## Iles IMSA

1700 South 15th Street
Springfield, IL 62703
217/525-3226

## Illinois Mathematics and Science Academy (IMSA) Problem of the Month Winners!

January 3, 2010

Problem of the Month Winners!

I am happy to announce the results for the IMSA Problem of the Month.
Congratulation Iles IMSA students!
Hrishi was selected for the December Problem of the Month random drawing.

October
There were 52 submissions for the October IMSA Problem of the Month and only six students had the correct answer. Three of the six correct answers were submitted by Iles students. Congratulations to the October winners:
Lillian Y. (4th grade), Hrishikesh and Geoffrey (5th grade).

The problem: How Much Does the Pumpkin Cost?

Mita and Brook went on a pumpkin search. They wanted to find the best pumpkin around. Mita and Brook found the perfect gourd to make their Jack-O’-Lantern. The pumpkin was \$10 plus one-half of its price.

Below are notes from Dr. Fraccaro:
Answer: \$20. The major concern is not to be tricked into thinking that
the pumpkin cost \$10. Guess and check will work or algebra. If x = the
price of the book, then .

Common mistakes: Some students just added 5 and 10 together to get 15.
That is incorrect because the problem stated that the pumpkin was \$10
plus ½ of its price. If the pumpkin were \$15 it wouldn’t satisfy the
clue (\$7.50 plus \$10 would does not equal \$15. Did you know that the
Leonid meteor shower peaks on November 17th? 500 meteors per hour could be produced depending upon location and clear skies. Keep looking up. You never know what you might see!

November
There were 38 submissions for the November IMSA Problem of the Month and only 4 students with correct answers. Congratulations to our one winner: Zoe (4th grade)

The Problem: Catching Mice at the Turkey Farm

Sarah and Andrew went on field trip to a turkey farm. The farm had a big problem with mice. The mice ate a lot of the food that was meant for the turkeys. Cats were used to help catch the mice. 10 cats could catch 10 mice in 10 minutes. Using this as a guideline, how many cats would be needed to catch 100 mice in 100 minutes?

Below are notes from Dr. Fraccaro:

*Answer:* Only 10 cats would be needed. 10 cats catch 10 mice in 10
minutes. 10 cats would catch 20 mice in 20 minutes. 10 cats would catch
30 mice in 30 minutes … 10 cats would catch 100 mice in 100 minutes.
Guess and check would work, but more importantly, reasoning logically
would steer the student away from the answer of 100 cats.

*Common mistakes:* Many students chose 100 cats, but given the rate of
capture by 10 cats, more than 10 would not be necessary.

"Did you know that it takes 60% less energy to produce a ton
of paper from recycled paper than from trees?"

-Dr. Fraccaro

December
WOW! 26 Iles students submitted the correct answer.

52 students submitted answers to December’s problem! (17-4th graders and 15-5th graders)! There was 0 Honorable Mentions. There were 32 students who submitted the correct answer along with a valid explanation. There were 20 incorrect submissions.

Students with correct responses and explanations:

Benjamin Y. Iles Elementary (Springfield) Grade 4
Erin B. Iles Elementary (Springfield) Grade 5
Lillian A. Iles Elementary (Springfield) Grade 4
Zoe R. Iles Elementary (Springfield) Grade 4
Eliott N. Iles Elementary (Springfield) Grade 4
Madison S. Iles Elementary (Springfield) Grade 5
Sameena K. Iles Elementary (Springfield) Grade 5
Reaney G. Iles Elementary (Springfield) Grade 4
Haley R. Iles Elementary (Springfield) Grade 4
Evan R. Iles Elementary (Springfield) Grade 4
Larry W. Iles Elementary (Springfield) Grade 4
Jade I. Iles Elementary (Springfield) Grade 4
Lillian Y. Iles Elementary (Springfield) Grade 4
Thomas V. Iles Elementary (Springfield) Grade 4
Edmund F. Iles Elementary (Springfield) Grade 4
Ke'Aira M. Iles Elementary (Springfield) Grade 4
Steven S. Iles Elementary (Springfield) Grade 5
Sage T. Iles Elementary (Springfield) Grade 4
Cole D. Iles Elementary (Springfield) Grade 4
Rishi K. Iles Elementary (Springfield) Grade 5
Joseph A. Iles Elementary (Springfield) Grade 5
Milan P. Iles Elementary (Springfield) Grade 5
Dylan C. Iles Elementary (Springfield) Grade 5
Alex R. Iles Elementary (Springfield) Grade 5
Auden H. Iles Elementary (Springfield) Grade 5
Krishi K. Iles Elementary (Springfield) Grade 5
Michelle D. Komarek School (North Riverside) Grade 5
Abraham Y. Fearn Elementary (North Aurora) Grade 4
Allyson B. Fearn Elementary (North Aurora) Grade 5
Kelsey H. Fearn Elementary (North Aurora) Grade 5
Natalie C. Fearn Elementary (North Aurora) Grade 5
Joey D. Fearn Elementary (North Aurora) Grade 4

The Problem: Let’s Go Shopping for Gifts!
Attiya and Elvin wanted to buy some presents for their parents. They found the perfect gifts. The store even promised not to charge them any sales tax on the gifts. The two presents together cost \$110. One gift was \$100 more than the other gift. How much did each present cost separately?

Answer: \$105 and \$5. Guess and check will work or algebra. If x = one gift, the other gift would be 100 + x. , , , , therefore the other gift is 100 more = 105. 105 + 5 = 110.

Common mistakes:

Most errors were made by determining that the two gifts were \$100 and \$10, totaling \$110. However, this would only make one gift \$95 more than the other gift. Other errors that students made were mistakes in calculation or by using an incorrect formula to solve the problem.

Thanks to everyone who submitted an answer and good luck on January’s Problem of the Month. By the way, did you know that on January 3rd and 4th - there will be the Quadrantids Meteor Shower? This is an above average shower, with up to 40 meteors per hour at the peak. The shower should be best on January 3 & 4, but some meteors can also be seen from January 1st – 5th. The best viewing will be from a dark location after midnight. Look at the constellation Bootes for the best viewing of this meteor shower. Keep looking up; you never know what you might see!

-Dr. Fraccaro