We are excited to offer two challenge problems to students.  Level 1 is geared for students in grades K-2 and Level 2 is geared for students in grades 3-6.  However, students should work on the problem that is appropriately challenging for them.  We encourage all students to participate.  

There is a new RMC display in the 2nd floor hallway across from 3L where you can find the problems.  There is also a box where students can submit their answers.  

You can expect to see new problems twice a month.  Give it a try!

10-24-11 candles on the cake

10-24-11 not so magic squares

 
Poems from 2v

Poems from 2K

Last week’s solution

45. From the definition, the first and second digits of an upright integer automatically determine the third digit, which is the sum of the first two digits. Consider those upright integers beginning with 1: 101, 112, 123, 134, 145, 156, 167, 178, and 189; there is a total of 9 such numbers. (Note that the second digit may not be 9; otherwise, the last digit would be 1+9=10.) Beginning with 2, the upright integers are 202, 213, 224, 235, 246, 257, 268, and 279; there is a total of 8 such numbers. We may continue this pattern of analysis to show that the numbers of upright integers beginning with a digit of 3, 4, 5, 6, 7, 8, or 9 are 7, 6, 5, 4, 3, 2, and 1, respectively.

Therefore, there is a total of 9+8+7+6+5+4+3+2+1=45 three-digit upright integers.

From Eric Lass, 7th & 8th grade Math Teacher

Last week’s question and solution

Problem: Daniel is having dinner with a friend. He buys five dishes and his friend buys three dishes. At the last minute another friend comes to eat with them and pays $4 for his share of the meal. If all the dishes have the same value, how should the money be divided between Daniel and his first friend?

Solution: Since the second friend paid $4, the total cost of the meal must be $4 x 3 = $12. Eight dishes were eaten, so each one costs $1.50. Daniel brought 5 x $1.50 = $7.50 worth of food, and since his share was $4, he should receive $3.50. The first friend brought 3 x $1.50 = $4.50 worth of food and should receive 50 cents.

From Eric Lass, 7th & 8th grade Math Teacher

Last week’s question and solution

Problem

The average house price in Boomtown rose 30 percent each year for the last five years. If the average house price is currently $250,000, what was the average house price five years ago?

Solution

Approximately $67,332. If P was the average house price five years ago, then the current average price is 1.35P or 3.71293P. Thus, 250,000 = 3.71293P, so P=250,000/3.71293, which equals $67,332.27

From Eric Lass, 7th & 8th grade Math Teacher

Last week’s problem and solution

999 Coins

Starting with a single pile of 999 coins, a person does the following in a series of steps: In step one, he splits the pile into two nonempty piles. Thereafter, at each step, he chooses a pile with 3 or more coins and splits this pile into two piles. What is the largest number of steps that is possible?

Solution

997. The number of steps is one less than the number of piles, and 998 is the largest number of piles, 997 with 1 coin and 1 with two coins.

From Eric Lass, 7th & 8th grade Math Teacher

Last week’s problem and solution

A Quarter Pounder

A quarter-pound hamburger contains approximately 80 calories per ounce of meat, an average french fry contains about 14 calories, a cola contains about 10 calories per ounce, and a bun contains 200 calories. Suppose you have a quarter-pound hamburger with a bun and six ounces of cola. How many french fries can you eat and still keep your meal below 800 calories?

Solution
15. We have 80h + 14f + 10c + 200 < 800. Using the information in the problem we can write 80(4) + 14f + 10(6) + 200 < 800. This implies that 14f < 220 and f < 16. Therefore, you can eat 15 french fries.

From Eric Lass, 7th & 8th grade Math Teacher

Great work, Everyone!

This week, 2V will be holding an open house as well on March 10, 2011 from 8:00 – 8:30 a.m.

How many french fries can you eat and still keep your meal below 800 calories?

Last week’s problem:

Perfect Squares and Cubes…NOT

How many numbers from 1 to 1 million, inclusive, are not perfect squares or perfect cubes?

Solution:

998,910. There are 1000 perfect squares between 1 and 1 million; these are the squares of the first 1000 integers. Similarly, there are 100 perfect cubesóthe cubes of the numbers from 1 to 100. Subtract the squares and the cubes from 1 million to get 998,900. However, every number that is a perfect sixth power has been subtracted twice (the largest of these is 106 = 1,000,000). Adding these back in gives 998,910.

Solution

The man wants to earn $500 in interest each year. Investing $4000 at 5 percent yields yearly interest of 0.05 x $4000, or $200; whereas $3500 invested at 4 percent yields 0.04 x $3500, or $140; so the remaining $2500 needs to be invested at a rate that yields interest of $160 per year (to have a total interest of $500 each year). If r is the annual percentage rate for the $2500, then

So the man needs to invest the remaining $2500 at 6.4 percent or higher to guarantee an interest income of at least $500 a year.

— Mr. Lass

There they all were. From Genghis Khan to rapper Kanye West, with Albert Einstein, author Pearl Buck, Charles Darwin, Amelia Earhart, Queen Elizabeth I, Coco Chanel and Steve Martin in between. Segway inventor Dean Kamen also made an appearance.

After eight weeks of preparation, 54 sixth graders stood on risers in front of more than 100 family members, teachers and administrators, ready to give a short introduction of their characters, in the style and voice of the person they had become during the project. For most, this was their first public speech. They were well prepared for this moment, the annual capstone event for sixth graders at the John D. Runkle School.

I am a parent of one of these students, and by an accident of availability and interest, had the gift of helping the teachers in the classroom during the project. It gave me a bird’s eye view of the commitment and dedication of the three sixth-grade teachers: language arts teacher Geri Belle, who developed this project and who is able to draw out the best of this varied group of 11- and 12-year-olds; Maxine Hunter (science and social studies), who holds everyone to high standards and is innovative in her teaching; and Saeed Ola (math and social studies), the terrific, newest member of the team, who uses humor while piling on the homework. Together — with thoughtfulness, intelligence, hard work, creativity, and big doses of humor and sternness — they push kids to stay focused and learn.

Read more …

Portrait of a girl

Here are some of the student artworks that appeared in the March 24, 2009, art show from the extended day program.

Thanks to a generous grant from the Runkle PTO and the gracious hospitality of our librarian, Ms. Gallo-Toth

This past Friday morning, March 20th, all three first grade classes experienced the awesome beauty of the night sky from within the Runkle Library thanks to a visit from Boston’s Museum of Science Portable Star Lab.  Mike A., an instructor from the MOS Portable Star Lab, served as guide and instructor to the first grade classes who attended three separate sessions.

Inside the domed space of the darkened Star Lab, the first graders had a chance to see what the night sky looks like at various stages of the evening.  Mike, the MOS instructor, pointed out various constellations and planets visible to the naked eye in the South (Orion) the West (Venus) the North (the Big Dipper which is part of The Great Bear constellation) and the East (Saturn).  He also pointed out many constellations we had never seen or heard about – Cassiopeia, her daughter Andromeda, Perseus and the Gorgon Medusa, as well as Hercules.  Not only did we have a lesson in the stars, we had an excellent lesson in Greek mythology!

The portable Star Lab visit was the perfect ending to our study of objects in the night sky – we really learned a lot and the Star Lab was incredibly cool!

All three first grades say :

“Thanks so much to the PTO and Ms. Gallo-Toth for making this wonderful experience possible!”

Ms. Dixon, Ms. Guzzi and Ms. Halwick
First Grade Teachers

Students in Ms. Kelly’s kindergarten class learned about animals and their habitats.  They created written reports and models of their subjects.  Parents were invited to see the results.

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