# Teaching

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spcs:winter2014:math

# Exploratory Math

Description: The SPCS Honors Academy in Exploratory Math introduces students to foundational concepts of problem solving, engineering, computer programming, and design. Topics covered include: permutations and combinations, probabilities, geometry, graph theory, circuits, Boolean algebra, and logic. Every day begins with morning challenges and problem solving exercises, followed by a lecture. Before lunch, students will work in groups to apply the theory and practice learned from the morning. The afternoon will be focused on design and creative activities. The first week, the students will learn how to program in Processing, and create their own online programming portfolio and research blog in Wordpress. In week two, the students will have hands on practice to using the Arduino microcontrollers. On the last day, the students will work together to design and build their own city as the final project. At the end of every class, students will compile a research journal with the day’s discoveries in addition to giving daily feedback to shape the pace and preference for course practices. The course concludes with group research projects for a poster presentation on selected course topics in Exploratory Math.

Teacher: Sherol Chen

TA: Pia

Location: Santiago, Chile

## Schedule

 Category Topic Project Application Numbers Game Theory Games Economics Numbers Probabilities Graphs & Dice Big Data Spatial Shapes Tangrams Computer Graphics Spatial 3-Dimensions 3D Garland 3-D Printing Spatial Graph Theory Models Social Networks Circuits Resistors Arduino LED Electronics Circuits Arduino Arduino Robotics Logic Logic Gates Logic Gates Computer Engineering Logic Formal Logic Arduino Storytelling Final Project City Design City Project Civil Engineering

## Topics

Numbers Spatial Circuits Logic
permutations circle/sphere/cylinder resistors number systems
combinations rectangles/squares/prism volts boolean algebra
probabilities triangles/special triangles current demorgans law
bayes cones/pyramids circuit diagrams logic gates
nash equilibrium Distance equation chips universal/existential quantifiers
socially optimal graph terminology karnaugh maps first order logic
prisoner's dilemma different types of graphs analog/digital propositional
rock paper scissors Traveling sales person multimeter induction
percentages Trees sensors abduction
compound probabilities Prefix notation microprocessors deduction

## Materials

Week 1MondayTuesdayWednesdayThursday Friday
9 Test Wordpress Writing Writing Writing
9:30 Processing Processing Design
10 Introduction Processing Processing Proj
10:30 Notebook Lisp/Trees
11 BREAK BREAK BREAK BREAK BREAK
12 Permutations Notebook Econ Review Problem Set Postfix Notation
12:45 LUNCH LUNCH LUNCH LUNCH LUNCH
1:30 Game Theory Review Pixel Activity 3-D Garland Spaghetti Graphs
2 Games Raindrops Geometrical Scale
2:30 Games Tangrams
3 Writing Time Writing Time Writing Time Writing Time Writing Time
Week 2MondayTuesdayWednesdayThursday Friday
9 Writing Graphs Writing Writing Writing Time
9:30 Electricity Traveling Sales Digital/Analog Research Proj City Building
10 Circuits Boolean Algebra Arduino Arduino
10:30 Resistors
11 BREAK BREAK BREAK BREAK BREAK
11:30 Current Demorgan's Law Arduino Deduct/Induct City Building
12 Double Imply First Order Vander Skype
12:45 LUNCH LUNCH LUNCH LUNCH LUNCH
1:30 Demo Logic Gates Review City Proposal City Building
2 MultiMeter Arduino Karnaugh Maps
2:30 Arduino City Planning Posters
3 Writing Time Writing Time Writing Time Writing Time

## NyanVille Design Group

City Name: NyanVille

Mayor: Josefina - \$9,999,999

Group 1 - \$3,000,000

• Andreina
• Francisca
• Isabella
• Chen
• Sebastian
• Josefina

Group 2 - \$4,000,000

• Laura
• Tomas
• Tomas
• Lorenzo
• Isabel
• Josefina

Group 3 - \$3,000,000

• Francisco
• Felipe
• Marina
• Camile
• Margarita
• Josefina

Group 4 - \$3,515,000

• Eitan
• Vittorio
• Nicolas
• Daniel
• Matias
• Josefina

1. Vittorio
2. Francisco
3. Marina
4. Eitan +1

## Research Group

Prisoner's Dilemma

• Isabel
• Camila

Combinations and Permutations

• Matias
• Tomas Ald

Boolean Algebra

• Eitan
• Nicolas

Circuits

• Francisco
• Tomas Alt

Arduino

• Josefina
• Andreina

Traveling Sales Person

• Lorenzo
• Margarita

Processing

• Sebatian
• Daniel
• Vittorio

Game Theory

• Felipe
• Chen

Probabilities

• Marina
• Laura

Game Trees and Graph Coloring

• Isabella
• Francisca

# Homework Challenges

These questions are meant to be challenges. They are meant to be hard. Try your best, but don't stress out over it. I will post the answers at the end of the program.

Q1. I want I fruit salad. I can choose from: apples, orange, bananas, mangos, kiwis, and watermelon. How many different fruit salads can I make?

Q2. I have 5 poker cards: 2 red and 3 black. What is the probability that I will pick a black card second. I do not put the first card back. The first card can be either red or black.

Q3. There are twelve coins, eleven of which are identical and one of which is different, but it is not known whether it is heavier or lighter than the others. The balance may be used three times to isolate the unique coin and determine its weight relative to the others.

Q4. My rulers come in 3 colors: R,G, and B. Every time you pick, you have a 1/3 chance of getting any color no matter what. What is the probability that I will get one red ruler or one green ruler in 2 picks?

Q5. What does (+ (* 4 5) (+ (- 9 2) 3 (+ 2 5 6)) (/ (* 10 2) 5)) equal?

Q6. Finite State Machine: Some friends downloaded a game from the Internet in which a robot flipped a coin and they had to guess whether it would turn up heads or tails. At first the game looked very easy. At least they would have a 50/50 chance of winning—or so they thought! After a while though they started to get suspicious. There seemed to be a pattern in the coin tosses. Was the game rigged? Surely not! They decided to investigate. Joe wrote down the results of their next attempts at the game and this is what they found: (h = heads, t = tails)

```hhthhthhhtthhhhtthttthhhhhthhhttthhhttthhhhhhtthtt
ttthtthttthhhtthhhthhhhhhhhhtthhhtttthhhhhttttttt```

Can you find a predictable pattern?

There is a very simple ‘map’ that will describe the sequence of coin tosses. See if you can figure it out. (Hint: it has just 4 ‘islands’). Below is an example Finite State Machine:

Q7. Can you make a hexaflexagon?

Letter to Parents

Dear Parent,

The Exploratory Math class has been going very well this first week. The students are getting along well, and the materials have been both challenging and fun for them. I have been collecting daily feedback and have been adjusting my teaching to their comments and feelings about the day.

The students are all very different, so some will like computer programming, and one or two won't like it. Some like the lessons of probabilities and some prefer the creative activities. The students understand that they may not be interested in everything, but have been trying to give everything a chance.

Please take a look at their journal and encourage them to continue to focus and stay engaged in class. It is a very fun and creative group of people. Everyone is very nice to each other and becoming good friends. Your encouragement is important too.

If you would like to see the course materials and schedule, please go to: http://chile.sherolchen.com

There are some challenge questions that are meant to be very hard. I want the students to use the internet and try simple examples to understand how to use mathematics to solve these problems. I've been teaching them to simplify the problems first.

Below (above) is the list of student online research journals/websites.

Handouts