Ipad and the split classroom.

I believe I mentioned before that I have one class that is half pre-algebra and half algebra.  This makes it a challenge to teach some days, especially as I sometimes have to test one half of the group while the other half is working.  As the semester progresses I am thrilled to have the ipads.  I find that I can put one group on the ipad to use an app that will strengthen their basic skills or that might give them additional practice on the current topic while I lecture or work with the other group. Part way through the period I switch the groups and lecture the other group.   For pre-algebra, I have to reteach fractions so right now I"m having them work on fractions.  What is nice is that i have at least two apps that have videos that students can watch as much as they want.  In addition, one app has manipulatives they can use to help understand adding and subtracting fractions with unlike denominators.  I have a third fractions app that allows students to use slider bars to calculate the common denominator and then add the numerators, again using a slider bar for the numerator.  This is a free app and students are only allowed 10 problems a day but it still gives them a chance to work on working with unlike denominators.  Finally, I have students go on IXL about 3 days a week to get additional practice with immediate feedback.  IXL also gives me information on how the students are doing.
In Algebra I we are getting ready to begin working with polynomials, more specifically monomials.  I just realized with certain topics I rely more on the internet for websites to send students, rather than apps.  I have one that works well on polynomials but I prefer using either IXL or a couple of web sites such as the Math is Fun or Cool math, both of which introduce the topics and provide some practice with immediate feedback.  This way they also have a chance to have material presented in a couple different ways.  Furthermore, due to a limited internet in the school, I usually show videos on my smart board but it is hard with the mixed classes.
So it is working pretty well.

Geoboard app + polygons

Usually when it is time to start a new section, I give the students a reading assignment before covering the material but this time I am approaching polygons and their interior measures a bit differently.  I am having them do the exploration before reading the section.  The exercise has them draw various polygons beginning with a triangle, then a quadrilateral, pentagon, etc.

 As they  create the polygon on geoboard, they subdivide the shape into triangles.  They use the triangles to calculate the total angle measure and the measure of each angle. 

This gives them a chance to create and discover the answer.  I've used this exercise in the past but had them actually draw the shapes but this time I decided to save paper and have them do it on the geoboard app.  The first part of the exercise has them create certain polygons and subdivide the shape into smaller triangles to find the formula 180(n-2). The second part requires that they find a point inside the shape and create lines from the point to the vertex to find smaller triangles.  This leads them to the 180(n-2) via 180n - 360. 
This exercise is allowing them to build or strengthen their foundational knowledge before they read the section tomorrow.  I am hoping this will give them a better understanding of the material since most of my students are ELL. 
This activity kept my students engaged the whole period and it was easier because no paper was used, no lost rubber bands or broken boards.  I am going to use this activity again.

Open ended questions and frustrations

I read on google plus Mathematics education about open ended questions.  I took one from under the real number system, adjusted it  and use it in my warm-up. It is simply requires that students only use the digits 1 to 9 without repeating any digits.  I put the boxes up there and usually include a total so they have a goal.  The students have helped define what is acceptable within the problem.  For instance, you cannot use -1 but you can use 2-3.  You can put (2 + 3) as one box but you cannot do two boxes with a ( ) around them.  I cannot use the digits in the answer and I cannot repeat any digits. When I ask for answers, students are quick to correct each other if they reuse a number.  I plan to use more questions from the website.  I love putting the basic equation on my smartboard so students can write the answers in the boxes and a simple click cleans it off.  They are really getting into this.
The big frustration I have simply boils down to many of the websites I want to use, cannot be used on the iPads because they use require flash or java.  I want to use the national site of manipulatives in Las Vegas,  The NCTM illustrations site, Manga High, and so many others that will not work due to java or flash.  Yes I know there are some apps that you can get to run the website programs but they don't always work well because it is being relayed and there is often a delay that can frustrate students.  In addition, if you have a very limited bandwidth within the building, the relay may not work well.  I would love to see these rewritten so that they can easily be used in the classroom on ipads.

