Thursday, November 12, 2009

American Math Challenge



This month, there are over 40 students participating in the American Math Challenge! Stay tuned for the results for Calvert School! There will be no Problems of the Month for November.

Visit www.americanmathchallenge.com for more information about the competition.

Wednesday, October 7, 2009

Problems of the Month--October

Back Home At Last!

Loggerhead Sea Turtle General info:
Size: Typically 2.5 to 3.5 feet in carapace length (73-107 cm).

Weight: Adult weigh up to 350 pounds (159 kg).

Diet: Primarily carnivorous and feed mostly on shellfish that live on the bottom of the ocean. They eat horseshoe crabs, clams, mussels, and other invertebrates. Their powerful jaw muscles help them to easily crush the shellfish.

Habitat: Prefer to feed in coastal bays and estuaries, as well as in the shallow water along the continental shelves of the Atlantic, Pacific and Indian Oceans.

Nesting: Nest at intervals of 2, 3, or more years. They lay 4 to 7 nests per season, approximately 12 to 14 days apart. Lays average of between 100 to 126 eggs in each nest. Eggs incubate for about 60 days.

Status:U.S. - Listed as Threatened (likely to become endangered, in danger of extinction, within the foreseeable future) under the U.S. Federal Endangered Species Act.International - Listed as Endangered (facing a very high risk of extinction in the wild in the near future) by the International Union for Conservation of Nature and Natural Resources.

Threats to Survival: The greatest threat is loss of nesting habitat due to coastal development, predation of nests, and human disturbances (such as coastal lighting and housing developments) that cause disorientations during the emergence of hatchlings. Other major threats include incidental capture in longline fishing, shrimp trawling and pollution. Incidental capture in fisheries is thought to have played a significant role in the recent population declines observed for the loggerhead.
Population Estimate: 44,560 nesting females.

________________________________________________

On September 19, the National Aquarium in Baltimore released a Loggerhead Sea Turtle that had been in their care for over a year. The turtle was back home at last!

1. When the turtle was rescued it couldn’t swim or dive properly (both skills are needed for catching food). Part of the reason for his impairment was the 10 pounds of hitchhiking barnacles, mollusks, and sea grass that had attached themselves to the turtles shell. Once the 10 pounds of “hitchhikers” were removed they found the turtle was severely underweight! Weighing only 64 pounds with a clean shell, what percent of his weight at capture was due to the “hitchhikers”? Express your answer to the nearest tenth.

2. Once the turtle’s shell was cleaned off he was able to swim and dive properly which allowed him to catch food and enabled him to reach a healthy weight. Upon release, the turtle weighed 90 pounds, which is an ideal weight for the turtle!! By what percent did the turtle’s weight (without the hitchhikers) increase while in rehabilitation? Express your answer to the nearest thousandth.

3. To track where the turtle goes and how he is doing after his release, researchers attached a tracking device to his shell that will naturally fall off after a while. From the morning of September 19, 2009 to the morning of September 24, 2009, the turtle had swum 76.4 miles. If the turtle slept 10 hours each day, what was his average swimming speed in miles per hour during the times in which he was awake? Express your answer as a decimal to the nearest hundredth.

Thursday, September 3, 2009

5th Grade Orientation Week


The students have had a great first week of school. So far, we have completed problem solving activites, and reviewed whole number operations. This is Mrs. Lawrence's homeroom, who spent the week with Mrs. Liotta for math class.

Tuesday, September 1, 2009

Welcome Back!!!

It is great to be back at Calvert School for the 2009-2010 school year. The Math Blog is a great place to find links to your textbooks and workbooks. There will also be problems of the month posted. Not only are the challenge problems fun, they also give you a chance to win prizes. Last year, as fifth graders, Joe Sakai and Tommy Diehl won gift cards from Cold Stone. Who will be the top winners this school year?

Problems of the Month--September

Cash for Clunkers

1. On July 31, 2009 the US government decided to make an additional two billion dollars available to the “Cash for Clunkers” program that is aimed at jump-starting the car industry. The bill was passed with a yes-to-no vote count of 316-to-109. What percent of the votes supported passing the bill? Express your answer to the nearest hundredth.

2. Jillian decides to take advantage of this program and trades in her old car (which only got 15 miles per gallon of gasoline) for a new car that gets 32 miles per gallon of gasoline. Gas currently costs $2.52 per gallon in her town. If she drives an average of 1000 miles per month and gas continues to average $2.52 per gallon, how much money will Jillian save on gas in one year?

