Monday, January 29, 2018

National Puzzle Day (Jan. 29, 2018)

NAME: TEACHER:

Problem of the Week (Jan. 29, 2018)
National Puzzle Day

Directions: Include your FULL name, and your teacher.

SHOW ALL YOUR WORK
January 29th is National Puzzle Day. This includes jigsaw puzzles, crossword puzzles, KenKens, and every other kind of puzzle you can imagine. In honor of my personal favorite day of the year, the POTW includes different kinds of math puzzles. Be warned, this is an extra thick issue of POTW.

Level 1: Secret Code: Use the hints to figure out the message.
Hint 1: The only letters used are A, E, U, D, N, R, S, and T.
Hint 2: The vowels are all even numbers. The consonants are odd numbers.

Hint 3: A + A = E   and   E + E = U

Hint 4: U - 3 = D

Hint 5: N + A = R

Hint 6: E + D = S

Hint 7: R + E = T

_____  _____  _____  _____          _____  _____  _____  _____  _____  _____  _____
  9           7          2          3                  9          7          8           5         4           1          7







Level 2: A ken for  KenKens: To solve fill in the blank squares so that each row and each column contain all of the digits 1 thru 3. The heavy lines surround areas (called cages) that contain groups of numbers that can be combined (in any order) to produce the result shown in the clue, either using addition (+) or subtraction (-) as shown in the clue. For example, 12+ means you can add the values together to produce 12. Numbers in cages may repeat, as long as they are not in the same row or column.
















Level 3: For the Birds (Mindware): Five birds named Beaky, Bob, Billy, Bosco, and Brainy decided to go to their local Pizza Nest for a pizza. They all wanted a different topping so they ordered their own individual pizzas. The birds were either a seagull, an owl, a pigeon, a robin, or a crow. The toppings they ordered were either worms, fishheads, slugs, bugs, or seeds. To drink, they ordered either water, root beer, iced tea, milk, or juice. Based on the clues, match the names with the type of bird, topping, and drink.

  1. The seagull, whose name is not Billy, didn’t order his favorite fishhead pizza this time.
  2. The milk drinker didn’t order worm pizza.
  3. The juice drinker is a crow and the robin eats slugs.
  4. Bob didn’t order water or iced tea.
  5. The owl, who isn’t Bosco or Brainy, ordered fishhead pizza and iced tea.
  6. Billy, who is not an owl or robin, didn’t drink juice or iced tea.
  7. Bob didn’t drink milk or juice.
  8. Billy and Bosco don’t drink water or eat seeds.
  9. The water drinker doesn’t eat bugs or seeds.


   BEAKY            BOB              BILLY            BOSCO            BRAINY
============================================================
  Seagulls         Seagulls        Seagulls           Seagulls         Seagulls
     Owl                 Owl                 Owl                  Owl                 Owl
   Pigeon     Pigeon           Pigeon              Pigeon            Pigeon
    Robin      Robin             Robin                Robin              Robin
     Crow              Crow              Crow                 Crow               Crow
--------------------------------------------------------------------------------------------------
    Worms      Worms           Worms             Worms            Worms
Fishheads        Fishheads      Fishheads        Fishheads      Fishheads
     Slugs      Slugs              Slugs               Slugs               Slugs
     Bugs               Bugs              Bugs                Bugs               Bugs
    Seeds            Seeds             Seeds              Seeds             Seeds
-------------------------------------------------------------------------------------------------
   Water              Water             Water               Water              Water
Rootbeer         Rootbeer       Rootbeer          Rootbeer        Rootbeer
Iced tea            Iced tea         Iced tea            Iced tea           Iced tea
   Milk                  Milk                Milk                  Milk                  Milk
  Juice               Juice               Juice                Juice                Juice
-------------------------------------------------------------------------------------------------


Monday, January 22, 2018

Captured in Time (Jan. 22, 2018)

NAME: TEACHER:

Problem of the Week (Jan. 22, 2018)
Captured in Time

Directions: Write your work on a separate sheet of paper. Label the paper with your FULL name, your teacher, and which problem(s) you are handing in, then staple it to this sheet.

SHOW ALL YOUR WORK
Time capsules are a fun way for people to store away meaningful items from their lifetime so people far into the future can find them and study them. Museum experts found a time capsule under the corner of the Massachusetts State House. The time capsule was buried there in 1795.

Level 1: Old, old money: Inside the time capsule were 24 coins with different shapes than you are used to seeing, including hexagon shaped coins. If 5 of the coins were hexagon shaped, how many were not hexagon shaped? Bonus: Draw a hexagon.


Level 2: How long ago?: The capsule was buried in 1795. Now it is the year 2018. How many years ago was the time capsule buried? Bonus: If you buried a time capsule this year and dug it up in 37 years, what year would that be?


Level 3: Bar models are your friend: Pretend you make a time capsule at some point in your life and then open it 25 years later. Your age when you open it is 6 times the age you were when you made the capsule. How old are you when you open it?

(Hint: Bar models will make this problem very easy. If you want a bigger hint as to what kind of bar model will help, contact Ms. Simonson.)



Thank you to Bedtime Math for the inspiration.




Sunday, January 7, 2018

Rubik's Cube (Jan. 9, 2018)

Problem of the Week (Jan. 9, 2018)
Rubik’s cube

Directions: Write your work on a separate sheet of paper. Label the paper with your FULL name, your teacher, and which problem(s) you are handing in, then staple it to this sheet.

