Problems of the Month-December

Sorry for the delay. Answers are due by December 23rd. More questions will be added later. There will be 10 altogether.

1. Claire loves making snowflakes. Mr. Little estimated that Claire should be able to create 1000 unique snowflake patterns, even though no two snowflakes are alike. Of course, there now needs to be a math problem involving 1000. How many pairs of positive integers add up to 1000? For example, 1 + 999 = 1000.

2. Elizabeth and Sophie were singing the 12 Days of Christmas with their math class. The teacher asked the class to complete the following challenge: Using the numbers 1, 2, 3, and 4 and basic rules of order of operations (+, -, x, ÷ and parentheses), write an expression for each number from 1 through 12. Each digit can only be used once, and they must all be used.

3. For a set of five whole numbers, the mean is 4, the mode is 1, and the median is 5. What are the five numbers?

4. At 10:00am, Mr. Little leaves his house in a car at a rate of 60 mi/h. At the same time, Mrs. Little, driving in another car, leaves the same house at a rate of 50 mi/h in the opposite direction. At what time will the cars be 330 miles apart? Don't worry, we will turn around and drive back home once you finish answering the question.

5. If a▲b = ab + b for all non-negative numbers, what is the value of 4▲3?

6. At Chipotle, a burrito with extra guacamole costs $7.75. Three burritos with two extra guacamole costs $21.60. What is the price of each burrito and each extra guacamole?

7. Find the area of the Christmas tree if the larger square is 4 inches x 4 inches.

American Math Challenge Results

GOLD wins! Gold scored 139,712 points compared to 113,484 for Black.

Gold Grade 7 won the group competition. These students will have Mr. Little's world famous chocolate chip cookies for dessert.

Individual Competition Results
1st place: Alex Liu
2nd place: Joe Sakai
3rd place: Tommy Diehl
4th place: William Little
5th place: Tyrese Duncan-Moore

136 students participated! Great job everyone!

Extended time for Problems of the Month

The problems of the month will be due November 10th. There will be fewer problems for November. Thanks to all who participated in the American Math Challenge. At least 129 students participated! I am still waiting for official results, but the competition looks very close... Stay tuned!

American Math Challenge

Practice has begun! The official dates of the competition are October 26-27. All students have login information. Just go to http://www.americanmathchallenge.com, login and start doing problems. Good luck!

Problems of the Month: October

Due November 1st at noon

1. At 11:20, what is the angle formed by the hands on a clock? Assume that the hour hand moves gradually, so the hour hand is between 11 and 12. (Yes, that is harder.) Partial credit given for the hour hand not moving.

2. Before heading out to do some Trick-or-Treating, Alexa had to choose which container to take with her to hold all of her candy. She had her plastic, spherical pumpkin with a radius of 5” from last year, or a bag she found in the kitchen. The bag measured 5” by 9” by 11.5” and had the same shape as a rectangular prism when it was open. Which of these containers has the greatest volume?

3. As Alexa’s mother was waiting for her to return from Trick-or-Treating, she started looking at the nutrition information on the bag from the candy she was distributing. According to this bag of candy bars, a serving size is equivalent to four candy bars, there are eight servings per bag and 200 calories per serving. According to this information, how many calories are in one candy bar? How many calories are in an entire bag of candy bars?

4. When Alexa returned home from Trick-or-Treating she spread all of her candy out on the kitchen table. She noticed that she had 14 Tootsie Pops, but she had exactly three different colors of Tootsie Pops (brown, red and purple). She had exactly twice as many purple as brown and less than 25% of the 14 Tootsie Pops were brown. According to this information, what is the average value of the possible amounts of red Tootsie Pops she could have had?

5. If every fourth trick-or -treater is a vampire, and every 6th, robot, how many of each will you see if seventy-five trick -or treaters come to your door?

6. Icha-Bo has searched the pumpkin patches and found 3 “perfect” spherical pumpkins. He measured and recorded the circumference of each pumpkin. From the least to greatest pumpkin the circumferences measured 22, 44 and 66 inches. What is the volume, in cubic inches, of each of the pumpkins? Use π = 3.14.

7. Icha-Bo noticed the ratio of the circumferences of the pumpkins was 22:44:66 from the least to the greatest circumference. What is this ratio in its simplest form?


