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.

Algebra Attack

Algebra Attack is an app with both a lite and full versions ($0.99).  I downloaded the free version which differs from many other lite versions in that it offers several practice sections for each topic.

The sections are not all the first one or two, but could be the fourth or seventh section so you have a good selection of practice problems.

The starting algebra section has four subsections that have students find the missing number using a question mark rather than a variable.  This has students look at the equations and mentally figure out the number.





There is a opaque screen which allows the students to see the problem while working it out on the screen.  Once the problem is solved, the student taps in the green print area to bring up the answer box which always has a question mark in it.  To input the answer, the green button is touched and a number matrix appears so the student selects the correct number and it appears.







If the answer is correct, everything stays green as the correct answer is shown, if its wrong, the correct answer appears and everything turns red indicating it is wrong.








This app provides immediate feedback so a student knows exactly how they did.  In addition, when each section is completed, the program shows the questions worked, the correct answer and if the questions were correctly done.  Its basically a report the student can check out.

If they retake the section, there are different questions so a person cannot just write down the answers and retake the questions to get a
100% 


This app is set up so students see the number they entered and the correct answer.  I purposely made a mistake so you can see how it shows your answer and the correct answer so you can compare.

This app takes students through a variety of problems from introductory algebraic problems up to working with radicals and functions, quadratics and systems of equations. 

This particular app could easily be used with Pre-Algebra, Algebra I and a review for Algebra II.  Even at full price, it has so much material, it is well worth it.

Google Earth

  I just finished sitting through a one hour presentation on using google earth in the classroom.  Although it was mostly focused on Social Studies and English topics, I discovered some nice uses for the math classrooms.

I was impressed by what I saw including the measurement tool and the historical photos to see change. I loved the way I could look at so many different views of the same place.  So some of the ideas I came up with for the math class.

1.  Using a topographic overlay of say mountains or valleys, students can calculate the slope for parts of the mountains.

2.  Using a map with a word problem so students see the actual route for a rate, time, distance problem to compare two different routes.

3.  Calculate area of certain geometric shapes on the planet, for instance the NYC metro area.  Students could easily look up the population and use the two pieces of info to find population density.

4.  This lesson is designed for students to compare ski runs to find the most extreme and longest ski run.  I think many kids would find this lots of fun, especially if into extreme skiing.

5. Use trig to figure out the height of something like a balcony out of Romeo and Juliet, a flag pole, something they can see in real life from the pictures.  Many times you can find a well known building, you know the height and the distance, so you figure out the angle.

6.  Look at the ways to get from point A to point B.  Figure out the distance for each route and explain which is the best route.  They could even figure out the % difference for each route and then rank the best routes.

7.  Figure out the distance the balloons the Japanese released in World War Two, look up the time it took and then have students calculate the rate.

8.  Use google earth to find the distance for several western trails used in the westward expansion, figure out the time it took to travel each trail and calculate the rate.

I see so many cross-curriculum uses for google earth and math.  The above are just off the top of my head so now I'll just think about this and share a few more ideas when I get another list put together.

Teaching Literacy in The Math Classroom

  Today I went to a workshop on increasing literacy in the math classroom.  There was one activity in the whole time that made an impression on me.  My school is slowly moving towards using google in a variety of ways.  The first step was simply moving our mail to gmail but we haven't done much more........Yet!

The coolest thing was the use of google docs as a live written discussion board.  I enjoyed watching people type answers to a question on the page at the same time.  So I looked at 10 ways to use literacy to help foster a deeper understanding of math.

1. Have students present problems on the board showing how they did a problem.  They explain how they solved the problem, their thought process, etc.

2. Have students write down how they solved a problem.

3.  Have students choose one problem they missed and explain what the mistake was.

4.  Have students make quizzes for each other.

5. Have students write down how they would explain a concept to a friend.

6.  Have students tell each other how they solved a problem.

7. Use exit slips to gauge understanding.

8. Require students to take notes

9. Let students help each other solve problems

10. Moderate an online discussion.

Many of these activities can easily be done either with pen and paper or digitally.  There are also LMS that would allow you to hold the discussions.

Pixar

  You all know who Pixar is.  They are the American company who created animation for various movies such as Wall-E, Cars, Brave and other wonderful movies.  So I bet you are wondering why I'm talking about Pixar in a math blog.

