## Mathletes Solution Archive

Week 10: Stair MasterEvery day at school, Jo has to go up a staircase with 7 steps. As she is going up the staircase, she can take the steps 1 or 2 at a time. How many different ways are there for Jo to climb the stairs? Due by 8 AM on February 11thShow your work using pictures, numbers or symbols. Download the answer sheet. |
SOLUTIONThere are 21 different ways Jo can go up the staircase. |

Week 9: George and TomGeorge was born 11 years before Tom. In 2015, George’s age was 3 more than 7 times the age that Tom was in 1993. What was the sum of George and Tom’s ages in 1995? Due by 8 AM on January 28thShow your work using pictures, numbers or symbols. Download the answer sheet. |
SOLUTIONThe sum of Tom and George's ages in 1995 was 25. This problem was based on Thomas Jefferson and George Washington. George was born 11 years before Tom. |

Week 8: It’s Off to Work I GoLet’s say today is my day off. If yesterday wasn’t also a day off, then I’m off again tomorrow. If, on the other hand, I was off yesterday, then tomorrow I’ll have to work. Bummer! But, let’s say I worked today. If I didn’t work two days before today, I’ll have to head to work tomorrow. But if I did work two days ago, I’m off tomorrow. Yes! Assuming a 365-day year, and ignoring weekends and holidays, how many days do I have to work in a year? Due by 8 AM on January 14thShow your work using pictures, numbers or symbols. Download the answer sheet. |
SOLUTIONI will work 219 days in one year. |

Week 7: There's an App for That?Michelle has a Number App on her phone. It follows two rules: 1. If an inserted number has exactly one digit, double the number. 2. If an inserted number has exactly two digits, compute the sum of the digits. The first number Michelle inserts is 1. Then every answer she gets is inserted back into the machine until one hundred fifty numbers have been inserted. What is the one hundred fiftieth number to be inserted? Due by 8 AM on December 17thShow your work using pictures, numbers or symbols. Download the answer sheet. |
SOLUTIONThe one hundred fiftieth number to be inserted is 7. |

Week 6: More Cheese Please!Mike and Joey each bought an identical loaf of bread and an identical package of cheese slices. Mike made sandwiches with 5 slices of cheese and 2 slices of bread each. He had 4 slices of bread left when he ran out of cheese. Joey made sandwiches with 4 slices of cheese and 2 slices of bread each. He had 4 slices of cheese left when he ran out of bread. How many slices of bread were in each loaf? Due by 8 AM on December 3rdShow your work using pictures, numbers or symbols. Download the answer sheet. |
SOLUTIONThere were 28 slices in each loaf of bread. |

Week 5: Bath TimeA hot water faucet will fill a tub in a half hour. A cold water faucet will fill the same tub in an hour. Running together, how long will it take to fill the tub? Due by 8 AM on November 13thShow your work using pictures, numbers or symbols. Download the answer sheet. |
SOLUTIONWith both faucets running together, it will take 20 minutes to fill the tub. |

## Week 4: How Many Rectangles Do You See?
The first figure above contains one rectangle (remember that a square is a rectangle!). The second figure above contains three rectangles (each of the two squares and then a rectangle containing both squares).
How many rectangles are in the third figure above? Due by 8 AM on October 30th.Show your work using pictures, numbers or symbols. Download the answer sheet |
SOLUTIONThere are 136 rectangles in the third figure. |

First, Anna gave Bill and Clare as much money as each one of them already had. Then, Bill gave Anna and Clare as much money as each one of them had. Finally, Clare gave Anna and Bill as much money as each one of them had. In the end, each one of them had $24. How much money did each have to begin with?
Due on October 16th.Prefer to work it out by hand? Download the paper copy here.Have fun doing the math! |
SOLUTIONAnna had $39, Bill had $21, and Clare had $12 to begin with. |

