INTEGRATED ALGEBRA AND GEOMETRY

With Applications to Sports, Arts/Crafts, Genetics, Physics, African Dance, Gardening, Architecture, Interior Design, Business, & Engineering.

COURSE LABS

Balogun Arinwaka (aka Gary C. Booker), Instructor

Contact Phone: 678-754-0498

Contact email: [email protected]

These are the labs that you will be doing for this course. The objective of these labs are:

1. To assist you with obtaining a hands-on, real world understanding of the concepts learned in your integrated Algebra & Geometry class.

2. To bring an understanding of why Algebra and Geometry are necessary for solving life problems.

3. To make the learning of Algebra and Geometry more entertaining.

For every lab you do, you are expected to make a powerpoint presentation with the exception of lab four.

LAB ONE: HOW LONG WOULD IT TAKE ME TO SAVE UP FOR MY FAVORITE ITEM?

SUMMARY: Everyone sees things they would like to have. Sometimes we are able to buy things that we have immediately. Other times, we must save up to get something.

MATERIALS:

• Lab Notebook

• Materials/Advertisements featuring the cost of an item you want

PROCEDURE:

1. Using the internet, find four things that you would like to purchase within the next three months. Use your favorite shopping store.

2. What is your salary/allowance? Write it down as a rate-of-change. For example, if your allowance is 50 dollars a week, write it as 50 $/wk.

3. Write an equation for your income in the form of i = At where “i” is your income, and “t” is time. Let “A” be your allowance, which is a constant. Substitute your allowance for “A.” For example, if your allowance is 30 $/day, write your equation as i = (30 $/day)t

4. Write another equation c – i = 0 to represent the relationship between the cost of your item, represented by “c”, and your income after you have saved enough to buy it.

5. For every item you picked, substitute it's cost for “c.” Solve for “i.” For example, if I am trying to purchase Marimba Ani's Book Yurugu, which is on sale for $40, I would substitute $40 – i = 0. This would make “i” equal zero.

6. Substitute your values for i into the equation from #3. For example, I would substitute the $40 from the example above for “i” to get $40 = (50$/wk)t.

7. Solve for t by dividing both sides of the equation by your allowance. It would take me 0.8 weeks to pay for Marimba Ani's book. Since I get paid by the week and not by any smaller incruments, I would round to the nearest whole number to get 1 week.

LAB TWO: AFRICAN NUMBERS & NUMBER THEORY

SUMMARY: Learning about African numbers will help you understand both African history and culture as well as number theory.

MATERIALS:

• Lab Notebook

PROCEDURE:

1. Define the word “Number

2. Research The following numbers:

   1. Egyptian Numbers

   2. Amharic Numbers

   3. Dogon Numbers

   4. Twi Numbers

   5. Yoruba Numbers

   6. Igbo Numbers

   7. Zulu Numbers

   8. Bambara Numbers

   9. Wolof Numbers

Write the numbers above from one to 20, if possible.

3. Go on Cornell University's site for African Writing Systems and look at writing systems (http://www.library.cornell.edu/africana/Writing_Systems/Welcome.html). Compare African writing systems to African number systems. What are your thoughts or Observations?

4. To the best of your ability, solve the following problems using Egyptian numbers

   1. 5 + 10

   2. 18 + 23

   3. 49 + 23

   4. 10 + 10

   5. 10 + 100

   6. 1000 + 1000

   7. 123 + 1092

   8. 2x + 4 = 8, solve for x

   9. 6x + 12 = 18, solve for x

LAB THREE: UNDERSTANDING METROLOGY

SUMMARY: These are a series of exercises to get you to understand units of measurement.

MATERIALS:

• Lab Notebook

• Arbitrary craft materials to be determined at your own wish

• Box

PROCEDURE:

1. Define the words “Measure” and “Metrology.”

2. Research and list at least four African Units of measurement. (A good resource for this is Africa Counts: Number and Pattern In African Culture by Claudia Zaslavsky. Use your local library to acquire the book)

3. Research The Metric System (aka, the SI System)

4. Research the US./British Measurement System

5. Using a word from an African Language and amounts familiar to you, create your own unit of measurement. Use an African language to name it.