SHOW ALL YOUR WORK
The Rubik’s cube was invented when I was a kid and has been a popular toy ever since, even though it was not originally designed to be a toy. The world’s record for a human to solve a Rubik’s cube is 5 seconds. Incredibly, there are 43,000,000,000,000,000,000 (43 quintillion) ways to arrange the squares. And now there are robots who can solve the cube just as fast.

Level 1: Speedy robot: If the robot takes 5 seconds to solve the puzzle and it starts at the 13 second mark in the video, what time does it finish solving?


Level 2: How fast can you go?: If the robot takes 5 seconds to solve the cube, how many seconds does it take you if you go 9 times slower? Bonus: What if you are 13 times slower?   


Level 3: Color me silly: If only 7 of the 9 cubes facing you are red, how many different combinations can there be for the final 2 cubes? (note: the colors on a Rubik’s cube include red, white, green, blue, yellow, and orange).  

To watch a video of a robot solving the Rubik’s cube, visit:

http://www.tubechop.com/watch/7520762 (Lego fans, notice the robot is built from Lego NXT robot parts).

Tuesday, January 2, 2018

Penguin Weather (Jan. 3, 2018)

Problem of the Week (Jan. 3, 2018)
Penguin Weather

Directions: Write your work on a separate sheet of paper. Label the paper with your FULL name, your teacher, and which problem(s) you are handing in, then staple it to this sheet.

SHOW ALL YOUR WORK
Wow, it has been cold enough to make a penguin feel right at home in Minnesota. Emperor penguins live in Antarctica where the temperature is usually below freezing even in the summer, and can get as cold as -60 degrees Celsius during the winter months. (Fun fact: It is summer in Antarctica now.)

Level 1: Chick escape: Penguin eggs have very thick shells and it can take 3 days for a chick to break out. If the chick starts cracking the shell on Tuesday, what day will it exit the egg?  Bonus: If the chick comes out of the shell on Sunday, what day did it start breaking the shell?

Level 2: Now That’s a Big Bird: Emperor penguins are about 4 feet tall. How many inches tall is 4 feet?  Bonus: How much taller or shorter are you than an Emperor penguin? Write your height in inches here: __________________. Who is taller, you or the penguin? How much taller? Show your work.

Level 3: Such a tiny baby: Human mothers weigh 15 to 20 times as much as their human babies at birth. But Emperor penguins weigh 50 times as much as their little chicks. If a baby penguin weighs 11 ounces and the mother weighs 50 times that, how much does the mother weigh in ounces. Bonus:  How much does the mother weigh in pounds? (Hint: There are 16 ounces in 1 pound).  

For more fun facts about Emperor penguins, visit:


Monday, November 27, 2017

Down, Down, Down Nov. 27, 2017

Problem of the Week (Nov. 27, 2017)
Down, Down, Down


Directions: Write your work on a separate sheet of paper. Label the paper with your FULL name, your teacher, and which problem(s) you are handing in, then staple it to this sheet.

SHOW ALL YOUR WORK
Have you ever heard the phrase “dig to China”? Have you ever wondered where you would actually end up if you were to dig a hole all the way through the center of the Earth and come out on the other side? Well, this website https://www.freemaptools.com/tunnel-to-other-side-of-the-earth.htm will let you figure that out. Unfortunately, if you dig from Breck you will end up in the middle of the Indian Ocean. Note that it would get a bit too hot to dig all the way through since the center of the Earth is 10,000 degrees Fahrenheit.

Level 1: My Arms Are So Tired: If you dig down for 6 miles, then you dig down another 2 miles, how many more miles do you have to dig to reach 12 miles total depth.

Level 2: Dig Battle: If you dig 6 miles every day for 6 days, and your friend digs 5 miles every day for a week, who digs farther? How much farther?

Level 3: Journey to the Center of the Earth: If the distance through the Earth is 7,916 miles, what is the distance to the center of the Earth?

SUPER BONUS: On day 1, you dig 10 miles. On Day 2, you dig 10 miles again. Then on Day 3 you dig 20 miles. You dig 30 miles on Day 4, and 50 miles on Day 5. If you dig another 80 miles on Day 6, then how many miles will you dig on Day 7?

Sunday, November 12, 2017

Lost and Found Nov. 13, 2017

Problem of the Week (Nov. 13, 2017)
Lost and Found
Directions: Write your work on a separate sheet of paper. Label the paper with your FULL name, your teacher, and which problem(s) you are handing in, then staple it to this sheet.

SHOW ALL YOUR WORK
Reminder: Check the Lower School lost and found before the Thanksgiving holiday. To help you remember, all the problems this week relate to lost things that were later found.

Level 1: Lost Lego: If one of your Lego bricks gets vacuumed up in June, and then pops out of the vacuum 3 months later, what month did it reappear?

Level 2: Long Lost Watch: A man named Ed lost his wristwatch 53 years ago when he was in the Navy. Someone returned it to him in 2012. What year did he lose it?

Level 3: A Long Way Down: Students at Stanford University sent up a weather balloon with a GoPro camera attached so they could take pictures of the Grand Canyon from miles above the ground. When the camera fell back to Earth, the students couldn’t find it. Two years later, some hikers in the Grand Canyon found it! If the camera went 5 miles up, and then came 5 miles down, how many feet did the camera travel? (Hint: One mile = 5,280 feet)

SUPER BONUS: If you lost your sneakers 10 months ago and found them 4 months later, and you lost your favorite shirt 2 years ago and found it halfway between losing and finding your sneakers, how long were you missing the shirt?  A drawing or bar model might be helpful.


Thank you to Bedtime Math for the problem idea.