If
4 gleeps are worth 3 glops and 2 glops are worth 5 glips, how many glips are
worth the same as 10 gleeps?
Due on October 2nd.Prefer to work it out by hand? Download the paper copy here.Have fun doing the math! |
SOLUTION18.75 glips are worth the same as 10 gleeps. |

Two-thirds
of the people in a room are seated in three-fourths of the chairs. The rest of
the people are standing. If there are six empty chairs, how many people are in
the room?
Due on September 18th.Prefer to work it out by hand? Download the paper copy here.Have fun doing the math! |
SOLUTIONThere are 27 people in the room |

**2014-2015 Archive**

Ms.
Kretschmar has challenged Pierce School students to
read a total of 10,000 books this summer!
Here’s a math challenge for you! Grades K-4: 10,000 is a lot of books! Could 10,000 books fit in the Brookline Library? Could 10,000 books fit in the Pierce School library? Could 10,000 books fit in your classroom? To get a sense of how many books that really is: - I challenge
**grades K-2**to estimate how many books are in your classroom! - I challenge
**grades 3-4**to estimate how many books are in the Pierce School Library!
Think about how you might do this. Will you and your classmates count all the books in your classroom? Will you count the books in half the classroom and then double that? Maybe you can find a better way to get a good estimate. Work together. Make a plan. Carry out your plan. Then, write out everything you did! Put your responses in the bin in the Math Center by June 17th. I’ll post some of the best ones from each grade! Have fun doing the math! Prefer to work it out by hand? Download the paper copy below: Grades 5-8: Imagine all of the students at Pierce School sitting on sofas, on beaches, in bed, and in the sun reading this summer. That’s a lot of reading! Just how much time will Pierce students spend reading this summer? I challenge you to estimate how many minutes (hours? days?) the 838 students of Pierce will need to spend reading altogether to meet our goal of 10,000 books read! Think about how you might solve this problem. How many books will each student need to read for us to meet the goal? Do younger students read fewer books or more books than older students? About how long does it take a 2nd grader to read one book? About how long does it take a 7th grader to read a book? Make a reasonable estimate for any information you think is relevant and use these to find your final estimate. Work together with a partner. Make a plan. Carry out your plan. Then, write out everything you did! Put your responses in the bin in the Math Center by June 17th. I’ll post some of the best ones from each grade! Have fun doing the math! Prefer to work it out by hand? Download the paper copy here. |
SOLUTION |

Mathletes Problem Of The Week #13String Theory Due: June 2, 2015 A 63-inch long string is cut into pieces so that their lengths form a sequence. First, a 1-inch piece is cut from the string, and each successive piece that is cut is twice as long as the previous piece cut. Into how many pieces can the original length of string be cut in this way? Copies of the POW are available in the lobby or on the Pierce website. Solutions are due June 2nd. Have fun doing the math! Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONThe original string can be cut into 6 pieces. |

Mathletes Problem Of The Week #12Copy Caps Due: May 19, 2015 Caps come in four colors (R= red, B = blue, Y= yellow, G = green). Place the six sets of colored caps shown on the right into the 4x4 box so that there is color symmetry across the dotted line. The sets of caps may not be flipped or rotated. From left to right, what are the colors of the caps in the bottom row? Copies of the POW are available in the lobby or on the Pierce website. Solutions are due May 19th. Have fun doing the math! Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONThe bottom row of caps is yellow, red, blue, yellow. |

Mathletes Problem of the Week #11 Welcome to Planet ForuxDue: May 5, 2015 On Planet Forux, there are Fourisies and Fourlegies. Every Fourisie has exactly 4 eyes and exactly 2 legs. Every Fourlegie has exactly 4 legs and exactly 1 eye. A gathering of Forisies and Fourlegies has an equal number of eyes and legs. What is the minimum of number of aliens present? Copies of the POW are available in the lobby or on the Pierce website. Solutions are due May 5th. Have fun doing the math! Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONThe minimum number of aliens needed to have an equal number of eyes and legs is 5. |