6. Research T-squares, and how to use them. Create a T-Square using one of our units of measurement.

7. Make a grid of your room using your unit of measurement.

8. Make a three dimensional small model measuring grid using a big cardboard box. Cut out two of the sides, while leaving the bottom and other two sides still intact. Make Three Rulers using your unit of measurement, and place them so that they can form an x, y and z axis.

Lab Four: Using Malcolm X's Study method for learning Algebra

SUMMARY: Malcolm X, (a.k.a., El-Hajj Malik El-Shabazz, Omowale) was one of the most respected Black Leaders of the 1960's. In watching Malcolm X's debates on TV with degreed experts on a variety of subjects, it is very easy to forget that Malcolm X only had a formal education of 8^th grade. Malcolm was mainly self-educated while an inmate in prison. One of Malcolm's methods was to copy words from a dictionary to help commit them to memory. Malcolm supplemented this method by reading periodicals.

MATERIALS:

• Lab Notebook

• Algebra Glossary

• Geometry Glossary

PROCEDURE:

1. Using the Glossary in your Algebra book, or an Algebra glossary acquired online, copy the words from the source into your lab notebook. You should get a Geometry Glossary as well.

2. Think of at least 10 instances where you can apply some of the words you looked up to your everyday life.

3. Subscribe to a mathematics or science e-zine.

LAB FIVE: ALGEBRA VIDEO GAMES

SUMMARY: The student will practice newfound skills while enjoying themselves.

MATERIALS:

• Software (See procedure)

PROCEDURE:

1. Download Math Arcade (http://www.download.com/Math-Arcade/3000-2053_4-10257757.html?tag=lst-0-4) and play it.

2. Download Algebra One on One (http://www.download.com/Algebra-One-on-One/3000-2053_4-2214794.html?tag=lst-0-1) and Play it.

3. What games did you do the best on?

4. What levels of each game did you do the best on?

LAB SIX: THREE DIMENSIONAL MEASUREMENT AND ARTS/CRAFTS

SUMMARY: You will gain hands-on experience with three dimensional objects.

MATERIALS:

• Lab Notebook

• Arbitrary arts, crafts supplies. (Lego Blocks might be useful in this activity)

• 3D measurement box created in lab three.

PROCEDURE:

1. Using the 3d measuring apparatus constructed in lab three, create and measure at least three the following 3D shapes using any hobby items, such as clay, Popsicle sticks. Balloons, etc.:

1. Planes

2. Sphere

3. Ellipsoid

4. Paraboloid

5. Hyperbolic Paraboloid

6. Elliptic Paraboloid

7. Hyperboloid

8. Cylinder

9. Elliptic Cylinder

10. Parabolic Cylinder

11. Cone

12. Elliptic Cone

13. Triangular Prism

14. Tetrahedron

15. Pyramid

16. Cubes, rectangles and trapezoidal prisms

17. Pentagonal prisms

2. Take a picture of the shapes

3. Try to use your 3D measurement apparatus in your homework problems.

LAB SEVEN: AFRICAN MATH GAMES

SUMMARY: The worlds oldest and most sophisticated math games come from the African continent. African Math games teach principles of sets, counting and combinatorics, which are lessons that you learn in Real Analysis. Examples of African math games include Mancala, Awale, Omweso, and Owari. There are countless other versions, with virtually every ethnic group in Africa having its own version to play.

MATERIALS:

• Awale Software

• Mancala Board (either purchased or created)

PROCEDURE:

1. Download Awale (http://www.myriad-online.com/win/awasetup.exe)

2. Play the game. Try playing with different versions from throughout Africa by selecting them under “rules.”

3. Either buy a Mancala Board, or make one yourself using an egg carton or small paper cups. Teach others how to play the game and play with them.

