Math, Infographics, and Graphs

 Most standards are already out of date by the time they are printed.  In fact, we have new ways of communicating information that are not taken into account by standards.  I love reading infographics because they condense information into easy to understand graphical representation.

The great thing is that infographics can be used to teach math while showing real world statistics.  Furthermore, infographics provide students with immediate understanding of certain topics.

One way to use infographics are to have students start with a graph.  It might be a graph on last 50 years and what happens with poverty rates, football statistics for the NFL, divorce rates, or the number of people traveling over Thanksgiving.  Once they have the graph, they might look into what causes the rate to go down or up.  This requires a bit of research possibly  but once the student has determined the reasons for a fall or increase, they are ready to create the infographic that will provide a story to accompany the graph.

Another way is to find two different graphs that are marked in the same unit and graph them on the same coordinate plane.  Once this is done, the student can compare and contrast the two graphs before looking for positive correlation, negative correlation, or there might be no correlation.  It is important to remind students that correlation does not necessarily imply causation.  This site puts two totally different graphs together to show correlation but also takes time to discuss how correlation can imply causation.

Or you could have students investigate how the interval and scale change the way we look at the graph.  For instance, a graph showing unemployment might change the time scale to every month instead of every six months to see how it changes the overall graph.  Another way to look at that same graph is to change the y axis so its every five instead of every one running only from 55 to 60 percent.

What about taking the cost of attending colleges from colleges the students are interested in and creating their own graphs comparing tuition, fees, etc to see how much they would owe after 4 years. The next step would be to present this same information in an infographic.  I know some colleges do not charge Native American students tuition while others do.

Another possible thing would be to have students look at the historical trend of something such as the Alaskan Permanent Fund Dividend and comparing it with the price of oil to see if there is a relationship.  Take this a step further by predicting what might happen to the check over the next few years based on what they conclude has happened so far.

Let students choose a topic, research it before creating a graph on that topic before creating an infographic to accompany it.  It might be something such as the cost of cars over the past years, or the  drop in value from new to 10 years old for a variety of models to see which has a history of the best resale.

There are so many possible topics.  One place to find wonderful graphs to use in some of these exercises is at the New York Times complete with ideas, graphs, and lesson plans.  Let me know what you think, I'd love to hear.  Have a great day.

Times in Music

I was at dance practice last night but its wasn't the usual dance practice you might be picturing.  It was a Cup'ik (Chewpick) practice.  That means they used a standard 4/4 beat with a slight variation but it was usually 4/4.

In the middle of doing a song about two men who went whale hunting one day and ran aground on a sand bar, my thoughts flittered to this piece that was rather complex.

It was like 2/4, then 3/4, back to 2/4, then 9/8 thrown in and it was crazy.  It was extremely easy to get lost in if you were not paying any attention.  In the middle of all this, I realized it's all a form of math.

In a sense, time signatures are a fraction where the top number or numerator indicates the number of beats in one measure of music while the bottom number or denominator indicates the type of note.  So a 4/4 means there are four beats in a measure and each note is a quarter note.

Not quite the same as parts of a whole but not all fractions are parts of a whole.  Look at ratios which are comparisons and time signatures which provide a different type of information. Neither one is really considered Part of a Whole.

Furthermore, musical notes and rests are the visual representation of the time signature.  Any musician can look at the music itself, count the number of notes, look at the value of each note to determine the time signature without looking at it.  This is much like mathematics where its numbers are like the time signature and the representations of those numbers are the notes.

There is a mathematical equation for determining the note value based on the number of flags on the note.  The equation is 2^(-2-n )where n = the number of flags.  If its a whole note, it is 2^0 power or 1 beat where as if it has 4 flags, it would be 2^(-2-4) = 2^-6 or 1/64.

In addition, most pieces of music have repeated sections in them denoted by a repeat sign.  Most pieces of music have some sort of repeating pattern just like math has.  I know I always take a few minutes to look for the repeating pattern in the music before playing it so I don't miss any.

Then you have the vibrating sound waves that are tuned to a certain standard of Hertz.  Middle C is found at about 262 Hertz while other notes are at a different frequency.  If the instruments are not tuned properly, they some times sound off.

Even Fibinocci contributes to music. If you look at a piano, you can see it with the 13 keys that make up an octave.  Five of the keys are black and eight are white and the black keys are grouped in a group of two followed by a group of three.  2 +3 = 5, 5+8 = 13.  Usually a scale is made up of 8 notes where the foundation of a chord is based on the 3rd and 5th notes.

