Week of February 25th.

Wishing for snow.

 Another winter storm hit the east coast hard last week! Most areas were left to shovel themselves out of deep snow. As one meteorologist explained, usually the ratio of the amount of rain (in inches) to the amount of snow (in inches) for the same amount of precipitation is 1 to 10. This means that 10 inches of snow would have come down as 1 inch of rain. According to this ratio, the total precipitation in 1 foot of snow is equal to how many inches of rain? Express your answer as a decimal to the nearest tenth.

Snow Day For Many Area Schools

News stations were reporting that due to the large amounts of snow, many schools were closed, allowing for a three-day weekend for many students.  One region had six different reporting stations calling in with their total snow accumulation measurements. The mode snowfall measurement for the six reporting stations was 6 inches, as was the median. The least amount of snow accumulation for any of the stations was 3 inches. With just this information, what is the least possible mean snowfall for the six reporting stations?

Treacherous Driving Conditions

It takes a lot of snow for the federal government in Washington, D.C. to shut down, but even they experienced a two-hour delay last Friday. This is to allow people to take it slow on their way in to work. A commute in to work that usually takes someone 24 minutes traveling at an average speed of 37.5 miles per hour was just not possible that day. On this snowy day, the average rate of speed this person could travel was only 15 miles per hour due to the conditions. How many minutes did the commute in to work take?

Solution was due on Monday March 3rd.

 Another winter storm hit the east coast hard last week! Most areas were left to shovel themselves out of deep snow. As one meteorologist explained, usually the ratio of the amount of rain (in inches) to the amount of snow (in inches) for the same amount of precipitation is 1 to 10. This means that 10 inches of snow would have come down as 1 inch of rain. According to this ratio, the total precipitation in 1 foot of snow is equal to how many inches of rain? Express your answer as a decimal to the nearest tenth.

Snow Day For Many Area Schools

News stations were reporting that due to the large amounts of snow, many schools were closed, allowing for a three-day weekend for many students.  One region had six different reporting stations calling in with their total snow accumulation measurements. The mode snowfall measurement for the six reporting stations was 6 inches, as was the median. The least amount of snow accumulation for any of the stations was 3 inches. With just this information, what is the least possible mean snowfall for the six reporting stations?

Treacherous Driving Conditions

It takes a lot of snow for the federal government in Washington, D.C. to shut down, but even they experienced a two-hour delay last Friday. This is to allow people to take it slow on their way in to work. A commute in to work that usually takes someone 24 minutes traveling at an average speed of 37.5 miles per hour was just not possible that day. On this snowy day, the average rate of speed this person could travel was only 15 miles per hour due to the conditions. How many minutes did the commute in to work take?

Solution was due on Monday March 3rd.

New Math

Evaluate each of the following using the definitions of these "new" mathematical symbols.

1) Let m ¶ n = (m/n) + (n/m) for all integers m, n ≠ 0.

   What is the value of 5 ¶ 8? Express your answer as a common fraction.

3) If x @ y = xy – 2x, what is the value of  (5 @ 3) – (3 @ 5)?

    What is the value of (2^{(4 ♣ 13)}) ♣ (3^{(3 ♣ 5)})?

Week of February 11th.

The race for the nomination!

Super Tuesday 2008 (February 5^th) has past and there is still no clear democratic leader in the race for the nomination. One county’s Super Tuesday 2008 turnout set a record with 50 percent of the 362,376 registered voters participating. Prior to 2008, the highest Super Tuesday turnout was in 1988 when 35 percent participated. If the population increased by 5 percent from 1988 to 2008, how many more voters voted in 2008 than in 1988?

Once the primary votes are tallied, the states’ delegates are divided up based on the proportion of votes each of the “top” candidates received compared to the other “top” candidates. (“Top” candidates refers to candidates receiving at least 15% of the vote in that state.) In Arizona, Clinton had 51% of the vote and Obama had 42% of the vote.  If Arizona has 56 delegates that are tied to the results of the primary, how many delegates did each candidate receive? Disregard any digits after the decimal, and express your answer as a whole number.