8. The mean weight of 9 pumpkins is 16 pounds. One of the pumpkins is removed. The mean weight of the remaining 8 pumpkins is 13 pounds. What is the weight of the pumpkin that was removed, in pounds?


9. The weights of the 8 remaining pumpkins are 11, 12, 14, 18, 15, 14, 8, 12 pounds. What is the median pumpkin weight?


10. A different set of 9 pumpkins has been divided into two groups. The mean weight of the 5 pumpkins that each weighs more than 10 pounds is 12 pounds. The mean weight of the 4 pumpkins that each weighs less than 10 pounds is 3 pounds. What is the mean weight per pumpkin for this group of 9 pumpkins?


11. Emma wants to be a princess for Halloween. When she gets to the costume store she realizes there are many options. There are five different princess crowns, eight different princess dresses, and three different pairs of princess shoes. How many possible combinations are there for Emma’s princess costume consisting of one crown, one dress and one pair of shoes?


12. Michael and Oliver went trick-or-treating and came back with A LOT of candy. However, when Emma gets back they find that, not only does she have more candy, she has better candy than they do. Emma agrees to trade some of the candy but they have to follow her trading rules.

3 smarties packs = 1 fun-size candy bar
2 tootsie pops = 1 skittles pack
15 candy corn = 1 smarties pack
5 candy corn = 2 bit-o-honeys
3 tootsie pops = 1 fun-size candy bar

Based on Emma’s rules, what item is the most valuable?

13. Based on Emma’s exchange rates above, how many of the least valuable item is required to get one of the most valuable item?

14. Thomas dressed us as a skeleton. He went out to frighten the kids on Halloween night. He fell down, and you guessed it, he suffered some broken bones. He went to see a doctor the following day. The doctor said it would take seven weeks for him to heal. In what month would Thomas be healed?

15. One of my favorite cartoons is Charlie Brown and the Great Pumpkin. Last year, the world record for the largest pumpkin was broken. Find the weight of the world’s largest pumpkin in grams.

Problems of the Month--September

Due October 2nd by 4:00pm

1. My son’s birthday is September 4th. What day of the week will his birthday fall on in 2020?

2. Imagine that you made a painting. The canvas costs $10, the paints cost $3.50, and the frame costs $7.49. You sold the painting for $35. How much profit did you make?

3. You are buying a computer on the Internet, and there are two offers. One is a discount of 30% off the original price, followed by a discount of 50% off the sale price. The other offer is a discount of 80% from the original price. Are the two discounts the same, or is one offer better?

4. There are five players on the basketball team named Tara, James, Jackie, Terry, and Corey. Their jersey numbers are 7, 11, 14, 24, and 42. Their positions are point guard, shooting guard, small forward, power forward, and center. Use the clues to match the players with their numbers and positions.
a. The tallest player is the center.
b. Tara is the smallest player.
c. James has an odd numbered jersey.
d. Terry has the smallest number.
e. Jackie is not a forward.
f. Corey is number 24.
g. The point guard is number 11.
h. The center is number 42.
i. The power forward has an odd number.
j. Corey is a small forward.

Problem of the Day: April 30, 2010

In the first modern Olympiad, hosted by Athens in 1896, there were 241 competitors. All of the competitors were men. In the 2008 Olympics hosted by Beijing, there were 6305 men and 4637 women.
a.) In 2008, what was the percentage of women Olympians?
b.) Assuming that the increase in the number of men and women participating in the Olympics is constant, in what year would the number of women equal the number of men?

Problem of the Day: April 29, 2010

In badminton, the court dimensions (for doubles) are 20 ft wide and 44 feet long. When a player serves, they must serve the birdie into the service court. The service court is half the width of the full court, and begins 6 ft 6 inches from the net and extends to the baseline. What percentage of the full court is one service court?

Hint: It may help to make a sketch or find a picture of the badminton court.

Problem of the Day: April 28, 2010

This sport is full-contact basketball, with trampolines. Points are scored by shooting the ball through the net, as in basketball, though the point-scoring rules are modified. There are four trampolines set into the floor which serve to propel players to great heights for slam dunks. The rules also permit some physical contact between the members of the four-player teams. Name the sport.

Problem of the Day: April 27, 2010

Winning streaks in sports are exciting and fun to experience. For example, the UConn women’s basketball team won the championship two years in a row and currently have a winning streak. They are far from the longest winning streak in sports history. Name the sport in which the longest winning streak occurred and the number of wins.