It is said that Mozart based many of his piano sonatas on the golden ratio.  In addition, the violin's parts are also based on the golden ratio and provides the basis for saxophone mouth pieces, speaker wires, and even used when designing certain cathedrals.

So math is found in so many places in music.  Let me know what you think, I'd love to hear.  Have a great day.

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.

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.

Found a nice ebook

I was looking at the iBooks shop for books on iBook author and stumbled across a 21 page ebook on using the iPad to teach math called "Transforming Math with iPad Strategies for best practices".  It is a nice guide with specific suggestions for activities including the use of three dimensional figures and how they are created.  There are lots of examples to check out and it gives me some ideas along with enough information to start playing with it.  

The best thing of all is that this short ebook is free.  I just bought my first Mac and have installed iBook Author on it.  I have been downloading free ebook on iBook author and in the process discovered free ebooks on using the iPad in the classroom so I am exploring those. Tomorrow, I am going to look at "The Teachers iPadoPedia An A-z of using iPad in the classroom." 

In the meantime, I am going to checkout some of the apps mentioned in the ebook I looked at today.

NASA space math problems

I forgot about NASA space math problems until I got one of their regular updates in my e-mail this morning.  The latest problem is Problem 607: The Launch of LADEE to the Moon.
The description is :
Students plot the altitude, range and speed of the LADEE rocket launch and investigate rates of change including acceleration by graphing the tabular data and determining the slope of the graph using the definition of the slope of a line between two points.
This is a wonderful example of rate of change in a real situation where students can try it themselves.  The material NASA offers covers grades 6 to 12 and has all the past problems available for use along with some other items such as a space math book for grades 6 to 8 which is a standards based with multi-media math resources. 
The information is in PDF form so I can bring it into an app like subtext to interject questions, tags, activities, etc.  Most will require use of a calculator/graphing app, a drawing or note app and they could place their answers into a QR code to turn in.  Hmmmm the possibilities.

More on navigation

I gave further thought to my thoughts from yesterday and the reason I looked at maritime navigation is simply that we live on a river about 15 miles from the ocean.  People here go to the ocean and up and down various rivers to go fishing, etc.  So there are apps for mobile devices and the boat captain said he has seen people using the navigation apps on their ipads to navigate on water.  This lead to the thoughts of are there GPS apps for mobile devices.  I checked and yes there are so that means students can have GPS access with them at all times.  So as part of our navigation unit, we plan to have the students learn and use GPS in a geocaching activity.  I am thinking for the math portion of the activity, students can calculate the distance between stops and write that down.  We can also give them a map with longitude and latitude to mark down the stops and show the distances between stops.  That is going to be awesome.  We probably won't do it till the end of the year, after state mandated testing is done.

Algeboats lite

Found a nice little game called Algeboats lite for students to practice evaluating one and two step equations.  There are boats with equations such as x-3.  On the dock are four loads each with numbers you could substitute in for x and there are four flags at the top with the answer to the problem based on which value of x you choose.  Once the value for the variable is substituted and the correct answer is put on the flag pole, the boat moves away. There are three levels, rowboat, speedboat and yacht and each level has three sublevels which are unlocked as the first sublevel is completed.  The student can get a fair bit of practice.  The only thing that might frustrate students is that the loads and the flags do not always move as directed and it can sometimes take a while before moving.
I mention games because my students love playing games and this is something that could be done when there is time left in the class after they have completed the assignments or done after the weekly quiz on Friday or perhaps to obtain an exit pass.
Games provide possibilities for students, especially the lower performing ones, to practice in a fun and safe environment.

Preparing lesson plans

I am rewriting my lesson plans to utilize technology better.  One of the things I've done is to look at what I usually teach and divide the topics into units and not as a weekly thing.  Next I am breaking down the units into the concepts they really need to know to move on in Math vs trying to get through the chapters in the book.  Once I identify the concepts, I figure out what they should already know.  For instance in algebra 1 and 2, students will be using fractions with variables.  I know they struggle with finding LCM and GCF using only numerical denominators.  In order to find the LCM and GCF, they need to know prime factoring.  So my first unit in algebra 1 will be a review unit to cover prime numbers and prime factorization, LCM, GCF, expressions, and order of operations.  Simultaneous to breaking down things, I have been checking the iTunes Store for apps that can easily reinforce these concepts.  I am also going to set up work in Subtext and a couple other apps to ensure that they actually read material associated with the topic.  I want to make sure that any technology I use will further their understanding of math.  Tomorrow, I am going to review a nice game on finding primes.

More thoughts on Infographics plus apology.

