Read a Book Day (Sept. 6) Meeting Also ideal for Read Across America Day (March 2) or Children s Book Week (May 12-18) (Multiple Topics)

Transcription

1 Read a Book Day (Sept. 6) Meeting Also ideal for Read Across America Day (March 2) or Children s Book Week (May 12-18) (Multiple Topics) Topic There are a variety of math topics covered in the problems used for this meeting. The problems are not provided in order of level of difficulty. Materials Needed Copies of the Read a Book Day problem set (Problems and answers can be viewed here, but a more student-friendly version in larger font is available for download from on the MCP Members Only page of the Club Program section.) Calculators Meeting Plan This meeting idea is great to use at a variety of times throughout the year. We have identified three particular holidays that are relevant: Read a Book Day (Sept. 6), Read Across America Day (March 2) and Children s Book Week (May 12-18). The problems that follow come from a problem set that originally was printed in the MATHCOUNTS School Handbook. If you use this for your first meeting, we suggest letting the students work in groups on this set of problems. The difficulty level from problem to problem varies. When students are finished with the 10 problems we have provided, encourage them to write some of their own that are based on books and characters they are familiar with. Students then can swap papers with each other, or you can consolidate the problems and make another handout for the next meeting. Also, ask students to keep an eye out for opportunities to create similar problems based on the books they read throughout the year. Perhaps speak with the English teachers in your school to see if they have suggestions for problem scenarios based on the books students will be reading in class. 1. Tweedledum says, The sum of your weight and twice mine is 361 pounds. Tweedledee says, Contrariwise, the sum of your weight and twice mine is 362 pounds. If they are both correct, how many pounds do Tweedledum and Tweedledee weigh together? [Through the Looking Glass by Lewis Carroll] 2. Caractacus Pott invents a candy for which he is paid one shilling for every thousand candies sold. He expects to sell 5 million candies every year, and one shilling is equivalent to 14 U.S. cents. How much will Caractacus make in one year in U.S. dollars? [Chitty Chitty Bang Bang by Ian Fleming] 3. Sherlock Holmes states, If a rod of six feet threw a shadow of nine feet, a tree of 64 feet would throw one of What length, in feet, should Sherlock say next? [Sherlock Holmes: The Complete Novels & Stories, Volume I by Sir Arthur Conan Doyle] 4. Four children find a magic token that grants half of any wish. Their mother takes the token with her to a destination 20 miles away, and when she wishes she was home, she magically ends up halfway home. If the mother continues to make the same wish, how many more wishes will it take for her to be within 100 feet of her house? There are 5280 feet in 1 mile. [Half Magic by Edward Eager] 5. Charlie Bucket receives one bar of chocolate on his birthday. He eats one nibble of the same size each day and manages to make the bar last for 30 days. What percent of his chocolate bar is left after 18 days? [Charlie and the Chocolate Factory by Roald Dahl] MATHCOUNTS Club Resource Guide 21 Club Resource Guide.pdf 21 8/18/08 11:24:14 AM