In a race that has people at the edge of their seats, Obama and Clinton will undoubtedly need a steady flow of income to sustain a level of campaign activity necessary to win the democratic nomination.  At the end of the day last Thursday (February 7^th), both candidates reported huge fundraising gains from online sources. In the 2 days following Super Tuesday Obama’s campaign reported bringing in $7.5 million online. Clinton reported taking in $7.5 million online starting February 1st. According to these reports, by what percentage did Obama’s rate of fundraising (millions of dollar per day) exceed Clinton’s rate of fundraising (millions of dollar per day)? Express your answer as a decimal to the nearest tenth.

Solution due on Tuesday February 19th.

Week of February 5th.

Groundhog Day

1) Every year on February 2^nd in Punxsutawney, PA, Groundhog Phil is called upon to predict how much more winter there will be.  If Phil sees his shadow there will be six more weeks of winter, but if he does not see his shadow spring is near. In 2006 Phil saw his shadow. If Phil’s shadow was 25 inches long (when he stands on his back legs) at the same time that a 12 foot tree cast a 15 foot shadow, how tall was Phil, in inches, in 2006?

2) Groundhog Phil’s cousin Henry lives in Moundsville with his family.  At the beginning of 2006, Moundsville had a population of 2500 groundhogs but by the beginning of 2008 the population had grown to 3025 groundhogs. If the annual percentage of growth was the same in 2006 as it was in 2007, how many groundhogs lived in Moundsville at the beginning of 2007?

3) Groundhog Henry is digging a new tunnel in a flat field outside of his home.  He starts by digging 3 ft straight down and then digs north 4 times the distance that he dug down. At this point Henry digs straight west for 17 ft before running into a boulder. Since he doesn’t know how big the boulder is, he backs up 1 ft and digs 3 ft straight up to the surface. How far is the end of Henry’s tunnel from the beginning of Henry’s tunnel? (You may use graph paper if you want)

Solution was due on Monday February 11th.

With the start of 2008 comes a rash of caucuses and primaries to determine who each party will choose to run in the national presidential election.  In light of this, here are a few questions surrounding voting, percentages, etc.

1) On January 3^rd, both the democratic and republican parties in Iowa saw a record number of voters turn out for the caucus.  In 2004, the Democratic Party had 124,000 at the caucus.  This year, the Democratic Party had a turn out of 227,000 voters. By what percent did this year’s democratic voter participation beat 2004 democratic voter participation? Express your answer to the nearest tenth.

2) In Mr. Hoolihan's 8^th grade Social Studies class, students are holding mock-elections to learn about our nation’s voting process. In this class exercise, only Vonda, Emma, Frank, and Bobby are running for the class republican bid for president. During the “primary vote” Vonda received 10% of the votes, Emma received 35% of the votes, Frank received 30% of the votes, and Bobby received the rest of the votes. If Bobby received 10 votes, how many votes did each candidate receive?

3) After the “primary vote,” Vonda dropped out of the race. If Vonda had dropped out before the “primary vote,” what is the minimum percentage of Vonda’s votes that Frank would have had to receive in order to beat Emma in the primary vote?

Happy New Year!

1) Tokyo is 9 hours ahead of London and London is 7 hours ahead of Denver. If Denver is 2 hours behind Washington DC, what time is it in Washington DC at the moment 2008 begins in Tokyo?

2) During Jillian’s New Year’s Eve party she wants to have several candles lit.  Each candle she plans to use burns at a rate of 5 mL of wax per 15 minutes. One of these candles has a diameter of 8 centimeters and a height of 15 cm (Use a formula for the volume of a cylinder) . How long will it take the candle to burn down completely? Express your answer to the nearest whole number. (Note: 1 mL = 1 cm³)

3) Mike and Barbara and going to a New Year’s Eve gala and Barbara needs a new dress.  She found a dress that is perfect and it is on sale for 20% off.  After the discount and a 5% sales tax, the total cost of the dress was $117.60.  What was the original price of the dress?

Solution was due on Monday January 7th.

Late Papers will not be accepted!

On December 10^th, Common Cents unveiled this year’s Penny Harvest collection of 100 million pennies. Collected by children, the money will be distributed to charities at the children’s discretion. 536 non-profits have already received money and/or time from Penny Harvest this year.

1) Prior to 1982 pennies had a mass of 3.1 grams, however during 1982 they changed the constitution of the pennies, which changed the mass of pennies to 2.5 grams each. If the Penny Harvest display of 100 million pennies contained only pennies made during 1958 or after, and there are an equal number of pennies from each of the years 1958 through 2007, inclusive, what is the mass in grams of the 100 million pennies in the display? Assume that each penny from 1982 or after has a mass of 2.5 grams. 

