# Leap Years

Happy February 29th! Make the most of a day that only comes every four years…or does it?

I learned that Leap Years happen every four years but that is not accurate. They do not happen on years that are multiples of 100 like 1900 or 2100. Unless the year is also a multiple of 400. A bit more complicated than you thought, right?

How to tell if a year is Leap Year:

1. Leap years are any year that can be evenly divided by 4.

2. Unless they can be evenly divided by 100. Then they are not leap years.

3. Unless they can be evenly divided by 400. Then they are leap years.

Here are a few examples to help clarify. The year 1900 was not a leap year because it is divisible by 4 but also by 100. The year 2000 was a leap year because it is divisible by 400. And of course, the year 2016 is a leap year because it is divisible by 4 (and not by 100).

This is because the earth rotates around the sun about every 365.242375 days. So if we add an extra day every four years that makes up for that .242375. Except that about every 100 years we will end up being a whole day ahead. So we skip the leap year on those years.

Here is a graph from Math is Fun that helps you picture what is happening:

So now when someone says February 29th comes every four years you can smile, feel superior, and say “well, actually….”

Learning about slope has also meant learning about the streets of San Francisco in my algebra class. Check out what 31.5% grade looks like.

# The Winter Hiker

This was my opener for my Algebra class this past week. Here are the discussion questions we used. Activities like this help you think about slope in a real life context.

1. Which path do you think the hiker should definitely avoid?
2. Which path is the easiest in your opinion?
3. Which path leads sharply uphill?

# Stained Glass Slope Activity

In my Algebra class we are studying slope. It is such an important concept, it is worth spending extra time making sure students really understand it. A fun activity to add some art into the mixture is this stained glass activity from ilovemath.org.

stained glass window- graphing linear equations

The first page gives you a list of different equations in slope-intercept from. The second page is the answer key. The fun part is coloring in with your own personalized design at the end.

To make it look even cooler tape a piece of tracing paper or wax paper over your graph paper. Draw the lines for the equations on top. When you are finished remove the graph paper and color in your design. Now you can tape the stained glass window graph to a window and the light will pass through.

# Probability and Punxsutawney Phil

From the archives…

Here are a few math problems to keep your math skills warmed up on this cold February 2nd 🙂

1. A groundhog is a true hibernator. When it hibernates, its heart rate can drop from seventy-five beats per minute to five beats per minute. In four hours, how many fewer heartbeats will a hibernating groundhog have than a groundhog not hibernating?

2.When Phil came out of his burrow in 1971, it was negative fourteen degrees Fahrenheit. If the temperature this year is thirty-five degrees Fahrenheit, how much warmer will it be than it was in 1971?

3. If Punxsutawney Phil sees his shadow on the first Monday in February, then legend says that winter will last 6 more weeks. In 118 years, Phil has seen his shadow 104 times. (a) What is the probability that Phil will see his shadow on a randomly chosen Groundhog Day? (b) What kind of probability is this?