IBM MentorPlace Online Activity: Algebraic Reasoning Scientist
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           In this project students and mentors will meet Hubert the Great
            and participate in a number of algebraic reasoning adventures!
 
Activity 1: The Mad Scientist
          As I overcame my recent chaotic experiment on the entire school, I was
         instantly regarded as the "mad scientist." It was said as an endearing
        nickname. "Hey look! It's the mad scientist," students would say. However,
       this time, students would stay and talk with me. They had so many questions
    for me. I was an elementary school celebrity.
Space Space

                  The bell rang, as I pulled out my "Playground Etiquette" book. "Our lesson today
        children is about the swing sets and why one must always swing appropriately. There
are eight rules to govern your proper behavior on a swing set. I will check to make sure you
wrote all of the rules. Pencils up!," Priscilla Prudence our homeroom teacher spoke with
her thick British accent.

Suddenly, the announcements began. "Today is Monday. Today's lunch is split pea mash
casserole. Oh and hot off the press! The principal has cleared his schedule. He is waiting
to meet with the perpetrator of last week's terrible shenanigans. Report now Hubert!!!"
Suddenly, an abrupt silence, as the whole school waited to hear my black shoes creak
down the hallway. I walked out of class a fallen hero.

As I walked every step moved me closer to my future in a high security prison for bad
elementary school kids. The secretary stood with her arm extended and pointed with a
long nail to the big chief's office. The leather back chair was turned so I could not see him.

"Shut the door," a deep voice whispered from the other side of the chair.

As I shut the door, a painful sinking feeling happened as I sat on the wooden chair.

"Hubert," a deep voice chimed as the chair turned around slowly, "we need your help.
You see, last week showed your incredible mathematical ability."

Professor Bottoms sat across in the leather-backed chair.

"Where's the principal?"

"Well, you see, that's part of the problem. I could be in grave trouble Hubert. I devised a device
to speed up the food machine in the cafeteria. By developing a Super Deluxe Masher 2000,
I thought I was saving the cafeteria workers time. Instead, it has caused total mayhem and chaos."

"What do you mean Professor?"

"The principal was coming to see my incredible feat when he stepped closer to examine the
machine, and he was sucked up. Since then, the machine has been acting up."

"Just turn off the machine and give him a ladder."

"I haven't come to the worst part Hubert. This is no ordinary potato masher. The principal is being
held hostage. The Super Deluxe Masher 2000 has developed artificial intelligence."

"You don't mean that the machine is alive, do you?"

"I unplugged it and everything. The Super Deluxe Masher 2000 still hummed
and a message appeared on the main operating controls reading:

 

     

YOU WILL NOT SILENCE ME. I WILL MASH AND
MASH POTATOES AND CARROTS AND PEAS.
VEGGIE SOUFFLE FOR EVERYONE EVERYDAY
NO MORE PIZZA, UNLESS YOU CAN BRAKE
THE CODE. UNTIL THEN, LONG LIVE THE VEGGIES!

Sincerely yours, Super Deluxe Masher

 

   

"At least he has a cause sir, although a weird one."

"The cafeteria workers said the machine hummed loudly whenever they mentioned that pizza
was being served tomorrow. It's almost as if the machine became jealous. We better act quickly.
The code works in a weird way. When you put in one potato, you have to see how many the
machine releases. Then, you put in two potatoes and try to figure out the machine's pattern.
If you can figure out eight of the puzzles, the machine shuts down. We better get going."

ASSIGNMENT: Breaking the Super Deluxe Masher 2000's Riddle

Fill in the missing values and describe the rule for each of the problems below.


1.
Input Output
1 3
2 4
3 5
4 6
5 ?
8 ?

 

2.
Input Output
0 0
1 1
2 4
3 9
4 ?
? 100

 

3.
Input Output
0 ?
2 6
3 8
4 10
5 ?
? 20

 

4.
Input Output
2 3
3 5
4 7
5 ?
? 19

 

5.
Input Output
0 0
1 0
2 0
3 0
4 0
5 ?
10 ?

 

6.
Input Output
1 5
2 6
3 7
4 ?
? 25

 

7.
Input Output
0 0
1 1
2 2
3 3
4 4
5 5
? 10

 

8.
Input Output
1 1
2 8
3 27
4 ?
? 125

 

   

What rules can you develop about the number 0 based on what happened to the potatoes
in problems 5 and 7?