2) In order to perform the enormous feat of getting 100 million pennies into Rockefeller Center, in the middle of New York City, during the holiday season, many volunteers worked many hours. One hundred volunteers spent an entire night unloading 30-lb bags of pennies from crates and placing them next to the display. At daybreak, another group of volunteers took over and began pouring the bags of pennies into the display. Simply pouring the coins from their transport bags into the display took 100 volunteers 3 hours to complete. If each volunteer poured the same number of penny bags into the display, based on the calculation from the previous question, how many bags did each person pour? Express your answer as whole number. (Note: 1 lb = 454.59 grams)

3) The pennies are poured into a display area that is 30 ft-by-165 ft. Given that each penny is 0.061 inches thick and has a diameter of 0.75 inches, if the pennies were first melted down and then poured, how many feet deep would the melted penny mixture be in the display? Express your answer as a decimal to the nearest hundredth.

4) When Common Cents is ready to pick up the coins and distribute the money to charities, they use a special vacuum to suck up the coins. The vacuum sucks up the coins at a rate of $1000.00 per minute. At this rate how many hours does it take to suck up all of the coins. Express your answer as a mixed number.

Solution was due on Friday December 21st.

Extra Credit Week of October 29th.

1) Bridgette 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 Bridgette’s princess costume consisting of one crown, one dress and one pair of shoes?

Joseph and Dante went trick-or-treating and came back with A LOT of candy.  However, when Samantha, Joseph’s little sister, gets back they find that, not only does she have more candy, she has better candy than they do.  Samantha 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

2) Based on Samantha’s rules, what item is the most valuable?

3) Based on Samantha’s exchange rates above, how many of the least valuable item is required to get one of the most valuable item?

Solution was due on Monday November 5th.

Extra Credit Week of October 22nd.

Mole Day

On October 23^rd between 6:02am and 6:02 pm, Mole Day is celebrated by science enthusiasts across the country!  What is “Mole Day,” you ask?  Mole day is a day (well, 12 hours really) in honor of Avogadro’s number, 6.022 × 10²³, which equals 1 mole. (The idea is similar to that of a dozen; there are 12 eggs in a dozen… there are 6.022 × 10²³ particles in a mole.) The mole is a standard international unit of measure used in chemistry to determine the amount of substance in 6.022 × 10²³ particles. The number has been named for Amedeo Avogadro because he discovered that when an element’s mass in grams is the same as its atomic number, there will be exactly 6.022 × 10²³ atoms present!  This relationship is used in MANY chemistry calculations. 

1) When 6.022 × 10²³ in written as an integer (standard notation), what is the total number of zeroes written?

2) How many particles are in 3 moles of a substance? Express your answer in scientific notion with 4 significant digits.

3) How many moles are in 9.033 × 10²³ particles? Express your answer to the nearest tenth.

4) Water molecules (H₂O) are made up of 2 hydrogen atoms and 1oxygen atom. (An atom is the smallest particle of an element that is still the element.) If we have 1 mole of water molecules, how many oxygen atoms do we have? How many hydrogen atoms do we have? Express your answers in scientific notation with 4 significant digits.

Solution was due on Monday October 29th.

Extra Credit Week of October 15th.

1) Alex loves fall!  Every year before raking the yard, he walks around and picks up his favorite leaves.  In his yard there are yellow hickory leaves, red oak leaves, orange maple leaves, and yellow willow leaves.  If Alex will pick up exactly 3 leaves, how many combinations of 3 distinct leaf types could he pick up?

2) Now it is time for Alex to rake his yard.  How many square feet of yard need to be raked based on the diagram of his yard below?

3) Last year Alex used 1 bag per 10 square feet of yard raked.  This year he used 5% more bags.  If he bought 300 bags for this year, how many did he not use at all?

4) Alex decides to make some money raking leaves and charges his neighbors 5 cents per square foot that he rakes.  If Alex wants to make $500 raking leaves, how many square feet must he rake?

Solution was due on Monday October 22nd.

Extra Credit Week of October 8th.

