10-Minute Math

As an enrichment activity I had a student fill a large sheet of graph paper with Pascal’s triangle – just the ones digits, anyway.  Then he colored the digits in different ways to discover patterns.  After doing this by hand, the student was interested in saving some time with Excel, so I devised this method:

1. Make a grid of 0’s.  Really you just need a border of 0’s, but filling an area is faster.  It should be twice as wide as tall.
2. Select cell B2, and give it the formula =MOD(A1+c1,10).
   
3. Copy B2 and paste it into all the cells in the grid except for the top row and the left and right columns.
4. Now they are all adding the values of the two cells diagonally above them.  Just put a “1″ in the middle of the top row and see what happens.
   
5. To color the different digits, click Format, Conditional Formatting, and make some stuff up.
   
6. I changed the font color to white and clicked File > Web Page Preview:
   

You could do some fun experiments with this, leading kids toward the idea of cellular automata!

A couple sweet math books for a broad audience (and, coincidentally, the last two additions to my collection) include:

Logicomix, a graphic novel about Bertrand Russell’s quest for certainty in the foundations of math, and the madness that mysteriously infuses the study of logic.

The Math Book, a survey of important ideas in mathematics throughout history, distilled into 1-page summaries with full-color graphics.

An extra credit assignment for my calculus class:

A pack of zombie dogs (ZDs) is reproducing quickly and killing humans. Scientists and calculus students have determined that the the total number of human deaths due to ZDs t days after the start of 2010 is given by

1. At the end of January 1st (t = 1), how many deaths have occurred?

2. At the end of January, how many deaths will have occurred?

3. Determine the number of deaths/day after t days: h′(t).
Hint: you may want to go “outside-in” with the chain rule.

4. Graph both h(t) and h’(t) on the same axes:

5. On what day will 90% of the human population (6.8 billion) be annihilated by ZDs?

6. When does the death rate reach half a billion per day?

7. When does the death rate hit its peak?

I collected a set of various nonlinear graphs and hid the labels and scales.  They’re good for discussions (I’m teaching exponential growth now).  Here’s the Word file.

Can you match them all? Height of a projectile, iTunes sales, World Population of gorillas, Transfer speed versus message size on several networks, Heights of a group of men, Population of fruit flies in a container, Decay of radioactive atoms, Heights of babies over time.

I created a review game with this online tool today:

If you want to play it, here it is.

My students asked how you could have positive acceleration but negative velocity. The spacebus holds the answer: click on the bus, then use Page Up and Page Down keys.