Now, create your own messed up Super Deluxe Masher and see if your mentor can figure
out the pattern.

Finally, after a lot of hard work, we were able to figure out the machine's puzzles. Because
I saved the school from a lifetime of veggie soufflés and freed the principal, I was allowed
to pick my favorite meal for the rest of the year. Of course, I ordered pizza. Again, I was
honored by all of the students for this newest accomplishment. Besides, no one had to
eat split pea mashed soufflé.

     
  Activity 2: The Code Breaker
   

As I woke up one morning, the snow was falling outside my window. As the trees crystallized,
the branches looked as if they were carrying crystal ornaments. However, this weather was
very confusing. It was the middle of July. It didn't make any sense. So, the television stations
and radio stations kept talking about the Earth slipping on its axis, causing catastrophic
changes to the seasons. However, I knew something else was up.

So, I set out to the school's laboratory to check with Professor Bottoms. He lived in the dome
at the top of the elementary school. I walked up the spiral staircase into the circular brick
building. As I reached the top of the staircase, I rang the huge bell outside his door. A deafening
bell sound seemed to make the building shake. Professor Bottoms opened up his door,
and he looked very worried.

"Hello Hubert. Come in!"

"Professor Bottoms, what is going on? I am really concerned."

"Well Hubert, I have very bad news."

"What do you mean?"

"He finally succeeded. I can't believe he was able to do it."

"Who? What do you mean professor?"

"Well, a man named Demetrius who I went to college with has been working on a weather machine for many years. He has been trying to be able to make it winter year-round, because he loves cold weather. Something about hating sunburn."

"What can we do? I have swim practice tomorrow. The pool will be frozen. Help me professor."

"I would, but I hate the cold. I won't go in this. However, you can go to his house and turn off the machine."

"How?"

"You have to solve the puzzle."

"Not this again. More mathematical puzzles to solve. When will this end?"

"And you thought you would never use your math skills to save the world. You should have
listened to your first grade teacher."

Hubert left quickly to go to Professor Demetrius's house, where he saw the professor
playing in the snow.

"I love snow. I love snow."

"Hey! I'm Hubert, and I know what you have been doing."

"I don't have any idea what you mean young man."

"Yes you do Professor Demetrius. Stop playing with your snowman and listen."

"Young man, even if I had something to do with this weird weather, there's nothing you can do."

"Oh yeah! Watch me. I'm mathematically powerful. Move aside," I spoke with pride.

I walked inside the old house and followed the beeping sound to the roof. There was a
crystal orb floating in a purple sphere rotating. The purple light went directly to the sky, and
the snow continued to fall. Below, there was an old laptop computer with a message blinking:

BREAK THE FREEZING RAY CODE IF YOU CAN
OR SNOW WILL FALL ALL OVER THE LAND.

Then, a bunch of weird mathematical equations appeared below, and I knew then that I had
to undo the equations to get back to summer.

Help me to break the code of this puzzle and to set the season back to summer.

In each of the equations below, find the value of the variable.

E + 3 = 5
A - 12 = 0
O - 4 = 10
10S = 100
N + 3 = 12
10 + W = 30
T/4 = 1
21/I = 3
5H = 25
6U = 36
Y/2 = 3

___   ___   ___   ___   ___   ___
  4        5       2       10      6        9

___   ___   ___   ___   ___   ___
 10       5       7        9       2      10

___   ___   ___   ___
 12     20     12     60

___   ___   ___  
  4        5       2

___   ___   ___   ___
 10       9      14     20

Send the answer to the coded message to your mentor. If you had to write a strategy for solving
these equations, what would it be?

The Weather Machine instantly shut down, and the purple orb of light disappeared. Along
with it, the clouds opened up, and the sun shined down. Professor Demetrius ran inside quickly
whimpering to himself saying, "I want to play with my snowman!" I saved the day again, with
your help. I immediately ran to Professor Bottom's house to share the good news. When I arrived,
he was on a skateboard with Bermuda shorts singing "Happy Days Are Here Again." He gave me
a pat on the back and bought me a pizza. It was a great summer day.