Phantom Lake Math Challenge March 2016 A Trip to the Circus

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1 Phantom Lake Math Challenge March 2016 A Trip to the Circus These problems are generally in an order of increasing difficulty (A-L). Choose the one that fits your math ability and solve the problem. People at home can help you. Usually, you ll need to submit your answer using the response form attached. You should turn in one form for each problem you solve. Occasionally a poster or chart might be a better way to show an answer. Feel free to be creative. Please put the letter or title of your problem, your first and last name and your teacher s name on the form when you submit it. All solutions are due to Mrs. Gaylord by,thursday, March 31 st.. Bring your completed form(s), charts, and posters to your teacher. Students who successfully complete the challenge with the correct answer and a logical explanation of their mathematical thinking will receive a certificate and their name listed in the PTA newsletter. Happy problem solving! A. Elephants, Tigers, & Lions The circus this year has 3 elephants, 4 tigers, and 2 lions. How many animals are there altogether? Show by drawing a picture. After you draw your picture tell how you counted or added the numbers. B. Tubs of Popcorn Abby and Miguel bought 10 tubs of popcorn. They ate some during the show and have 6 tubs left. How many tubs of popcorn did Abby and Miguel eat during the show? If they share the leftover tubs equally, how many tubs will Miguel bring home? Draw a picture showing your work.

2 C. Time at the Circus At half an hour past 4 p.m., Lizzy s dad tells her that the circus starts in 1 hour. When the circus begins Lizzy watches the lions for 1 hour before the elephants enter the ring for 30 minutes. Afterward the tightrope walkers will perform for an hour. What time will the show end? Draw the time on an analog clock. How long will the entire show last? D. Tickets Andrew buys 1 ticket to the circus using a $20 bill. He receives a $5bill, for $1 bills, and 2 quarters in change. He uses the rest of his money to buy popcorn and a drink. How much did the ticket cost? Show the strategy used and your thinking. E. Elephants Moises counts 8 elephants in the circus. Each elephant has 6 stars on its head. Then, 2 more elephants join the show, but 1 of them has only 3 stars. How many total stars are there? Describe in writing how you solved this problem and show your equations.

3 F. Tightrope Walkers The circus begins at half an hour past 5 p.m. Once the circus starts, the lions jump through rings of fire for 15 minutes. Immediately following, the tightrope walkers perform for 7 minutes. What time do the tightrope walkers end their part of the show? G. Clowns Only ½ of the 12 circus elephants will be in the show. The circus has 21 clowns, but 1/3 of them are sick this week and will not be in the show. Will more elephants or clowns be in the show? How do you know? Show how you solved this problem. H. Circus Tent The circus tent is set up on a piece of ground that is rectangle 70 yards long and 42 yards wide. Use graph paper to draw a picture to help you find the perimeter and area of the circus grounds. If a show area of the circus takes up 1/5 of the space, how many show areas could have performances at the same time? How much square footage would each performance require? If Phil can walk 5 yards every 3 second, how long would it take him to walk halfway around the circus so he could see the acts on the other side?

4 I. Acrobats and Animals Each of 5 groups at the circus has 6 elephants and 3 tigers. The law says that there must be at least 1 person (acrobat) for every 3 animals. This means for 9 animals there will be 3 acrobats. The ratio is 9:3. Before the show, 2 elephants from each group hurt their leg and had to leave. Local laws require that the circus maintain a ratio of 1 person (acrobat) to every 3 animals. Now that the number of animals in each group has changed, how many acrobats would you suggest each group have now in order meet the requirements of the law? What is the new ratio of animals to acrobats? J. Candy The box to hold candy at the circus is 6 in long, 3 in. wide, and 2 in. deep. Each piece of candy is ¾ in. long, ¾ in. wide, and 1 in. deep. If the candy pieces were to fit together perfectly with no spaces in between, how much candy could fit into the box? Explain your thinking and illustrate how you solved the problem with a drawing and an equation. K. Flying Acrobats Joe and Morgan are watching an acrobat performance. Acrobat A is on a platform that is 25 ft. above the ground. Acrobat B is on a platform that is 31 ½ ft. above the ground. Acrobat C is on a platform that is 40 ft. above the ground. The acrobats must do their routines from their respective platforms and then drop to the landing pad below. They all do their routine and drop at the same time. Acrobat A drops at a velocity of 15 ft/sec. Acrobat B drops at a velocity of 18 ft./sec. Acrobat C drops at a velocity of 20 ft./sec. In what order will they land on the pad?

5 L. Friends at the Circus At the circus Cindy, Gracie, Belinda, and Giovanni bought 4 popcorn tubs for a total of $ Taylor and Julian bought 2 tubs for $ If 2 families buy popcorn tubs for each family member for $50.00 total, what is the rate per tub of popcorn? When Cindy wants to buy more popcorn later during the circus, the concession stand is have a sale! She buys 3 tubs for $9.75. What is the rate per tub during the sale? What was the rate of change in the individual price per tub of popcorn? Please show your thinking through math drawings, equations and a simple explanation.