Fall is a beautiful time of year for hiking. Many students will be walking in the woods and mountains to enjoy the colorful leaves and the cool weather outside. Let them combine what they are doing with their families and friends with a little mathematics about percent grade change. Why are there warnings about a 6% road grade change ahead? Why does everyone talk about the vertical gain on a trail that is only 3 miles long? Enjoy using slope and the Pythagorean Theorem in a new way.

# Pascal’s Triangle coloring and Probability

Working with Pascal's Triangle offers some interesting and varied mathematics. We love to color and the end results are prettier than most math homeworks. Here is the second of 3 activities using Pascal's coloring.

**Pascal's Triangle and Probability** - This activity could be used to explore the probability of coin tossing results. When the combinations get too complicated to list, students can use the numbers in Pascal's Triangle.

# Fall equinox

Thursday, September 22^{nd} of this year will be the Autumnal Equinox. It is the time of year when the imaginary plane that might pass through the Earth's Equator would also travel through the center of the Sun. At this auspicious moment the number of sunlight hours and night time hours are about the same all over the Earth. In the Northern Hemisphere we move into the Fall season.

We love the seasons and Ecliptic animation from the Magic of Physics site. Below is a screen shot of the applet. By clicking on the link, a new window will open and students, or the teacher using a projector, can change the position of the person on the globe and other variables to enjoy a discussion of this auspicious moment.

# Another year of Never Ending Pasta

On September 15, 2016, Olive Garden again offered a $100 pass for never-ending pasta, bread sticks, salad and coca cola soft drinks. The 21,000 patrons who quickly (in less than a minute) bought all of the passes will be entitled to as much pasta as they like (with toppings) from October 3 to November 20. Ask the class to consider these questions:

# Extra Point or 2-Point Conversion?

In 2015 the NFL changed the extra point kick distance to 33 yards and now teams have a tough decision to make, go for one or two points? The one point extra point is no longer a given with a success rate of about 94%. Teams can go for two by trying to get the ball in the end zone from the two yard line. Teams have been successful at two-point conversions in the past about 50% of the time. So we ask students, which does it make more sense to do? Given the data, should teams go for one or two points? Which do you expect will pay off with more points over the long run? See this interesting article on the Steelers and their 2-point conversion strategy.

# iPhone 7 opening weekend

Yep, Apple just announced a new iPhone ... the iPhone 7. It will be in their stores on September 16, 2016. What will their record sales be like this time? How many iPhones will they sell?

In this activity kids explore past iPhone launch sales data and predict how many iPhone 7's will be sold during the opening weekend in 2016.