LAB EIGHT: JUST WHAT DOES THE WEATHER FORECASTER KNOW ABOUT TEMPERATURE ANYWAY?

Summary:

MATERIALS:

• Lab Notebook

• Weather forecasts from the National Weather Service

• Weather forecasts from 3 different private-sector weather websites

  • http://www.wx.xom

  • http://www.weather.com

  • http://www.accuweather.com

PROCEDURE:

1. Pick a day and get a weather forecast for five days. Record the expected day temperatures in your lab notebook. Make a note of any expected precipitation and the expected cloud formation.

2. For the next five days, record the actual day and evening temperatures in your notebook. Try to make your recordings around the same time. If any precipitation occurred (or didn't occur), record it. Also record the cloud formation.

3. At the end of the five day period, calculate and record the Accuracy of the original five day forecast by using the following formula:

Percent Accuracy = [(Forecast)/(actual amount)] x 100

4. Find The Average Accuracy by taking the average of all of your recorded accuracies.

5. Find The Variance and Standard Deviation of the forecast accuracies.

6. Make a line graph to represent your actual temperatures. Make another line graph to represent your accuracy percentages.

7. Based on your findings, answer the following questions:

   1. On what days was the original forecast the most accurate?

   2. On what days was the original forecast the least accurate?

   3. Which website provided the most accurate information?

LAB NINE: THE STOCK MARKET.

Summary: You will, both mathematically and socioeconomically, understand exactly why the stock market is so unpredictable.

Materials:

• Lab Notebook.

• The New York Times Business Section

• The Atlanta Journal and Constitution Business Section

Procedure:

1. Before you do anything, familiarize yourself with what the Stock Market is. Here are some resources you can use:

• http://en.wikipedia.org/wiki/Stock_market

• http://library.thinkquest.org/3088/stockmarket/introduction.html

2. Look up business news by checking out the New York Times Business section (http://www.nytimes.com/pages/business/index.html), and the Atlanta Journal and Constitution's Business section (http://www.ajc.com/business/content/business/index.html). Document the following:

   1. What companies are the subject of good news? What is the news? Why, when, where and how is this news happening?

   2. What companies are the subject of bad news? What is the news? Why, when, where, and how is this news happening?

3. Research The company that is in the news. Answer the following questions:

• What does the company offer?

• Who are the company's competitors?

• What type of consumers buy the company's products?

• How long has the company been around?

• Is the company publicly traded? (meaning, can people invest in stock from this company?) What is the company's stock symbol? (If this isn't listed on their web page, you may be able to find it on the New York Times stock symbol lookup tool, which is featured on their business section web page.) If so, which market is this company on?

4. Look up how these companies performed over the last ten days. By using the New York Times' stock symbol lookup. Save and print the chart.

5. Look up the stock symbols of the companies competitors and look at their stocks.

6. Continue to monitor the performance of the stock over the next two days. Look at some of the stocks of the companies competitors for 5 days.

7. What were the results? Did the company's news appear to effect the stock performance?

8. How would you generalize the effect of publicity on stock performance?

LAB TEN: CHAOS EGGS

Summary: When studying chaos theory, it is very easy to think about highly complicated things such as weather patterns. In the process, we loose sight of the simple things in our life that function on a basis of unpredictability. This activity will

MATERIALS:

• Stove top

• Two pots of water

• Three eggs

• Lab notebook

PROCEDURE:

1. Before doing anything, research what convection is. Here are some resources:

• http://theory.uwinnipeg.ca/mod_tech/node76.html

• http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html#c3

2. Draw five circles in your notebook.

3. Bring one pot of water to a boil.

4. Place an egg in the boiling water. For five minutes, draw a dot in one of the circles to record the position of the egg inside of the pot every minute on the minute.

5. Could you notice a pattern? If so, write it down.

6. Remove the egg. Do not turn the boiling water off. Draw two rows of five circles in your lab notebook.

7. Bring a second pot of water to a boil. Try to simultaneoulsy put the egs in the water. As before, use the circles to record the positions of the eggs every minute on the minute.