Tangrams, scrap books and MPG

I think I found an ipad app that will work for my geometry class.  I need to bring home the activity I've assigned my geometry class to see if it will work.  In addition to various figures, this app does have a square as the first item and I can move pieces around to make whatever figure I want.  So I plan to try other figures using that first choice.  In side, I also wonder if the students would loose the kinesthetic element when finding the solution if they are only using virtual manipulatives.  Once they finish each figure they can do a screen shot and create a book, a slide show etc to explain each figure. They could even import the screen shot into an that would allow them to annotate before using each shot.
I did find out that snowmachines and ATV's have odometers so I can have them figure out rough mpg for various models and then do a comparison between the theoretical and experimental mpg.  This would require internet research and they could provide information on an infographic, or a series of charts or other visual representation. Out here in the Alaskan Bush, people do not keep track of miles per gallon and do not know how.  I don't think my students even know the difference between the mpg on the sticker and what they are likely to get.
Finally, I am finding apps are a live safer in my combined pre-algebra/algebra I class.  My pre-algebra class is really struggling with fractions to the point that I am having to reteach adding or subtracting fractions with unlike denominators.  Since most of the pre-algebra students are classified as ELL (English Language Learners), I need to include material that can easily be read.  I have been having them go through a packet, IXL and Fraction Basics.  Fraction Basics is great because the study of fractions has been broken down into small topics such as the addition of fractions which is taught through the use of a video.  The next section after addition of fractions is filled with video examples.  In addition, each section has a very short review of previous material.  This was great because my pre-algebra students were on fraction basics so I could give review notes for an upcoming Algebra I test on inequalites  It was awesome.

Octane ratings and algebra.

I found a nice little exercise in Mathematics Teaching in the Middle School vol. 19, No. 4, November 2013 called Octane Algebra. It is on the Math for real page aka "When will I ever use this?".  The exercise introduces how the octane rating is calculated and what the standard ratings are for types of gas. During the warm-up, I asked "What is Octane?" and several used the iPad to find an answer.  I needed to build prior knowledge because out here in the bush of Alaska, most student just buy gas.  I do not have a vehicle so I don't buy gas out here.  I told the students the next time they fill their snowmachine or 4 wheeler (ATV) look to see what octane rating the gas has.  One student told me, it is not there but knowing the young person, they didn't even look.
The worksheet even has them figuring out a range of possibilities based on the fact that the gasoline is a mixture of gasoline and ethanol fuel.  The last activity on the sheet has them looking for possible values to produce certain rates and then graphing the results.  This is a very nice activity as it has them learning about real world applications for averages.
I am planing on extending this activity to have students research a variety of snowmachines, ATV's, cars, and trucks to see what the recommended octane rating is.  Once they have the data, I want them to create infographics, fill out an excel sheet and create graphs.  I might even have them create a presentation/video/ etc to share the information.  This activity has a lot of potential for literacy and technology.

Geometry and Tangrams

Every year when I get to teaching polygons I have a worksheet I give out so students can use certain pieces out of a tangram set to create shapes that are either concave or convex.  This activity requires students to think hard and work out ideas to create the shape.  Once they have created the shape, they copy it onto paper with the parts numbered and labeled on the drawing so I can see how they put the pieces together.  I have been wondering how this same assignment would work on an ipad either using a Tangram app or using a drawing app to put the drawings on so they could save their work and just ship it to me when its done.  I could actually have them create a small book showing their work and they could write a short caption for each picture and then explain what parts they used. Hmmm, ohhh the possibilities.
I checked the apple store for Tangram apps that might work.  Unfortunately, most of the ones I've found are actually games where the person matches pieces to create the picture given.  I want one that would allow the students to create what they want.  So I plan to download a few apps to see how well they work.
I also plan on trying the book idea at home to see how feasible the idea is.  I hope to share the results with you in a couple of days.

