palette of
problems
David Rock and Joel Amidon
–2, 6, –18, 54, –162, 486, _____, _____, _____
2. Pierre tossed two standard, fair, six-sided dice. How
many of the 36 different possible outcomes will result in a
sum that is divisible by either 2 or 3?
3. From birth, a normal person blinks an average of 25
times a minute when awake. When Katelyn was 10 years
old, she blinked an average of 27 times per minute. When
she was 11, she blinked 26 times per minute. When she
was 12, she blinked 25 times per minute. At 10 years old,
Katelyn averaged 9 hours, 45 minutes of sleep each day; at
age 11, she slept 9 hours, 30 minutes; and at age 12, she
slept 9 hours, 15 minutes. What is the sum of the number
of times Katelyn blinked when she was 10, 11, and 12
years old? (Calculate using 365 days in a year.)
4. Andi bought 9 ice-cream cones costing 11 dollars and
x cents for her friends. If she had bought 13 cones at the
same price, the cost would have been 15 dollars and
y cents. Find x and y, the cents parts of the costs for
9 and 13 cones.
5. A farmer in Mississippi grows several different crops:
1/2 his acreage is planted in peanuts; he planted 1/4 of
the remaining ground in sweet potatoes; after that, he
planted okra in 1/2 of what remained. The rest of the
garden is planted in green beans. What percentage of his
acreage is in green beans?
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6. Two lumberjacks can cut a log into
5 pieces in 30 minutes. At the
same average cutting rate, how
long will it take the 2 lumberjacks to
cut a similar log into 12 pieces?
7. Students in Mr. Lee’s class developed a code to give
numerical values to names of animals. Hint: Consider the
letters in each word.
CAT = 60
BEAR = 180
DOG = 420
EAGLE = 2100
Can you determine the value of a BEAVER?
8. The average (mean) of 17 numbers is 37.4. If the
smallest of these 17 numbers is removed, the average
(mean) of the remaining numbers is 41. What is the value
of the number that was removed from the original
17 numbers?
9. The Wildlife Rehabilitation Center received a $2000 gift
from a private donor to care for injured animals. Another
donor pledged $5 for every animal that the center accepts
and $8 for every animal that is released into the wild. It
costs the center $650 for the government permit to care
for wild animals, and $40 a day to care for all the animals.
If workers take in and release 1 animal each day, how long
will these monetary gifts support their work?
Vol. 18, No. 9, May 2013
Copyright © 2013 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.
This material may not be copied or distributed electronically or in any other format without written permission from NCTM.
MIPAN/ISTOCKPHOTO
1. Find the next three numbers in the sequence:
Prepared by David Rock, [email protected], and Joel Amidon, [email protected], University of Mississippi, Oxford. Teachers,
student groups, or mathematics clubs are encouraged to submit single problems or groups of problems to the editor, Joel Amidon, at
[email protected]. Published problems will be credited.
10. Deterrian looks in the refrigerator for a snack. He
finds a bag of baby carrots (4 calories per carrot) and a
bag of Nickers Candy Bar Bites (170 calories per Bite).
If every carrot is 0.035 pound, how many pounds of
carrots would have the same number of calories as
1 Nickers Candy Bar Bite?
11. At her apple stand, Stevie had to discard 1/4 of her
apples because of rot. Of those remaining, someone bought
10 percent and another person bought 2.5 dozen. A delivery of fresh apples then quadrupled her remaining supply. She ended the morning with 744 apples. How many
apples did she start with?
12. The Internet search company, Big Number, is looking forward to celebrating the day when a googol Internet
queries will have been executed through its search engine.
Currently, 2 × 1012 searches are done each year. At this
pace, in how many years will Big Number need to reserve
a room for its Googolth Internet Query party?
13. To open the new AlphaLock, a user must enter a
sequence of 4 letters in the correct order. Letters may
repeat. Paige has forgotten her sequence. She calculated
how many combinations she would have to check to be
sure of getting the right one. She suddenly remembered
that exactly 1 letter in the sequence is P. How many fewer
combinations does she need to check than originally
calculated, now that she remembered the P?
14. The dimensions of a
first generation tablet computer
are 243 mm × 190 mm × 13 mm.
The latest generation of the tablet measures
200 mm × 134.7 mm × 7.2 mm. What percentage of the
volume of the first generation tablet is the volume of the
latest generation?
15. Alice gave 1 widget and received 3; Brandi gave
3 widgets and received 13; and Carl forgot how many
widgets he gave, but he received 28. David’s conjecture
was that the pattern was linear, which was verified when
he gave 4 widgets. How many widgets did David receive,
and how many widgets did Carl give?
16. The quotient of the product and sum of 3 consecutive
prime numbers is equal to the largest of the 3 consecutive
prime numbers. What are the 3 numbers?
(Answers on page 583)
(Ed. note. Online solutions are available to NCTM members only.)
Download one of the free apps for your
smartphone. Then scan this tag to access the
Palette of Problems solutions that are online at
http://www.nctm.org/mtms045.
Vol. 18, No. 9, May 2013
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Mathematics Teaching in the Middle School
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