3. Franklin is also taking advantage of the Cash for Clunker program and is trading in his car that got 18 miles per gallon of gas (which is the highest gas mileage that a car can get and still qualify as a “clunker”). The original price of the car he plans to purchase is $15,095, but because the new car will improve Franklin’s gas mileage by over 10 miles per gallon, he will get $4500 off of the price of the new car. If Franklin has to pay a 6% sales tax on the discounted price of this car, how much will he end-up paying for the car and the sales tax combined?

Tuesday, May 12, 2009

Problems of the Month--May

1. When a water tank is 30% full, it contains 27 gallons less than when it is 20% empty. How many gallons of water does the tank hold when it is full?

2. Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove 360 miles in 6 hours, 40 minutes. What was Stan’s average speed in miles per hour for the total trip?

3. What is the difference between the 2000th term and the 2005th term of the arithmetic sequence −8, −2, 4, 10, ... ? An arithmetic sequence is found by adding the same amount over and over to find each term. For example, in the sequence 1, 3, 5, 7, 8… the amount being added is two. You can use this to find numbers in the sequence.

4. In the game “Cover It Up” two standard six-faced dice are rolled and their sum determined. The player can then cover that number on the game board or any two numbers that have that sum. For example, if you roll a 3 and 5, you can cover the 8, the 1 and 7, the 2 and 6, or the 3 and 5. What is the probability of being able to cover the 9 on the first roll of the two dice? Express your answer as a common fraction.

5. A teacher has made eight statements for a True-False test. Three statements are true and five are false. How many distinct answer keys could there be for the test?

Wednesday, April 8, 2009

Problem of the Month--April

Responses have dwindled each week since these questions do not count for Black and Gold points, but there are a few dedicated students that still have been waiting for the problems of the week. Instead, there will be a set of problems for the month of April and the month of May. The prize list is still up for grabs for 4th quarter. Good luck!

Problems of the Month

1. If b is positive, what is the value of b in the geometric sequence 9, a, 4, b? Express your answer as a common fraction. A geometric sequence is found by multiplying by a common factor. For example, in the sequence 1, 2, 4, 8... the common factor is 2. Find the common factor, and then use it to solve.

2. Noel earns $25 each week mowing lawns. Each week he spends two-fifths of his earnings on himself and has the rest of his earnings placed directly into a savings account. Every third week he withdraws $20 from his savings account to take his girlfriend to the movies. If he continues this same spending pattern, how many weeks will it take Noel to first exceed $125 in his savings account? Express your answer as a whole number.

3. Two complementary angles A and B have measures in the ratio of 13 to 17. What is the ratio of the measure of the supplement of angle A to the supplement of angle B? Express your answer as a common fraction.

4. Amy and Belinda each roll a sheet of 6-inch by 8-inch paper to form a cylindrical tube. Amy tapes the two 8-inch sides together without overlap. Belinda tapes the two 6-inch sides together without overlap. What is the difference of the volumes of the two tubes?

5. The scale of a certain map is 0.8 inch = 16 miles. A square park is represented on this map by a square with side length 0.625 inch. What is the actual area of this park? Express your answer as a decimal to the nearest hundredth.

Monday, March 2, 2009

Problems of the Week

Not a lot of people turned in answers last week, so keep the same problems for this week. Also, learn the sequence for pi. Awards will be given for Pi Day! March 3, 2009 is Square Root Day. 3 is the square root of 9, and 3 times 3 is 9.

1. February 2, 2004 was the last Square Root Day. When is the next Square Root Day?
2. Name two formulas that use square roots.
3. How many Square Root Days occur each century?
4. What is the sum of the first five squares? 9 is a square because 32 = 9.
5. Figure out my wife’s height using the following clues. Her height is x feet and y inches. (x + y)2 = 144. (x – y)2 = 4.
6. For the first time since 1997, the Dow Jones finished below 7000. It finished at 6,763. What is the closet square to 6,763?
7. I am thinking of a number. If I take the square root of my number, add two, square the number, and then divide by 5, the result is 45. What is my number?
8. A googol is a 1 followed by 100 zeros. What is the square root of a googol?

