platter of chocolate wafers. He ate 5 of them and then gave his brother 3, he then handed them to his ball team of 8 members. The first player to arrive took 1, the second player took 3, the third player took 5 and so on. When the last player took his, the platter was empty. How many chocolate wafers did Tom start with?
3. Jasmine has 50 marbles in a bag. 20% of the marbles are blue. How many marbles are blue?
4. An Olympic runner set a record for the 100m dash. The time was ten and sixty-two hundredths seconds. How would you write this as a number?
5. The tables at the party are shaped like the hexagon. If you put the tables together, how many would you need for 50 people? )1 person per side.)
6. At your birthday party, you had 7 8-slice pizzas. 41 slices were eaten. What fraction of pizza is left?
