Roller Coasters

  I love the time of the year when I get to study polynomials with my math classes.  I don't worry about all the possible real world uses because there is only one real use I focus on with my students.

I absolutely love having students create their own roller coasters.  Fortunately, there are several sites one can use to help students learn which type of curves are best for a roller coaster so the car does not fly off.

After studying polynomials, I usually have students create their own roller coasters for an amusement park.  I start off with videos so they can see what they need to think about.

1. The science channel  has a nice little video discussing forces, acceleration, mechanics and provides a great introduction to roller coasters.

There are other videos one can find including videos by roller coaster designers who speak about the factors ones has to keep in mind when creating a new ride like this.

1. Although the Amusement Park Physics site uses physics to design the coaster, it does an excellent job of taking a student through the design process step by step.  It starts by having the student select the height of the hill from three choices for the part of the ride where the car is pulled up to the top of the hill just before being released for the rest of the ride.  The process takes the student through choosing the shape of the hill, the exit path, height of the second hill, the loop, and it gives a report on the finished product.

2.  Discovery Kids also has a nice site for students to use to build their own roller coaster.  They have a choice of pieces to put in and once its done they can submit their creation.  The program will run through it, complete with sounds and screams and at the end, it will give a report on how scary. It was.  This is more of a game, than an activity in creating a real roller coaster.

This article gives a great step by step perspective of a person riding a huge scary roller coaster.  it gives so much information with height and angles so a person can read the article and create a drawing of the coaster the author wrote about.

For a hands on version check out this link. It uses foam and marbles so students create their own roller coaster on the wall.

I love having students also prepare a report of their finished roller coaster with details and a drawing of the max, min, curves, etc so we can see what it looks like if flat rather than connected.  They include photos of their creations and explain the choices they made for various parts of the whole creation.

This gives them a chance to see polynomials in real life.  I love playing with them.

Other uses of Logs and Natural Logs in real life.

  Logs are one of the easiest topics to find examples to use when asked by students "When will I ever use this?"  Without thinking about it, I can come up with:

1.  Richter Scale.
2. Population growth or decrease.
3. Half - Life.
4.  Continuous Interest.

These are the usual types of problems I find in the problems sections of text books but what are the other uses of logs and natural logs in real life.  Ways we might not think about as we are trying to convince students that math is used outside of the classroom.

1. It turns out that decibel levels are log based.
 

2. Newtons law of cooling - This is concept is used to figure out the change in temperature when an item is taken from one temperature and placed in a place with a different temperature.
T = e^kt+C  + R

3.  Calculating the monthly mortgage payment.




4. The ph scale for acids and bases -
pH = − log [H₃O⁺]

5.   Carbon dating which makes sense because of half life decay.

6. Finance - interest rates, stock prices, and value of currency.

7. Benford's Law which looks at frequency distribution of digits in data.  It is applied to street addresses, stock prices, and death rates.

8. Tones and intervals in music and sound intensity.

So eight more ways logs and natural logs are used in real life.  It would make a really good short project in upper level maths, to have students research each use and them create part of a presentation so the final presentation would include all 8 ways.

I actually was unaware of a couple of these so even I've learned something.  Great.

11 + Maths Volume 1 Lite

 The other day, I stumbled across 11 + Maths - Volume 1 lite.  This app is designed more to test student knowledge rather than teach the material. 

This app provides practice in 7 different topics.  Each topic has multiple subtopics but the free version only allows access to the first two subtopics. 

I check out Algebra and played with the first sub topic on expressions.  The problems were expressions written so you had to select the correct numerical equivalence from a choice of four possibilities.  This particular topic had 50 problems.

It was easy to leave the topic when I wanted to and I could have the completed questions graded.  What is nice is if you return to the quiz, you have to start all over again.

Once you leave the quiz, this screen pops up telling you exactly which questions you got correct, incorrect, or never took.  If you miss a question, you can click on it and see your answer versus the correct answer so you can review the material.

Once of the nicest things about this app is that the questions are not in the same order if you retake the test. 

There is the option of taking a test with all types of questions mixed together.  You should be aware - this app appears to be from the UK so many of the word problems have a British slant.

I would consider this app for my classroom mostly because it is multiple choice and it will give my students a chance to practice those types of questions in preparation for state wide testing, ACT, SAT, WorkKeys and other standardized tests.

I do like it because you get quite a few practice questions for the subtopics you have access to.  The questions are in a different order every time you take it, and you can see which problems you missed and what the answers should have been.  This means students can study the questions to help them improve.

What Math Classes Help Prepare For College.

   One thing that came up in the conference I just attended had to do with the question of how much math should a student prepare them better to attend college and to ensure the greatest chance of success.

The major response to this questions is for students to take higher level math classes during high school.  It is recommended that students take at least Algebra II. 

If a student takes at least Algebra II in high school, they do better in college and increase their chances of success.  If they take classes beyond Algebra II, they double their chances of completing a four year degree.   Imagine, we can help more students improve their chances of graduating from college by having them take trigonometry.

In addition, students need a good grade point average, at least a B or better in high school, to do increase their chances of completing a degree.  So students need to do well in their math classes in high school and not just skim along with a D.

Very few of my students take the higher level of mathematics.  Most end up blowing off the lower level classes so they end up with possibly Geometry as their highest class.  Others decide to quit taking math after they have taken their three credits of math.  In addition, too many of my students put enough effort into getting anything higher than a D.