IXL

I have had the pleasure of piloting IXL in all my classes.  I really enjoy it because the topics offered in each class match up quite well with what I teach.  It gives me great reports so I can see how well each individual student is doing on certain topics.  It tells me if the student is performing below level, at level or even if they fully understand the material.  In fact, IXL provides 35 different reports.  I can go so far as to see which problems they've missed.  Furthermore, if a student misses a problem IXL shows them how to do it. 
There are two other things I like.  Since my pre-algebra class has problems working with fractions, I can move them down to the 5th level to learn to work with fractions.  I started them on the adding and subtracting fractions with unlike denominators using manipulatives so they can see precisely how the lowest common denominator works.  In addition, I do have one pre-algebra student who is at a level between the pre-algebra and the algebra class and I've got her doing some 8th grade work. 
The second thing I like is that students earn a reward after 5 min of working with IXL  They see pieces being turned over on a large board and it helps them see how they are doing. 
Overall, I am really liking the data I get from IXL because it is helping me create better instruction that meets the students needs.

Which one does not belong?

Recently, I've been seeing more information on the idea of which one does not belong, kind of like Sesame Street with their song only the modern one usually has multiple possibilities.  It allows students to look at 4 possibilities and choose which one they think does not belong but the choices are such that there is not only one "right" answers.  I require students to explain why they chose their answer.  It helps develop their mathematical vocabulary.  In fact, if you go to this website started by M^3 (making math meaningful) blog.  It has several divided into Shapes, Numbers and Graphs.  I never though about using graphs but that would work well for my upper level students especially if the graphs apply to the unit we are working on.
After we've done a couple weeks of "Which ones does not belong?" I plan to have my students create their on on the iPad and send them to me to use in class.  I like the form the website uses and it is an easy form my students can use.  I believe we could easily use zoodle comic, doodle buddy or similar app to create these.  It will help the students with their higher order thinking skills especially if I ask them to include possible answers with justifications.

Discussion questions

Today instead of standardized practice test question today during the warm-up  I  put up the question "What does 4<x<8 actually mean?"  This lead to a great conversation and showed me that although the students knew it was an "and" complex inequality, they had no idea of the real meaning.  I actually had a couple students who had lightbulbs go off in their heads.  I was able to extend this to inequalities in 2 variables and one student was able to connect the number line to the graph itself in terms of the closed circle is the same as the solid line while the open circle is the same as the dashed line.  As a final step, I introduced some real world example and this same young man was able to relate the previous information in the discussion to the real world. 
I decided that I would start off with a discussion question before we do the annotation because most of my students need to get used to changes in the daily routine.  I think integrating discussion questions into the daily routine is going to help them do better in math because they will have a better understanding of the mathematical principal.  I think when I start introduce new topics, I will give my usual reading assignment, then do a picture and annotate the photos to contain information on the material.  It will be the mathematical equivalent of unpacking the standards.  Unpacking the concept?  That actually makes sense.  We spend so much time teaching mechanics that we do not make sure they have a full understanding of the concept behind it.  What do you think?

Reading in Mathematics

I read something on the google about people not liking to read mathematics texts.  I can understand that thought because a mathematical statement can be quite information dense and most of my students are not taught to read mathematics.  I realized today that I am using normal reading techniques with my students rather than actually teaching my students to break down a statement into its component parts.  I need to start doing that beginning Monday.  I think I will have the students take a picture of a sentence off the board, import it into an app that allows students to write notes on top of the photo.  This way they can add notes to the photo and incorporate it into their over all notes.  On the other hand if the notetaking app already allows them to import photos and annotate them directly in their notes, then they do not need the extra steep.
This would give them a dictionary of sorts that could help them improve their mathematical reading skills so they are both more willing to read and to comprehend better what they are reading so they might do better in the subject.

The top 10 or 20 or 100 apps for teachers lists

When I was working on my masters, I discovered all sorts of technology you could use in the classroom.  My focus was on integrating technology into the math classroom and I would search out all sorts of articles and suggestions online.  Once I began practicing the integration, I discovered various lists of apps that were recommended for teachers to use in the classroom.  Some lists even came already sorted into levels of Blooms Technology.  The problem I had with most of the lists, is just that, they are lists with a description and price but not much more.  Even the apps recommended for the math classroom had the descriptions and price but not much more.  Most of the apps are for elementary school. 
What I would like is to see suggestions for using some of the recommended apps in a high school math class.  I see some of these apps and I would love to use them but have no idea how to use them.  I finally figured out how to use the app that puts a speaking mouth on something.  If I make posters of certain things like a slide to show negative slope, I can cause the bottom of it to speak and tell the student about slope. 
So if you publish a best list of apps, please include ideas for math teachers.  It makes it much easier for us to seriously look at the app.

