Classifying Rational & Irrational

At the beginning of the year one of the first things we do in Algebra 2 is go over types of numbers. We classify natural, whole, integers, rational, and irrational numbers. The next day we do a group formative assessment where in a group they take turns organizing different numbers into rational/irrational numbers. Then I give each of the groups a get a sheet where they have to organize a list of numbers into rational/irrational and explain why.

Students did an excellent job discussing the numbers and classifying them.

The Math Assessment Project has other amazing resources like this one at their website.

Zombies and Math (AAH!!)

Zombies and mathematics looks like it would be two things that didn't quite go together.  Andrew Miller had a project-based learning project about Zombie-based Learning.

With math and zombies most of the material has to do with diseases that increase at an exponential rate.  Students could analyze different population centers and predict its spread using exponential functions.  They could determine when everyone is infected and map the spread using the math data they calculate, or even explore the rate of decay.  Students could also investigate what happens when a certain number of people are vaccinated to help prevent the spread.

These are some ideas that have been implemented as part of a PBL project or would be a good entry point for zombie-based learning across the curriculum.

Zombie-based Learning

Math Movies

There are great math movies and clips on the internet that can get your students interested in mathematics by showing them the "real drama" behind mathematics.

There is a great show on YouTube that features "Math Warriors," which is a dramatic web series that takes places with great math concepts behind them.  Its creator, Kristina Harris- has a Ph.D. in microbial biochemistry and has taught at both New York and Columbia Universities- thinks of the series as "The Big Bang" meets "The Office," if on a much tighter budget.

Harris says a growing number of public school teachers have been using the series to de-mystify math for their students. The short length of each episode, she says, makes it a good ice-breaker at the beginning of a class.

“I think often times, people feel discouraged or overwhelmed by math and science, and if we can kind of dispel the myth that it’s something that is unattainable or make it somehow more popular or accessible then that’s something I’d like to be able to do.”

You can watch the first webcast below, I recommend subscribing to the channel.

You can view other videos of theirs here: http://www.youtube.com/

Or you can go to their website here: http://www.mathwarriorswebseries.com/

You can view other articles like this one here: Math Movies

Angle of Impact

Blood splatter analysis is a powerful forensic tool.  Spatter patterns allow investigators to reconstruct what happened at a crime scene.  The blood spatter pattern "tells a story" of the crime and help the investigators determine if eyewitness accounts are consistent with the evidence.  To study impact angle, you will need to use trigonometry math skills.

Use trigonometric functions to determine if the impact angle for any given blood droplet.

By accurately measuring the length and width of a bloodstain, you can calculate the impact angle using the following sine formula:

c=opposite/hypotenuse=width(a-b)/length(b-c).

To determine the angle of impact, take the inverse sine to get degrees.

Lesson: Angle of Impact Lab

Objective: For students to learn and use trig functions in the real world.  Students should be able to solve for angles in a right triangle.

Standards: Apply content to real-world scenarios.

Time: 45 minute class.

Set-up: 10 minutes before class.

Procedure:

• As students enter the classroom, students will begin work on the daily question.
• After two students go up to the board to work out the daily question, go over the correct answer with them.
• Spend 5 minutes going over any missed or confusing questions the students had on the assignment.
• Before the start of the angle of impact lab share with them a quick way of determining the blood splatter pattern. It should look like the image to the right.
• Have students spend 20-30 minutes working on the angle of impact lab.  Worksheet is attached.  Students should be in groups of 2 or 3.
• When students are finished with the angle of impact lab, students are to complete the final part of the lab with a poster.  Students should spend the remainder of the classroom working on the poster and putting their finishing touches on the assignment.
• 2-3 minutes before the bell rings students should fill out their exit slip, for an informal assessment.

Goals: Students should be able to use their knowledge to real-world scenarios.  Students should be able to use the angle of impact formula and know how it is derived.  Students should be creative and put their math knowledge to the test to apply the concepts provided. 

Forgetting Proofs

I was reading Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity by Loren R. Graham and I came across a great little quote, but we will get back to that later. The book was like Paul Erdos book The Man Who Loved Only Numbers style of quick writing.  It was a fascinating book with history of some of the most famous Russian mathematicians of the 19th- 20th Century.  This book reminded me of a professor that I had at the University of Nebraska at Omaha.

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A quick quote gave me inspiration to get students up to the board.

He would begin a proof at the blackboard, pause, and then say, "I cannot recall the proof; perhaps one of my colleagues could remind me."  This was a challenge that the class felt obligated to meet.  One student would jump up, go to the blackboard, attempt the proof, fail, and then sit down with a red face.  Another would get up, perhaps a 17 year old, successfully write the proof on the blackboard while the entire class stared enviously, and then sit down.  Professor Luzin would turn to that student, bow slightly, and say "Thank you, my colleague."  Luzin treated the students as intellectual equals, and his teaching led them to prepare for and anticipate coming lectures.

One of them later ask, "Had Luzin [really] forgotten the proof, or was it a well-constructed game, a method of arousing activity and independence?" They never knew.

This small process of accidentally forgetting the proof or answer to an example is a great way to get students up to the board and motivated to do mathematics.  I especially love the part where the instructor bows to the student and offers a sincere Thank you and recognizes the student as an equal, in mathematics you are always trying to get students to enjoy math and approve of their mathematics.

How could you incorporate this small idea of forgetting proofs in to your teaching?  What benefit do you think would this have in your classroom?  How do you do this now in your room?