2 6. Milo sees this sign that describes the distance to Digitopolis in six different ways. According to this sign, how many inches are in a rod? [The Phantom Tollbooth by Norton Juster] DIGITOPOLIS 5 miles 1600 rods 8800 yards 26,400 feet 316,800 inches 633,600 half-inches 7. Five men were to share a treasure of gold with Long John Silver. If the treasure were split in the following ratio 2:5:7:10:20:50, and the least amount any of the six pirates received was 14,000 pounds of gold, what is the total weight of the gold treasure? [Treasure Island by Robert Louis Stevenson] 8. The Emperor of Lilliput gives Gulliver a daily allowance of food and drink that is equivalent to the amount given to 1728 Lilliputians. If Gulliver s allowance of food and drink will fit in a cubical box that measures 24 blots along each edge, what is the edge length, in blots, of the cubical box for one Lilliputian s daily allowance of food and drink? [Gulliver s Travels by Jonathan Swift] 9. A ship travels the 200-mile route from Fort Kearney to Omaha at an average rate of 40 miles per hour. The ship reaches Omaha at 1 p.m. What time did it leave Fort Kearney? (Assume the ship did not cross any time zones.) [Around the World in Eighty Days by Jules Verne] 10. Alice changes size several times. The ratio of her original height to her second height is 24 to 5. The ratio of her second height to her third height is 1 to 12. The ratio of her original height to her fourth height is 16 to 1. The tallest of these four heights is 10 feet. What is her shortest height, in inches? [Alice in Wonderland by Lewis Carroll] Answers: 241 pounds; $700; 96 feet; 10 wishes; 40%; 198 inches; 658,000 pounds; 2 blots; 8 a.m.; 3 inches Please share any additional literature-related questions you and/or your club members create during this meeting or throughout the year. We would love to share these with other clubs while crediting you for your creativity. Send your submissions to info@ mathcounts.org with the subject line, MATHCOUNTS Club Program Ideas. Thank you in advance! MATHCOUNTS Club Resource Guide Club Resource Guide.pdf 22 8/18/08 11:24:14 AM

3 Alice in Wonderland Read a Book Day Meeting Problem Set Alice in Wonderland 1. Tweedledum says, The sum of your weight and twice mine is 361 pounds. Tweedledee says, Contrariwise, the sum of your weight and twice mine is 362 pounds. If they are both correct, how many pounds do Tweedledum and Tweedledee weigh together? [Through the Looking Glass by Lewis Carroll] 2. Caractacus Pott invents a candy for which he is paid one shilling for every thousand candies sold. He expects to sell 5 million candies every year, and one shilling is equivalent to 14 U.S. cents. How much will Caractacus make in one year in U.S. dollars? [Chitty Chitty Bang Bang by Ian Fleming] 3. Sherlock Holmes states, If a rod of six feet threw a shadow of nine feet, a tree of 64 feet would throw one of What length, in feet, should Sherlock say next? [Sherlock Holmes: The Complete Novels & Stories, Volume I by Sir Arthur Conan Doyle] 4. Four children find a magic token that grants half of any wish. Their mother takes the token with her to a destination 20 miles away, and when she wishes she was home, she magically ends up halfway home. If the mother continues to make the same wish, how many more wishes will it take for her to be within 100 feet of her house? There are 5280 feet in 1 mile. [Half Magic by Edward Eager] 5. Charlie Bucket receives one bar of chocolate on his birthday. He eats one nibble of the same size each day and manages to make the bar last for 30 days. What percent of his chocolate bar is left after 18 days? [Charlie and the Chocolate Factory by Roald Dahl] 6. Milo sees this sign that describes the distance to Digitopolis in six different ways. According to this sign, how many inches are in a rod? [The Phantom Tollbooth by Norton Juster] DIGITOPOLIS 5 miles 1600 rods 8800 yards 26,400 feet 316,800 inches 633,600 half inches Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Problem Set

4 7. Five men were to share a treasure of gold with Long John Silver. If the treasure were split in the following ratio 2:5:7:10:20:50, and the least amount any of the six pirates received was 14,000 pounds of gold, what is the total weight of the gold treasure, in pounds? [Treasure Island by Robert Louis Stevenson] 8. The Emperor of Lilliput gives Gulliver a daily allowance of food and drink that is equivalent to the amount given to 1728 Lilliputians. If Gulliver s allowance of food and drink will fit in a cubical box that measures 24 blots along each edge, what is the edge length, in blots, of the cubical box for one Lilliputian s daily allowance of food and drink? [Gulliver s Travels by Jonathan Swift] 9. A ship travels the 200-mile route from Fort Kearney to Omaha at an average rate of 40 miles per hour. The ship reaches Omaha at 1 p.m. What time did it leave Fort Kearney? (Assume the ship did not cross any time zones.) [Around the World in Eighty Days by Jules Verne] 10. Alice changes size several times. The ratio of her original height to her second height is 24 to 5. The ratio of her second height to her third height is 1 to 12. The ratio of her original height to her fourth height is 16 to 1. The tallest of these four heights is 10 feet. What is her shortest height, in inches? [Alice in Wonderland by Lewis Carroll] **Answers to these problems are on page 22 of the Club Resource Guide.** Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Problem Set

