# The Emperor and the Chess Board

To complete this activity, you’ll need some rice and a checkerboard. You can download the checkerboard… I can’t fit the rice through the slot in my computer, though.

There is a famous story about the meeting between a Chinese emperor and the inventor of the game of chess. There is a less famous story about the meeting between the emperor and the inventor of the game of checkers.

However, the emperor was so overjoyed by both games that he offered each inventor anything he wanted in the kingdom. Both inventors said they wanted some grains of rice.

The inventor of chess said, “I would like one grain of rice on the first square of the board, two grains on the second, four on the third, eight on the fourth, and so on. I would like all of the grains of rice that are placed on the board in this way.”

The inventor of checkers, however, was greedy and said, “ I would like one million grains of rice for every square on the board. I would like all of the grains of rice that are placed on the checker board in this way.”

The Chinese emperor laughed in the face of the inventor of checkers and said he wouldn’t be able to afford such an amount of rice. Instead, the emperor said he would give the checkers inventor the same amount he gave to the chess inventor.

1. What do you think of each inventor’s proposition and the emperor’s response?
2. What do you notice about the amount on a square of the chessboard and the amount on the previous square?
3. What do you notice about the amount on a square of the chessboard and the amount on all the previous squares put together?
4. What do you notice about the amount on a square of the checkerboard and the amount on the previous square?
5. How many grains of rice will be on the entire checkerboard? The entire chessboard?

The Legend of Chess and Checkers

Printable Checkerboard

# A Mile of Pi

If your class did not get a chance to see this video, please take a few minutes to watch it. Remember that irrational numbers (like Pi) really do go on forever. They don’t end after a million digits or even a billion digits.

# The formula for calculating monthly payments

Some of you have expressed interest in the formula for monthly payments. Here it is.

$\begin{array}{l}\text{Monthly Payment}=\frac{rP}{1-{{(1+r)}^{-n}}}\\r=\text{periodic rate=}\frac{\text{annual rate}}{\text{number of periods per year}}\\n=\text{number of periods to pay back loan}\end{array}$

You can find the total cost of repaying a loan by multiplying both sides by n, the number of payments to be made.

$n\cdot Paymen{{t}_{monthly}}=\frac{rPn}{1-{{(1+r)}^{-n}}}$

I hope this will help you all remember that you can’t just plug in the interest rate and some numbers to your calculator to get an answer when finding the cost of repaying loans!

# Finding Volume

The project this six weeks involves finding the volume of a 3-D object both by modeling it as a composite figure made up of prisms, pyramids, cylinders, and hemispheres, as well as by using the displacement method.

Students should choose their object carefully as there will be a competition for the coolest object resulting in some bonus points.

Finding Volume Project Guide

# The female mathematician who changed the course of Physics…

… but couldn’t get a job.

This may delve a little too far into physics, but it may interest you to see the names we’ve discussed in class today appear in modern news and commentary.

# Finding net worth

In class yesterday and today, students spent some time exploring the net worth of companies as we prepare to explore personal net worth.

Take some time to discuss stocks at home and look through the net worth of some companies that you own stock in or are interested in.

In class, we used the Google Finance site, but you may want to use the information provided by your brokerage since it may provide better explanations of the terms used in the reports.

If you need help finding a report, remember to search for a public company, click Financials, and then Balance Sheet. You should wind up with something like this: Statement for Apple (Click on Balance Sheet). Continue reading Finding net worth

# Estimating family budgets

In class today, we talked about estimating family budgets. I apologize for the late update, but here is the link to the site we used to estimate costs in class. You may have found a better site, and any site you use will be fine.

Family Budget Estimator

# The Science of Luck

Are you lucky? Good luck? Bad luck?

Before we move too far away from our discussions of probability and statistics, consider this. Is there such a thing as luck, or is luck just something you think happens because of how you perceive the world around you? Does your brain control your luck by preventing you from seeing things around you or making some things more apparent?

So what do you think? Is luck real, or can everything be explained away by science?

# Data in Real Life: The Middle Class

NPR’s Planet Money featured this story that posed the question “What is the middle class in your city?”

Since we’ve recently talked about box and whisker plots as well as biases, take a look at the data presented in the article. How is it similar to a box and whisker plot? How is it different?

Do you think there may be biases in the way the data was collected? Does the article indicate any of these biases? Can you depend on article authors to identify biases in the data they reference? Can you trust that the data presented is factual?