Tuesday, February 17, 2009

Problems of the Week--2/17/09

Answers due by Friday

1. What is the 20th term of the arithmetic sequence shown below?
13, 19, 25, 31, ...

2. What is the sum of A and B from the arithmetic sequence shown below?
7, 15, 23, A, 39, B, ...

3. What is the sum of A and B from the geometric sequence shown below?
32, A, 72, B, 162, 243...

4. The NBA All-Star Game was last weekend. The top vote-getter was Dwight Howard. Below is a breakdown of the voting for all Eastern Conference centers. Determine the percentage of these votes that Dwight Howard received.

Dwight Howard 3,150,181; Kendrick Perkins (Bos) 621,709; Rasheed Wallace (Det) 402,991; Samuel Dalembert (Phi) 396,119; Andrew Bogut (Mil) 357,997; Jermaine ONeal (Tor) 342,723; Al Horford (Atl) 323,302; Brendan Haywood (Wash) 291,490; Ben Wallace (Clev) 263,862; Zydrunas Ilgauskas (Cle) 219,697; Emeka Okafor (Char) 212,539

Monday, February 9, 2009

Problems of the Week--1/9/09

MathCounts Inspired Problems
Double points week! Answers due Friday by noon.

1. February 2 was Groundhog Day. Every February 2, Punxsutawney Phil lumbers out of his home to predict the end of winter by looking for his shadow. If Phil sees his shadow, legend says that we will have 6 more weeks of winter. If the groundhog does NOT see his shadow we will have an early spring.

2. According to the “official” Groundhog Day website, Punxsutawney Phil is 123 years old. Normally, groundhogs live up to 6 years in the wild. If Phil is 123 years, by what percent has he exceeded the normal, unaided lifespan of his species?

3. A groundhog is also known as a woodchuck. Diana writes the letters w, o, o, d, c, h, u, c and k on separate pieces of paper and places the pieces of paper in a bag. If Diana randomly draws one piece of paper from the bag, what it the probability that the letter drawn is also contained in the word groundhog? Express your answer as a common fraction.

4. Groundhog Greg’s burrow has 5 holes he can enter or exit through. If he never exits through the same hole he entered through, how many entrance/exit combinations can Greg choose from? Note that entering through A and leaving through B is not the same as entering through B and leaving through A.

5. What is the 20th term of the arithmetic sequence shown below?
13, 19, 25, 31, ...

6. What is the sum of A and B from the arithmetic sequence shown below?
7, 15, 23, A, 39, B, ...

7. What is the sum of A and B from the geometric sequence shown below?
32, A, 72, B, 162, 243...

8. A worm has to climb a barrier 19 feet high. It climbs 8 feet every day and slips down 5 feet every night. Starting from the bottom of the barrier on Sunday morning, on which day of the week will the worm reach the top of the barrier?

9. How many fifteen-minute appointments can a doctor fit into her schedule if she works from 8:30 am to noon and from 1 pm to 4:30 pm?

10. On a $12.00 purchase, Michael was offered 3 successive discounts of 25%, 20% and 10% each in any order he wished. What is the difference in dollars between applying the discounts in order from greatest to least and in order from least to greatest?

MathCounts Competition


On Saturday, February 7th, nine Calvert students spend the morning and afternoon competing with other schools in the MathCounts Chapter Competition. For the second year in a row, Calvert School placed as a team with the state qualifiers. Last year we placed 5th, and this year we placed 4th. Before last year, we never had a team place in the chapter competition.

In addition, Joshua Khuvis placed 4th in the region out of around 200 participants. Robby Vint, Paul Berman, Bert Schmickel and Joseph White placed in the top 16 students. Tess Kamauff also placed in the top 36 students. All six of these students have qualified for the State Competition in March.

The other students that participated in the competition are Peter Cooke, Ashley Mitchell, and Dale Waters. These students also did very well, but their scores were not quite high enough to qualify for the state competition.

Stay tuned for the results from the State Competition next month!

Tuesday, January 27, 2009

Problems of the Week—January 27, 2009

Bowling Buddies
Anita, Cheri, Miguel, and Jake went bowling one night. For fun, they decided to pit the girls against the boys, with the highest total score for each team winning.

Anita scored 18 less than Miguel. Cheri's score was 16 less than twice Anita's. Cheri outscored Jake by 21.

If the total scored by all four kids was 529, what was the final score of the match?


Dimensions
A rectangle has an area of 147 ft2. The length is three times longer than the width. What are the length and the width of the rectangle?