A balance.

I finally found a balance between graphing using technology and doing things the old fashioned way.  Today in Algebra II, I added a couple small things to the assignment on filling out tables and then graphing the results for polynomial equations.  I had the students write down the number of possible zeros, if it were an even or odd function and number of possible turns.  The next step was using Free Graph calc to enter the equation so they could switch to the table.  They copied the values down on the table but before I let them go to the graph.  I showed them how to read the graph for zero's, max, min from the table.  Final step was to look at the graph and compare the information we got off the table with the graph and they drew the graph from the iPad.  We are going to do this again tomorrow and the next day to give them additional practice in understanding the correlation among the equation, the table, and the graph itself. 
I think we can get by without always having students do it only on the calculator or only by hand.  In the working world, they will be using graphing calculators or programs to do much of the work we do in class but they need to know how to interpret the information they are given.  I know I tend to rush through explanations and I've had to make myself slow down and only give them one step at a time so they follow along without getting lost.

Today is Pi day!

The interesting thing about pi day today is that it is celebrating its 27th anniversary.  Today is March 14, 2015 or 3.1415, the first 5 digits of pi.  If you carry it out, then you could celebrate pi day on March 14, 2015 at 9:26:53 either in the morning or afternoon.  The date and time comprise the first 10 digits of pi.  I heard someone once say that pi is a beautiful number because it contains all the birth dates, social securities, phone numbers plus so many other important numbers in the world.  That made it in my eyes, something more exciting than just the number I need to use when calculating the volume of a cylinder.
When you teach math, you end up having students use something to measure the circumference of a circle and a ruler to find the diameter and most of the time, students end up with a number that actually ends because most students do not measure as accurately as they should.  In class we usually end up using a piece of yarn or twine, both of which has a certain amount of stretch.  I've tried a small piece of paper but the students often find it difficult to get it to match the actual circle. 
I am wondering if I can get a small device that would allow me to use some sort of laser to determine the distance around the circle.  I vaguely recall seeing something that looks like a pen light that can do that.  I also wonder how much closer students calculations would be using something like that?
Just for fun the world science festival has 10 trivia questions on pi.  Enjoy! 

Pi day is coming up

In the past, I've had students research pi and how it is used.  In addition, they need to see where it is found in life because the 22nd squadron of the Royal Air Force has pi as part of their badge.  It was approved back in May 1936.  There are several articles on transforming the numbers from pi into a never ending musical piece.  Pi plays a part in the great pyramid in Giza.  In fact, a place in Indiana passed a bill declaring pi is 22/7.
Once students have gathered enough information, they can create an infographic, make an interactive book, a poster, a QR scavenger hunt, a music video based on the digits in pi, a video or podcast on the topic.  Why not even find out which famous people celebrate their birthday on March 14th?  There are so many possibilities.

Transformations in real life

I was sitting on my sofa last night when I realized I wasn't sure where we used transformations in real life.  I picked up the latest issue of the middle school NCTM magazine and it struck me where these occur.  You find transformations in carpet, tile, fences, cement pathways, robotics in that you have to give the robot the information to move him, turn around, etc.  You can see it in art, in twister, in so many other places.  In addition, transformations can occur in landscaping such as the Taj Mahal or Lincoln Memorial Reflecting pools, Longwood gardens, geology, a merry go round, the planets as they spin on their axis, etc.
I see having the students research the topic to find examples of real world transformations and then creating a presentation such as Prezi, Haiku Deck, Keynote or maybe a movie or podcast with the information on these examples.  They could have a picture in which they identify the type of translation, where it moved from to where it ended up, or if it rotated.  They could identify using diagrams the exact movement so they would have to discuss it and finally they could explain how their thinking process in regard to identifying the transformation.
This sort of activity would have them using technology, mathematics, higher level thinking skills, and they would be showing their mathematical literacy.