5 Read a Book Day Solutions ( MCP Club Resource Guide) Problem 1. We can find the weight of Tweedledum and Tweedledee together without finding their individual weights. Combining both of their statements, we know that three Tweedledums and three Tweedledees would weigh = 723 pounds. Tweedledum and Tweedledee must weigh = 241 pounds together. Problem 2. One shilling for every 1000 candies is equivalent to 5000 shillings for every 5,000,000 candies. If every shilling is worth 14 cents, Caractacus Pott will make = 70,000 cents or $700 in one year. Problem 3. A 9-foot shadow is half again as long as the 6-foot rod that casts the shadow (9/6 = 3/2 = 1.5). The shadow of a 64-foot tree will be 3/2 64 = 96 feet, so Sherlock Holmes should say 96 next. Problem 4. There are 5280 feet in one mile, so 20 miles is equal to = 105,600 feet. The question is how many times do we need to multiply 105,600 feet by 1/2 to make it less than 100 feet. We would need to know about logarithms to solve an inequality such as 105,600 (1/2) y < 100. We can certainly keep multiplying by 1/2 (or dividing by 2) until the value drops below 100, but we might start with the educated guess that y = 10. Many Mathletes will know 2 10 = 1024, and 105, will be about 100. In fact, it is so we need to multiply by 1/2 (or divide by 2) one more time. The mother will need to make her wish a total of 11 times, but she already has made the wish once. She will need to make the wish 10 more times, and then she will be about 51.6 feet from her house. Problem 5. After 18 days Charlie Bucket has eaten 18/30 or 6/10 or 60% of his chocolate bar, so 40% of the chocolate bar is left. Problem 6. According to the sign, 1600 rods is the same as 316,800 inches, so there must be 316, = 198 inches in a rod. Problem 7. If the pirates split the treasure in the ratio 2:5:7:10:20:50, then there are a total of = 94 equal portions of treasure. If the least amount any of the six pirates received is 14,000 pounds, then that must belong to the pirate who received two equal portions. This means that one portion must be 14,000 2 = 7000 pounds. The total weight of the treasure must be = 658,000 pounds. Problem 8. Gulliver s food and drink will fit in a cubical box that measures 24 blots along each edge. This cube has a volume of = 13,824 cubic blots. (A student who recognizes that 1728 is a perfect cube equal to will already know that the Lilliputian s cubical box measures blots.) Dividing 13,824 cubic blots by the 1728 Lilliputians who would eat an equivalent amount of food and drink, we find that a Lilliputian must eat and drink about 13, = 8 cubic blots per day. The cube root of 8 is 2, so the cubical box for one Lilliputian s daily allowance of food and drink must measure 2 blots along an edge. Problem 9. It would take = 5 hours to go 200 miles at 40 miles per hour. If the ship reaches Omaha at 1 p.m., then it must have left Fort Kearney at 8 a.m. Problem 10. If the ratio of Alice s original height to her second height is 24 to 5, then her second height was 5/24 of her original height. If the ratio of her second height to her third height is 1 to 12, then her third height was 12/1 5/24 = 5/2 or 2.5 times her original height. This was Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Solution Set

6 her tallest stage. If 2.5 times her original height is 10 feet tall, then her original height must have been 10/2.5 = 4 feet. The ratio of her original height to her fourth height is 16 to 1, which means her fourth height is 1/16 of 4 feet, which is 1/16 of 48 inches or 1/16 48 = 3 inches tall. This is her shortest height. Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Solution Set