To them, a D is fine because its passing but they continue to struggle with the next class because they have not developed a persistence needed to obtain higher grades.  I keep trying to think of ways to encourage these students to do better than a D. 

I think I'll start sharing this information with all my classes to help them.  I don't know if it will succeed but I'm going to try.

I checked out why math is needed in real life because about half of my students are not going to college and I found 11 reasons from the Huffington Post on why students should learn math.

1.  Students who are good at math will become parents who are good at math.

2. Teachers need to have a solid background in math.  Some programs only require a 40 percent passing grade in math on the entrance test to get into the program.  Imagine having teachers who have  much understanding of math. The future teachers will be current students who need to be good at math.

3.  Kids need math to see if what they are doing is making an impact in the world.

4.  Students need the math if they hope to predict the long term consequences of certain actions.

5.  A math savvy person can determine if a deal is good or bad.

6.  If students know math, they can calculate tips properly.

7.  Math can help people make healthy choices for their life.

8.  Kids can learn to make choices that make saving easier.

9.  You can determine how long it will take to drive somewhere.

10. Knowing math, allows someone to determine how valuable their time is.

11.  Math educated people know about financial realities and most know that winning the lottery is probably not going to happen and it costs more than the price of the ticket when you have to drive somewhere to buy the ticket.

All good reasons to know math for your daily life.  So now you have a basis for arguing to have all students math literate and to take higher levels of mathematics.

Real World Applications of Matrices

  I am extremely good at the theoretical part of math. I can look at the general equation and figure out how to plug numbers in and complete the calculations but I'm not so good at what in real life can be turned in to matrices.  So today's search was for real life applications of matrices.

1. Math Warehouse which had a lovely discussion on turning tables in to matrices.  It gives examples and then has the students try it themselves. 

2. Edurite discusses real life uses of matrices from physics to geology to computer science to gross national product.  Even why matrices are great for producing 3D in a 2D environment.  I learned something new just reading the material here.

3. You Tube has a great 2:35 video where two students show how matrices are used in real life.  Its got a early cinema feel with some cute drawings.  The sound is a bit weak but its very creative and well done.

4. This Prezi presentation rocks in the way it connects matrices with real life.  I never thought about matrices and groceries.  I had never thought they were connected but they are! This presentation even shows matrix math being used with the real life situations.  That is cool.

5. Finally is a transcript with diagrams on using matrices in real life.  It has everything you need to use it in class and its from Western Kentucky University.  I love some of the examples because the narrator states that some of the examples are contrived but is still used.  This transcript is for episode 13.  The free podcast can be downloaded and used in the classroom while you as the teacher use the transcript.

I am bookmarking all of these for the next time I teach matrices in my upper level math classes.  I really like being able to give some real life examples because most math books are set up so students seldom see the relationship to real life.  Yeah!

Origami, Paper Circuits, and Math

  I've been thinking more possible uses of origami in my math classroom.  I did a bit of research to see what is already out there on the internet for idea and came up with these.

1.  A lit origami cube -  I love the idea of making these lanterns out of different sized squares of paper to see how volume increases relate to the mathematical change in the cube measurements.  If we had them make the fully lit cube that might make it more fun and the students could see the reality. 

I often see questions in the math textbook that state something like "If you double the measurements of the sides of a cube, what happens to the over all volume?".  This type of fun activity would give it a hands on experience so they can see what is happening.

2.  Light up origami flowers - Imagine having students create these and then discuss finding the surface area of such a creation.  I know that many of the problems for finding surface area in the book are straight forward problems. This would be a much more challenging application.

3.  Flat paper circuits - The Exploratorium has a great little pamphlet on paper circuits.  In it is a pop-up with a lit bridge.  Think about the fun they might have creating the picture and then calculating the formula for the parabolic part of the bridge supports?  This could be extended to creating a pumpkin that is launched and its flight path is shown with lights.  They can then figure out the height and time ahead of time and set the path up with the correct points.

4. Maker Education has a wonderful information page filled with links on basics. It even includes links to create pop-ups.

I always love looking for ideas and let my mind fly free to imagine uses.

Origami and Movement.

  I am always looking for ways to include fun activities in my math class.  The other day, I went to a STEM workshop with wonderful learning using paper circuits and other neat things.

One thing we did was to create a moving origami bug complete with wings and eyes.  The first step in the process - fold the square paper into the bug.  Think of this as a lovely writing activity where students can write about:

a. The shapes they used as they folded such as triangles, etc.
b.  Things they had trouble with following the directions to make the bug.
c.  Find the area of various shapes within the whole bug.

Once we folded the creature, we added the eyes using a glue dot so it looked like a real bug.  Now comes the fun part.  We added a battery under the bug, tied in a small vibrating piece that came from an old cell phone, then added a bit of copper tape to connect the vibrator to the underside of the bug. 

Guess what!  It started when I connected the wires to the battery, the bug started moving all over table.  This offers the chance for students to create:

a. Graphs on distance traveled.
b. Rate times time equals distance.
c. Figuring out how you do measure distance.  Is it distance if the bug is moving sideways?  Can you compare distance if you are comparing one length sideways versus going forward?
d. Build the bug out of different sizes of paper and compare weight with distances traveled due to the size of the paper.

These are ideas just off the top of my head.  I plan to explore more with paper circuits, lights, movements, etc.    Keep an eye on this column as I figure out ways to use it in class.