Who likes which snack?
-Cindy does not like sweet treats.
-Carl loves fruit.
-Catherine does not like cantaloupe or cinnamon rolls.
-Chuck likes cake.
-Carrie likes icing.
-Someone likes cookies, and another likes cereal.


Say What?!?
The sum of a certain number of consecutive integers, starting with -22, is 72. What is the largest number in the group of integers?

Thursday, January 22, 2009

Problems of the Week--Inauguration Day

Submit the answers by 8:15 am on Monday morning. I forgot to post these. I wrote them over Winter Break...

1. The 2009 inauguration is expected to see record levels of attendance. Lyndon B Johnson’s inauguration currently holds the record for attendance at 1.2 million people. Originally, attendance for the 2009 inauguration was projected to be as high as 5 million. Now, based on more accurate data, the projected attendance is around 2 million. What is the positive difference between the originally estimated percent increase over the current record attendance and the newly estimated percent increase over the current record attendance? Round your answer to the nearest whole number.


2. The National Mall is 300 acres. It stretches 1.9 miles from the Capitol building to the Lincoln Memorial. This will be the first time in history that the entire mall will be open for an inauguration. If attendance is the estimated 2 million people and all of the people spread out evenly over the mall, how many square feet will each person get? Note that 1 acre is equal to 43,560 square feet. Express your answer as a decimal to the nearest tenth.

Wednesday, January 14, 2009

Problems of the Week

Sorry for the delay. I will accept the answers by midnight on Friday, January 16th.

Football – The Problems
January 12, 2009

The minimum starting annual salary for rookies in the NFL is $295,000. The minimum annual salary is $370,000 for second year players and $445,000 for third year players. For a player earning the minimum salary for their experience, what is the positive difference between the percent increase the $75,000 represents from the first to second year and the percent increase the $75,000 represents from the second to third year? Round your answer to the nearest tenth.

There are 32 teams in the NFL. Sixteen of the teams are in the American Football Conference (AFC) and the other 16 teams are in the National Football Conference (NFC). At the beginning of the season, Julia tried to predict the teams that would be in each conference's championship by randomly drawing 4 teams (2 AFC teams and 2 NFC teams) from a hat. What is the probability that the 4 teams she selected are the same four teams that will be in the conferences' championships? Express your answer as a common fraction.

In football, teams can score 6 points with a touchdown, 3 points with a field goal or 2 points with a safety. Additionally, after a touchdown, teams can score 1 bonus point with a field goal kick or 2 bonus points with a 2-point conversion. The final score of a particular football game was 23 to 11. If every touchdown is followed with a successful bonus point attempt (1 or 2 points), how many different scoring combinations could have resulted in the losing team's 11 points?

Using the remaining teams, I have created a formula for determining the Super Bowl Champion. Based on their ranking in each category, a team is awarded points. The highest ranked team receives a 1, and second ranked team receives a 2, and so on. In the case of a tie, give both teams the lower score. For example, if two teams are tied for second in a category, give both teams 2 points. The lowest total score is the team that should win the Super Bowl. Using this formula, which team should win?

Sunday, January 4, 2009

Problems of the Week--1/5/2009

Welcome Back!!! Answers are due by noon on Friday, January 9, 2009

Cool Riddles

All the words referred to in the riddles are from this list:

ice, hat, snow, cold, cool, sleet, freeze, snowman, iceberg, glacier, subzero, blizzard, refrigerator, precipitation

1. I am a word. The number of my letters equals 4% (1/25) of the number of years in two centuries. I am _______________.

2. I am the number of letters in a word from the list above. There are only two words in the above list that have fewer letters than that word. I am _______________.

3. I am a word. The number of my letters equals the square root of a gross. A dictionary might help you realize that I am _______________.

4. My name means less than nothing.
(Can that be really so?)
But when you freeze
Just think “degrees”
And then my name you’ll know!
I am _______________.

5. I am a word. The number of my letters equals 1/15th of the number of letters in all of the above words combined. I am _______________.

6. I am the number of letters in a word from the list above. If you take the number of letters in the longest word, add two, and then divide by the number of letters in the smallest word, you get the number of letters in my word. I am _______________.

7. I am a word. There are four words with the same number of letters, and I am one of them. I last longer than anything else on the list, other than the refrigerator. You should realize that I am _______________.

8. Find the item that could be purchased at Dairy Queen. Take the number of letters and divide by two. The number of words with this number of letters is the number of letters that I have. I share more letters with the first word in this puzzle than any other word with the same number of letters as me. I am _______________.