I've been playing with infographics and discovered a couple web sites that allow me to make my own infographics.  I have been playing around with them.  One is www.easel.ly and the other is visual.ly.  I've only played with each site a short time but so far the first one is much easier to use for me.  I am going to check out some other sites over the summer and play with them to see which I like best.  I want to use them to produce posters that I will target exactly what I want covered on certain topics.  I want to bring in pictures such as a slide for slow and show that the stairs going up have positive slope and the slide down is negative.  My students need to see real world examples to start relating and I will also be building prior knowledge.
No for the apologies.  I got my dates mixed up the my ebook "Teaching math using iPads" is offered today and tomorrow for free.  Please enjoy

Thoughts on mastery

I just got some of the results back from the state on my students.  One or two of the ones who should have passed did not.  I realized today one reason they may have had difficulty is they want every single problem they do in class checked to make sure it is correct and they want me there guiding them on each problem.  I think they are afraid to make mistakes.  So I am going to implement a weekly mastery test on the computer so they can do 4 or 5 problems once a week and they will select the correct multiple choice answer.  I hope this will help them prepare for the State Tests better and will give me a better assessment tool to use. 
I struggle to get the students past the "I can't do it so why even try" attitude many of them have.  If I can help them succeed, their attitude changes and many go from disrupting the class to actually working. 
I am open to suggestions.

update on myscript calculator

I did a bit of reading on the web and tried it out a bit more and discovered a couple things about it.
1.  You can write an equation like 2x ? + 1 =9 and it will write 2 x  4 + 1 = 8.  It will actually solve the problem.
2.  If you do 2 x 3 = 5, it will give you the answer 2 x 3 = 5  + 1  so it takes your answer and tells you how far off it is.
3.  Since it only does nth roots by using the fractional form of the radical signs, this means that students get more practice on converting radicals into fractional exponents.  I like this because too many of my students have trouble with the connection.
Finally, the student I let try it out for some work, loved it. 
I am going to continue exploring it this summer but I think I will put it n the iPads in the fall.

I showed the subtext app to the principal who used to be the science teacher.  His first comment out was that you could set up a whole week doing this type of app.  He was impressed.
So I have 3 to 5 apps that I will be working on over the summer to prepare for the fall.  I will be sharing things as I set them up.

One last thing.  My 9th graders love using the Venn diagrams to find LCM and GCF  because it allows them to see the relationship between the two.  I am going to see about creating a document that I can use with subtext or with the students that they can fill out for themselves.

Gem of a free calculator app

Last night I stumbled across a neat little calculator program that so far is great for many HS math classes.  It can also be used at the lower levels.  Most calculator apps mimic a real calculator with the buttons, clear, memory, etc but this one does not.  My Script calculator is quite different. You write the problem out with your finger and it transforms it into print and gives you an answer.  It does ln, log base something, nth roots using the exponential form of the radical.  It even recognizes pi and changes it to 3.14 for calculations of volume or area.  I discovered it does sin, cos, and tan using either degrees or rads automatically.
The only down side I have found but I am planning on checking with the company that makes the app is that it gives answers to all problems in decimal form, even fractions.  Other than that I love it and I think it is faster for the students to use as they are not hunting for various keys.
I showed it to the sped dept and the lady in charge loved it.
Has anyone used this particular app? How do you like it?

Flipped classroom

I just read an infographic on ways to flip your classroom and many of the suggestions do not require that my students watch a video on the internet.  This opens more opportunities for me to be able to flip my classroom.  Many of my students do not have internet at home and have a limited data plan so they cannot watch videos on their mobile devices.  I feel stupid for not knowing I could have them interview a parent to see where math fits into their job, or read a blog, or write something or even visit the library to find information.  I am glad to have options because my students would get bored watching a video all the time.  If it involved reading up on a topic, maybe I ask students to install certain apps on their mobile devices so they can take the work home to do on the device and then put the answer in a QR code to return to me.  Ohhh the possibilities.  Homework could become more mobile......LOL

