## Problem of the Week (POTW)

1) Handshake Problem:  If there are 20 students in the classroom and each students shakes hands with every other student in the classroom, how many total handshakes will there be?

2) How many squares (any size) can be found on a checkerboard?

3) Find the LCM of 1, 2, 3, 4, 5, 6, 7, 8, and 9
Hint: Try a simpler problem. Find the LCM of 2, 3, and 4 using listing and ladder. What do you notice?

4) Four Fours:
Create numerical expressions for the number 1 through 20 using only four 4s.
For example:     4 + 4 / 4 + 4 = 9
Acceptable symbols and operators:  addition, subtraction, multiplication, division, square root, exponents, factorial and decimal point (0.4)

5) Alphametics Puzzle #5 from Math Puzzles and Brainteaser Grades 6-8 by Terry Stickels pg

6) What is the units digit (the number in the ones place) of the number 2^2015
Hint:
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32

7) Express this complex fraction in lowest terms:
Hint: Start at the bottom
From Math Puzzles and Brainteaser Grades 6-8 by Terry Stickels pg. 54

8) Find the sum of the whole numbers from 1 to 500 (without adding up each number individually).

9)

From Math Puzzles and Brainteaser Grades 6-8 by Terry Stickels pg. 11

10)  What's the secret code?
1. Use the clues to find the code number:
• It is between 8,500 and 8,800.
• When multiplied by 8, the result is a whole number.
• The digit in the hundreds place is ¾ the digit in the thousands place.
• The sum of all digits in the number is 26.
• The digit in the hundredths place is 200% of the digit in the tenths place.
• There are no zeros in the decimal places.
2. What code numbers fit these clues?
3. Explain how you used all of these clues to find these possibilities.
4. Write one more clue so that there is only one possible code number.
Task found on youcubed.org
From Math for All: Differentiating Instruction, Grades 6-8 by Linda Dacey & Karen Gartland (Sausalito, CA: Math Solutions), pp. 257.

11)

12) Dad's Cookies
Dad bakes some cookies. He eats one hot out of the oven and leaves the rest on the counter to cool. He goes outside to read. Dave comes into the kitchen and finds the cookies. Since he is hungry, he eats half a dozen of them. Then Kate wanders by, feeling rather hungry as well. She eats half as many as Dave did. Jim and Eileen walk through next, and each of them eats one third of the remaining cookies. Hollis comes into the kitchen and eats half of the cookies that are left on the counter. Last of all, Mom eats just one cookie. Dad comes back inside, ready to pig out. “Hey!” he exclaims. “There is only one cookie left!” How many cookies did Dad bake in all?

From The Math Forum@Drexel Problem of the Week Sample Math Fundamentals (3-5)

13) Ostrich Llama Count:  Raul and Esteban just started working at their uncle's farm on the weekends. Their first task was to count the ostriches and llamas. When they reported to their uncle, Raul said, "I counted 47 heads." Esteban added, " I counted 122 legs." "How many are ostriches? How many are llamas?" asked their uncle. "It's getting dark and I promised your mother I'd get you home for dinner. There's no time to count again. You'll have to figure out how many ostriches and how many llamas there are from the information when you get home. Can you give me a call after dinner and let me know your answer?" How did Raul and Esteban figure out how many ostriches and how many llamas there were?

14) A Zombie Add-pocalypse:  Zombies have arrived! Official are strongly advising people to remain in their homes and away from anyone who may b infected. Infected people turn into zombies and mus infect on other person each day to stay alive. An antidote is currently undergoing clinical trials, but will not b ready for use for 30 days. It all started with one zombie which arrived on day, then infected on other person on the second day. On the third day, each of those zombies infected one other person, and so on.
a) The Centre for Zombie Control (CZC) needs to know how many people are going to be affected. How many zombies should they expect to be roaming around at the end of each day for the next two weeks?
b) How many zombies will there be by the time the antidote is ready?
c) If the antidotes is ineffective, on what day will the population of zombies exceed that of the people on earth?

From University of Waterloo Center for Education in Mathematics and Computing:  Problem of the Week

15)

From The Best of Continental Math League Grades 7-9

16) At a Prime Age:  A family has three children. Each of their ages is a different prime number. The sum of their ages is 41 and the difference between two of their ages is 16. Determine the ages of the the three children.

From University of Waterloo Center for Education in Mathematics and Computing:  Problem of the Week