The math of roller coasters

The Mathematical Association of America (MAA) has a lovely unit on the design of a thrilling roller coaster that uses polynomials and trig to help model certain paths of the roller coaster.  This activity is for upper level students who may have had calculus.  On the other hand Mathplayground has a nice explanation of what they do when they create the roller coaster.  The NCTM has an activity called Roller Coasting Through Functons which looks at the time it takes for a car to complete the fall part.  This site discusses all the things the engineer has to consider when designing a roller coaster.
The Futures Channel has a lesson on Roller Coasters including the worksheets to go with it.  The link will take you to the pdf file for polynomial roller coasters.
Just found this one which has student use quadratics and linear equations to create a roller coaster.  It takes students through a process to create the roller coaster and it looks pretty good.
In addition there are several itunes university and podcasts that provide information on roller coasters including a STEM activity and podcasts by the Michigan Public Radio.
These resources are just a few I found on the internet and could be used either has a unit within math or as an exercise to show a real world application of polynomials.

neat idea for linear graphing.

I overheard this idea somewhere today that would be fun to have the kids do in class.  The suggestion was that students measure the thickness of their math book to provide slope for an equation.  So based on that, the students can measure a stack of two, three, four books to identify the pattern.  Then they take the information to create a graph and write the slope of a line.  If you want the line to start at a y intercept other than zero, you can start the pile on a footstool, a chair or a table.  Then you have the students use a different set of books such as a classroom set of goosebumps again on the floor, a stepstool, etc.  This can be repeated with several different books.
I just found out that quadratics are used to calculate vertical curves on the highway,  roller coasters, etc.  If I remember correctly, there is a free video or two on itunes university that help show how the math is used in building roller coasters.  That would make a nice cross unit involving both math and science.  That would be cool to include the mathematical equations for the roller coasters.

more real life graphing ideas

Over the weekend I watched every game at the regional basketball tournament.  Understand I know absolutely nothing about basketball other than a few things because I don't play it but my students do.  While watching the games, I realized that when they shot the ball during a free throw, the pattern was that of a parabola.  In addition, this parabola shape is used in other sports such as football, volleyball, shooting, etc.  So I know have sports in addition to dropping supplies from a helicopter or throwing a dead body off a building or a kid jumping off the top of a house. 
There was an episode of Numb3rs where Charlie was saying the kid must have been pushed off the building rather than jumping because the point where he hit the ground was off by a certain distance.  My brain started firing on that. 
I figured out most planets use an elliptical type orbital path around the sun.  This would be cool to have students calculate the actual equation for the orbit of most of the planets.  I also wonder about satellite  orbits around the earth.  What sort of systems do pilots use, how do they figure approach or liftoff? 
Then there are stock market up and downs that could be done.  Now I need to figure out where polynomials are being used in real life.   I need to research that and see  what I can find out.  I suspect one use might be when a ball bounces, or perhaps the path of a jumping fish. 
I am off to research the topic to see what other uses I can find.

Websites with real life type problems for graphing.

Math warehouse has two sets that look pretty good.  The first set is for linear equations and has the students write the equation associated with problems involving cabs.  Out where I am, the only cabs use a flat rate system such as $6.00 from the airport to the hotel and they often take 3 to 5 passengers in the cab to various locations.  These problems would help build a knowledge base for my students who are not accustomed to the way normal cabs charge.  After writing the equation, I can have them either build a table in a spread sheet and then graph it or I can have them create a graph on a graphing utility and then create the table by reading the graph.
The second set that the math warehouse has deals with dropping things from a certain height based on parabolas .  I like this because you can adjust some of the problems to discuss dropping supplies into an area that was hit by a tidal wave such as in Indonesia a few years ago.  The ones that deal with dropping something off a building, just change it to someone who is mischievous and then have them do the calculations.  Again, I can add in the spreadsheet, point graph or line graph.
I found this linear equation activity using bank deposits.  This activity focuses on straight deposits like in a piggy bank but could easily be extended to look at various interest rates to see how those effect the balance and could be done on a spread sheet.  This activity could easily be modified to discuss pay, theater or movie tickets, plane tickets, car rental, etc.
I am about to loose the internet for the afternoon so I will continue this tomorrow with one or two lesson plans/ideas tomorrow.