Mathletes Problem of the Week #10 Alli Takes a Swim Wanting some exercise, Alli decides to swim from the tree to the boulder and back. The distance between the tree and the boulder is 0.5 miles. When swimming from the tree to the boulder, Alli is swimming with the current. When swimming back from the boulder to the tree, Alli is swimming against the current. The current is moving at a rate of 2 miles per hour. If Alli’s normal swimming speed (in still water) is 3 miles per hour, how many minutes will the entire trip take Alli? Copies of the POW are available in the lobby or on the Pierce website. Solutions are due April 14th. Have fun doing the math! Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONThe entire trip from the tree to the boulder and back will take Alli 36 minutes. |

Mathletes Problem of the Week #9
Not from Around Here Of 600 students at Goodnight Middle School in Texas, 85% are not native Texans. Of those non-native students, 60% have lived in Texas more than 10 years, and 30 students have lived in Texas less than a year. How many of Goodnight Middle School's non-native students have lived in Texas for at least 1 year but not more than 10 years? Prefer to work it out by hand? Download the paper copy here. |
SOLUTION174 of Goodnight Middle School's non-native students have lived in Texas for at least 1 year but not more than 10 years. |

George Washington was 6 ft. 2 in. tall. The height of the Washington Monument is about 555 ft. 5 in. If you were to stack George Washington one on top of the other until the stack first exceeded the Washington Monument, by how many inches would the top-most Washington exceed the height of the monument? Mathletes Problem of the Week #8How Many George Washingtons in the Washington Monument? Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONThe top-most George Washington would exceed the monument by 69 inches. |

Mathletes Problem of the Week #7100 WatermelonsJoann ate a total of 100 watermelons in five days. Each day after the first day she ate six more than she had eaten on the previous day. How many watermelons did she eat on the third day? Show your work using pictures, numbers or symbols.Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONOn the third day, Joann ate 20 watermelons. |

Mathletes Problem of the Week #6:Zakim BridgeAt the exact moment Alejandro began to cross the 1432-ft Zakim Bridge from one end, cycling 28 ft/s, Bindi began to cross, running 12 ft/s from the opposite end. How much farther than Bindi had Alejandro traveled when they met? Show your work using pictures, numbers or symbols.Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONAlejandro will have traveled 572.8 feet farther than Bindi when they meet. |

Mathletes Problem of the Week #5:Happy New YearIt's 2015! What time on which date will it be 2015 days and 2015 seconds after the New Year begins? Show your work using pictures, numbers or symbols.Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONThe time will be 33 minutes and 35 seconds after midnight on July 8th, 2020. |

Mathletes Problem of the Week #4:Counting AbesAbe has a bag containing 340 coins and 160 bills, totaling $1,809. There are pennies, nickels, fives, tens, and twenties. The total value of the tens is equal to the total value of the twenties. There are the same number of fives and twenties. What is the total value of the coins and bills bearing Lincoln's portrait? Show your work using pictures, numbers or symbols.Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONThe value of coins and bills with Abe's portrait is $202.00. |

Mathletes Problem of the Week #3:Yummy Number CrunchThe ratio of yellow, red, and purple snacks in the bag is 10:3:1. If there are 549 red snacks, how many are not red? Show your work using pictures, numbers or symbols.Prefer to work it out by hand? Download the paper copy here. |
SOLUTION2,013 snacks are not red. |

Mathletes Problem of the Week #2: Storming the CastlePrella runs down the castle staircase taking 2 steps at a time. Bodo runs up the castle staircase taking 3 steps at a time. The castle has 1200 stairs. If Prella starts from the top and Bodo starts from the bottom, how many stairs were stepped on by both Prella and Bodo, not including their stop/start positions? Show your work using pictures, numbers or symbols.Prefer to work it out by hand? Download the paper copy here. |
SOLUTION199 steps were stepped on by both Prella and Bodo. |

Mathletes Problem of the Week #1:See the image below. Prefer to work it out by hand? Download the paper copy here. |
SOLUTIONThe equilateral triangle can be completely covered using 9 triangles. |