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?
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?
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.
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.
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