Graphs

We usually do graphing for linear equations, quadratics, etc from the book but we don't spend as much time having the students graph information from real life situations.  Since my pre-algebra are doing basic linear equations, I should have them spend time creating graphs from real life data so they can see a correlation between the data, the equation and the graphing.  If I add in technology, I can have students use a spread sheet to help create line graphs.  The spreadsheets would also give them practice in creating tables or data with input and output.  I could also have them create line graphs and bar graphs.  Perhaps I can even have them check the amortization for buying a house, a boat, a savings account, production of something local. 
For parabolas, dropping things out of a helicopter, firing a bullet, etc.  I think those types of things would be more interesting to my students and they need that connection.  Tomorrow I will share some of the sights I found with interesting activities.

Reasonableness

This week I have had students look up speeds for certain animals in preparation for other activities.  I wrote a warm-up problem based on information from that web search..  Today I asked if a cheetah can go 60 mph, would it be reasonable to say that the cheetah can go 180 miles in three hours.  I was stunned that most of my students stated "yes" because "180/3 = 60" So I asked if a cross country runner could maintain his/her top speed for a whole hour and the students said no but when I asked if a cheetah could go at top speed for an hour, they said "yes." 
I suddenly realized that my student's conception of reasonableness does not extend to something like this.  I wonder if we focus too much on the reasonableness of our calculated answers and not enough time on the general picture.  Using the straight math, yes it works but if you factor in that most humans and animals can only run at top speed for so long, then it does not work and my students have not looked at the whole picture.
In the fall, I had students calculate some rate/time/distance problems that gave them 120 mph and they would say yes its possible for a vehicle to go that fast if it has jet packs.  This lead to a discussion of possible vs probable and would it really happen in every day situations.  I am not sure that we spend enough time exploring the reasonableness under real world circumstances, rather than a strictly mathematical perspective.

speeds and number sense

Today, one of my students told me I was getting really weird because I wanted to know which was faster, a sloth or a snail, and by how much.  This required them to do  bit of an internet search.  Another class got to compare the speed of a cheetah vs man and this lead to a discussion on average speed via a math equation vs reality.  The other question I asked required them to convert units so they could actually compare 22 in/sec or 1 mph.  Turns out its the 22 in/sec by about 5 in/sec.  I need them to be fluent in conversions for their science class. The science teacher and I work together.  So last week, we looked at information given in parts such as 18 miles in 15 min to obtain a speed of miles per hour rather than miles per min.  This gave me a chance to initiate the idea that if you get information in one unit, it does not automatically mean that you must present it in that unit.  You need to step back and check to see what the common usage is.  In the 18 miles in 15 min, students were giving me the answer in miles per min even though they normally give speeds in miles per hour. 
The next step in this is to find information such as a guy ran the 100 yard dash in 28 sec so how fast was he going in mph and could he really maintain that speed. 
This falls under the student considering if the answer is reasonable.  Too often my students say yeah its reasonable without stopping to really think about the information and I am hoping things like this will improve their internet research skills and help them develop the number sense they really need in everyday life.

Found a book

Today I found a book on Amazon that was on sale called the" Joy of X, the guided tour of math from one to infinity"by Steven Storgatz for $2.99. The description indicates the author goes through and shows real world applications of mathematics  connecting math to people's lives.  It says he explains why you need to turn your mattress on a regular basis or how Google searches the net.  I am going to read this and see if I can use some of the material in my math class.  I have students who ask me when are we going to use this and i don't have any answers for most of the math that I teach.  I would like to be able to say something like, you will use linear equations to help you decide the best price for your book that you are selling on Amazon, or we can determine the best speed on your snowmachine for fuel consumption.  This is actually one of my goals in math is to provide these examples my students can relate to because too many of the examples in the math book almost feel contrived.
Back to flipping your mattress to get maximum wear, I am willing to wager that most of my students do not know they are supposed to do that.  I know about it but the mattress I have is one with extra padding on one side and I can flip it over and over.  I can only rotate it.  My mother used to have us do it but I never understood why and I certainly didn't realize there was math associated with it.  I thought it was something my mother did because her mother did it.