Three apps

I have three apps I just downloaded from the apps store and I will be working with them to decided if I can use them in my classes and if I can plan ahead by making presentations, etc to use with them.  I am mostly thinking of the best way to use them.
The nearpad application which allows the teacher to share a presentation, quiz, etc with the students and actually be synchronized with student iPads so you swipe and it changes the page on their iPad.  One concern is giving a quiz during the time.  I think I would place that towards the end so each student has the chance to work at their own pace.  What impressed me simply is that you can try nearpad using your pc or mac instead of another iPad or iPod.  It worked quite well.
The ask3 app states that you can turn the ipad into an interactive white board with sound recording etc.  When I investigated it, it appears I can only set it up for one class and cannot carry the material over to the next semester.  The company stated they are working on that feature.
Subtext is a lovely app that allows you to pull in a worksheet, reading or book, add questions, notes, etc so that it becomes an interactive experience and helps the student improve their reading.  I can see using it for word problems and for material out of the book.  At this point in time, it does not do pdfs but they hope to have the app use pdfs come fall.  You have to convert the pdf to epubs first.
Now that I know about these apps, I can figure out how to incorporate them into my lesson plans but first I have to convince the tech dept that I need my iPad on the wireless system so I can use them. 

plans already

The school year here is down to the last two weeks.  We are finishing up inverse functions and I"m having the students use  a graphing app to graph their inverse functions.  Its been educational for me in that I will have to figure out news ways of teaching the material so they can see a continuity between the equations and their inverses.  They treat each problem as a new problem, different from all the others before.  I think this might have something to do with the local culture.
I had down loaded a couple apps that advertised they could be used by students to practice algebra or geometry.  The problem with these two apps is simply that neither the student nor I have a way to select the level or type of questions.  Since I had no voice in the selection of the questions, my students were getting questions that might be on material at the end of the year rather than at that moment.  In addition, the questions might quiz the student on something I am not teaching because it is AP material. 
I am going to explore apps over the summer to see which ones can be used to create more indepth teaching experiences for the students.  I want to use activities that are further up on Blooms digital taxonomy.  I want them to experience more authentic work.  Over the past few days, I have taken time to ask students where we use certain things in real life to try to build their knowledge base.
As I check out apps, I'll let you know what I find.

Factoring and Showme or educreation

I was able to use the venn diagram today to show my students to find the LCM of an algebraic fraction.  It worked beautifully and helped several of my students understand finding the LCM of this type of fraction.  They could find LCM's for numbers but had trouble extending their knowledge to an algebraic fraction.
I am thinking of having the students make a presentation showing how to use the venn diagrams for finding the LCM of algebraic fractions.  I am thinking of having them use showme or educreation which is what I'm familiar with.  I am going to research apps tonight to see if there is an app that would make more of a podcast type presentation with video/sound/etc. 
This might help them connect with their prior knowledge.  If anyone has  suggestion on apps that would be good for this type of presentation. I'd love to hear from you.

Announcement.

From midnight (12:00 AM) to 11:59 PM on April 30, 2013, my e-book is being offered from free at Amazon.com. The title is "Teaching Math Using the iPad".  I hope some of you will be kind enough to take advantage of this.

Back to learning menus

I've been giving a lot of thought to learning menus and writing.  I've worked hard this year to increase their verbal communications by asking why, how did you come up with that answer, and other questions. I have been projecting warm-up and standardized test questions on the smart board.
Unfortunately, they are not as strong on the written, so I am toying with the idea of having students create pamphlets or jingles/raps or create some sort of digital presentation on showme, iphoto, or make a pod cast. 
In the past when I've had students create digital presentations, they've struggled with the creativity.  Many of these students have grown up in an oral culture and have little if any printed material in their homes.  So if I ask them to create a printed ad, I'll have to show them an ad and discuss the parts.  The nice thing is that I can bring a few magazines along to give them ideas and they can take photos to keep a record for themselves so they have a guide. 
This is something I'm going to be working on over the summer so I set it up properly and introduce it slowly over the year.  Maybe start with a choice of two digital projects and increase the number of choices over the school year.
If anyone has suggestions on setting up and using digital learning menus, I would love to hear from you.

website and communicating.

One last website I like is www.coolmath.com.  It works for the most part on an iPad but the games do not work because they require flash.  Otherwise, the cruncher or practice problems work pretty well.  This site has some good material in it.  Tomorrow I am going to send my 9th graders to read up on prime numbers and prime factorization.  The prime numbers section has the Sieve of Eratosthenes in the definition.  I think I will provide an unmarked one for them to do along with the explanation.
Over the summer I am going to try to put a syllabus, homework and class info on the school wiki so come fall, I can just send students there to download information and check on assignments etc.  I just found out one of the teachers who runs an afterschool activity, uses Edmodo to communicate information, dates, etc to her students.  I need to further explore this option further. 
One thing I need to consider as I do more things on the iPad has to do with keeping student work safe.  I have one set of iPads which are shared among all my classes.  I have to research how email works on the iPad to see if my students can keep their privacy.  I have an idea but I need to pursue the idea further.