1) On Monday, October 8^th, 2007 we celebrate Columbus Day.  Columbus is credited with opening the doors for European expansion in the America’s when he mistakenly landed on San Salvador while trying to find an alternate route to Asia. Columbus hypothesized that instead of sailing south and then east around the tip of Africa, he could just sail southwest and get to Asia more easily.  When Columbus was planning this voyage he packed provisions based on his calculations of the Earth’s size.  Unfortunately, he did not realize that the map he was using was in an Arabic unit of measure and not in the Italian unit of measure he thought.  As a result, he calculated the Earth’s circumference to be 25,255 km when it is really 40,008 km.  By what percent was his calculation incorrect? Express your answer to the nearest whole number.

2) While much of the nation observes Columbus Day, people across the state of South Dakota celebrate Native American Day. Native American Day is a celebration of the cultures and great leaders of those who were here before the Europeans. One popular site for celebration is an unfinished memorial to Crazy Horse, one of the great Native American leaders. Despite the fact that the Crazy Horse Memorial is not complete it is still a very impressive site for holding the Native American Day festivities. Visitor’s can still see the artist’s complete vision in a smaller model of Crazy Horse that is on display. Given that Crazy Horse’s face on the model is 2.5 feet high but it is 85.5 feet high on the full-sized sculpture, how tall will the actual sculpture be when it is completed if the model is 16.5 feet tall? Express your answer to the nearest whole number.

3) Many people recognize and celebrate Columbus Day but fewer people realize that Oct 9^th is Leif Eriksson Day, which is the celebration of the first European known to set foot on North American soil.  Unfortunately, his expeditions did not lead to a lasting settlement in the new land.  About a year after creating settlements in mainland North America his father, Erik the Red (who discovered Greenland) passed away, and Leif was called back to Greenland to rule the colonies there. 

Imagine you wrote the names Leif Eriksson and Erik the Red on a piece of paper,  then cut up the paper such that each of the 22 letters is on its own piece, and  finally put all 22 pieces of paper into a bag. Assuming that each piece of paper is equally likely to be drawn, what is the probability that the first two pieces of paper drawn from the bag, without replacement, each have a letter that is in “Leif Eriksson” and “Erik the Red”?

Extra Credit Week of October 1st.

The Maize Maze

 1) Bethany and her family are attending the Funville Town Fall Festival, and the first thing they do is get in line for the Maize (corn) Maze.  When Bethany gets to the entrance of the Maze she is facing north.  Following the paths, she walks straight ahead for 10 feet and reaches and intersection at which she turns right and walks 40 feet east, at which point the path dead ends.  Bethany decides to back-track 15 feet and turns south.  She walks 5 feet south and then turns and walks 6 feet east.  If Bethany was to walk straight back to the entrance, cutting through the corn and disregarding the paths, how far would she have to walk?  Express your answer as a decimal to the nearest tenth. (You may want to do work on graph paper.)

2) Later that day Bethany and her brother Ben decide to go through the Maize Maze again.  When Bethany starts she walks 10 feet north, 30 feet west, and then 20 feet north.  During this same time, Ben walks 20 feet north, 25 feet east, and then 15 feet south.  Disregarding paths, what is the shortest distance between Ben and Bethany?  Express your answer to the nearest whole number.

3) When Bethany’s family is leaving the festival they pick up a flyer, and it says that the Maize Maze is on a square plot of land that is 100 yards by 100 yards. The path through the maze is 1.5 yards wide and 3000 yards long.  If one square yard of land holds 18 stalks of corn, how many stalks of corn are in the Maize Maze? Assume that the entire plot of land has corn planted on it except for what is cleared to create the paths.

Solution was due on Monday October 8th.

Extra Credit Week of September 24th.

Playing Cards

1) Margaret and her friends are playing a card game. In a deck of 36 solid colored cards, each card is purple, blue or green. There are twice as many blue cards as purple cards and the number of green cards is equal to half of the combined number of purple and blue cards. How many cards are green?

2) The deck of 36 cards from the previous question is shuffled and turned face down. What is the probability that Margaret draws a blue card?

3) From the 36 card deck mentioned above, 4 blue cards are removed. The remaining cards are shuffled and turned face down. What is the probability that Margaret draws a purple card from the deck?

 Solution was due on Monday October 1st.

Extra Credit Week of September 17th.