Problem of the Day: April 26, 2010

As the Beijing Olympics ended, it also marked the end of baseball and softball as Olympic medal sports. Although the two sports won’t be on the Olympic schedule for the 2012 Games in London, they won’t be alone. Throughout the years the IOC has slashed a number of sports from the official Olympic program. Name two of the 12 sports cut from the Olympics.

Problems of the Day from last week

Some students had trouble accessing the website last week, so they are included in the blog.

April 23, 2010

While we need to improve our pitching, the Orioles also have a weakness in hitting.

Currently, the O’s are 26th out of 30 major league baseball teams in batting average. If the team has 122 hits in 542 at bats, what is the team batting average?


No problems for April 22, 2010. This problem is worth 20 points altogether!

April 21, 2010

These eleven baseball players are often considered the greatest hitters of all time.

1. Copy and paste the chart into Excel. Change the font color to black if necessary.

2. Calculate the batting averages of the players.

3. Calculate the “Little Slugging Factor”. This is found my multiplying the batting average × RBIs × Home runs ÷ 100000

4. Sort the players by “Little Slugging Factor”. Email me your spreadsheet.

5. DOUBLE BONUS! Find another player, either current or recently retired, that has a high enough LSF to make the top five on this list and prove it in your spreadsheet.

Player: Games, At Bats, Hits, Runs Batted In (RBI), Home Runs
Hank Aaron 3298 12364 3771 2297 755
Rod Carew 2469 9315 3053 1015 92
Ty Cobb 3034 11429 4191 1961 118
Lou Gehrig 2164 8001 2721 1990 493
Rogers Hornsby 2259 8173 2930 1584 301
Reggie Jackson 2820 9864 2584 1702 563
Mickey Mantle 2401 8102 2415 1509 536
Willie Mays 2992 10881 3283 1903 660
Stan Musial 3026 10972 3630 1951 475
Babe Ruth 2503 8399 2873 2211 714
Ted Williams 2292 7706 2654 1839 521

Math Awareness Month

April is Math Awareness Month, and this year's theme is sports. Students are completing daily problems based on this theme at http://calvertschoolweb.org/wlittle/math_Awareness_Month_2010_DailyProblems.htm. The students are also completing specially designed activities in math class. These activites connect mathematics with one of their either history or English, and tie into the theme of Math and Sports. These can be viewed at http://calvertschoolweb.org/wlittle/Math_awareness_month_2010.htm.

MathCounts Competition

Calvert School's MathCounts team competed in February against schools from all over the Baltimore Metro and Chesapeake Bay areas. While we did not place in the top 6 this year, I am still proud of our team. The students who completed include Giorgio Caturegli, Dale Waters (top scoring team member!), Eddie Van Dyke, Alice White, Kendall Reitz, and Anna Dorsey.

Problems of the Month--January 2010

A Look At The Past Decade – The Problems
January 04, 2010

2010 is the start of a new decade, so here are a few New Year's problems.

1. At the start of the last decade everyone was concerned about Y2K... Well, we made it. Y2K was here and gone with no major problems. Interesting thing about the first date of the new millennium, 01/01/00 - when the digits of that date are added, it's the smallest possible sum of any date. What date during the next century, when written in that form, will have the greatest possible sum of its digits?

2. This New Year's date, 01/01/10, has a sum of digits equal to three. Find ten dates with the same sum of digits.

3. How many seconds will occur this millennium (the year 2000 through the year 2999)? Express your answer in scientific notation.

4. New Year's eve is a time when many people make resolutions...
Kaitlyn decided that she would like to read more during 2010, so she made a resolution to read 30 minutes each day. If Kaitlyn reads an average of 1 page every 2 minutes and she finishes her 6th book at the end of her reading session on March 31, 2010, what would be the average number of pages per book for these six books?

5. Nora’s resolution is to get more exercise. She decided that starting with the first full week in 2010, she will do a 45-minute workout four times each week (four days during every seven-day period). This means she will have to exercise four of the days during the week of Jan. 1 through Jan. 7, and then four of the days during the week of Jan. 8 through Jan. 14, and so on. If Nora sticks to her resolution, what is the first possible date on which she could reach a total of 25 hours of exercise for the year?