Well, surprise!!!!!! Pixar is working with Khan Academy to provide a free online animation course called Pixar in a Box.  This class has 7 topics already released.

The 7 topics include rigging (or how to animate characters), environmental modeling, character modeling, animation, crowds, sets and staging, and finally rendering.  Some very good topics to get anyone started who is interested in creating their own animation.

Each topic currently has two lessons.  The first lesson is general with the idea of appealing to all ages and provides a nice introduction to the topic.  The math in lesson one introduces the lesson using interactive tools and videos while showing a connection to mathematics.  The second lesson is the one geared more for grades 7 to 12 and focuses more on the actual mathematics introduced in lesson one.

Just for the fun of it, I decided to try the environmental modeling lesson.  I like starting at the beginning and working my way through.  Although, I'm interested in the animation lesson, I'm going to wait till I work my way through the first two topics.  Lesson one looks at using parabolic arcs to model blades of grass in animation.

Cool, imagine using parabolic arcs for something in real life the kids can relate to.  Lesson one covers the introduction, string art, midpoint formula, parabolic arcs and parabolic curve matching, modeling grass, animating grass, ending with a design challenge to model grass.  Each area comes with a short video to introduce the material, followed by an activity.

The second lesson is focused on the parabolas and associated math.  It goes into weighted averages, touching points (their definition and calculating them) along with parabolic construction.  This is the real life mathematics associated with creating the grass using parabolic arcs.

Sets and staging is the lesson that shows how geometric transformations help position objects within the scene.  The first lesson looks at the coordinate plane, rotations, scaling, translations, and other related topics.  The second lesson focuses on rotating points around the origin and the geometry of rotation.

 This is only the beginning.  Over the next few years, Pixar will be adding to the course until its complete.  I need to see if I can figure out a place to put this particular course into my geometry class.  I think many of my students would love to do this type of thing.  I know I would! Go and check it out, explore it and have fun.

More Math Jeopardy Games

  I love using jeopardy games as both review and practice but I don't always have the time to create one for each mathematical topic.  I prefer to use the computer geeks way of "borrowing" already created material.

The internet has made this easier because of how many people post completed material to share.  So a simple search helped find some that I can instantly use in my classroom.

1. Math-play has 15 different interactive jeopardy games ready to play.  These games cover topics such as the Pythagorean Theorem, fractions, decimals and percents, exponents, integers and several more basic topics needed by students in Pre-Algebra.

This website at Avon High School has three algebra I games. The three games cover quadratics, solving equations, inequalities, and formulas, and simplifying expressions, evaluating expressions and mathematical properties.  These are actually downloadable power point files to use for the jeopardy games.

Mathbits also has two nice Algebra I reviews for the whole year.  It can easily be played online and advertises itself to be iPad compatable.  Some of the topics include solving equations, functions, and graphing in part one while quadratics, inequalities and systems can be found in part two.  Both are ready to do and easy to access.

Mathbits also has a jeopardy review for Algebra II.  the Algebra II has two different games.  Part one covers trig, quadratics and three other topics while part two includes inequalities, complex numbers and logs plus two other topics.  This one can be used on the iPad and has some really good questions.

I've also found you can type in a topic to find a specific jeopardy game.  For instance, I typed in radical jeopardy games and found two power points ready to download plus several others.  I found a simplifying radicals game which I may use in my Algebra I class tomorrow as a review before I start teaching multiplication of radicals.

I love "borrowing" games as it saves me time.  Enjoy.

Online Coordinate Plane Games

I wanted to find a few online games for my students to play so they can strengthen their graphing skills.  My students love playing games and the more I use games to  help them practice, the more likely they are do develop the skills.

The Math is Fun website has a lovely game called Hit the Coordinate.  You have your choice of levels and using one or all the quadrants.  Once the perimeters have been set, the game is on.  I chose to use all four quadrants.  A coordinate flashed and I used my spotter to find the actual point and shot.  If I were right, I'd get points, if wrong then no points are awarded.  The thing that makes this different is that the look of the coordinate plane changes with each problem.

Math Playground has a lovely game called Locate the Aliens.   In this game, an alien appears on the coordinate grid.  It is your job to type in the location of the alien.  If you are right, you gain a point and another appears.  If you are wrong, you hear a funky noise and the coordinates of the "Lost Alien" appear in the box.  This is a timed game but if played regularly, a student can get better at identifying coordinates.

Math Playground has a second game called Space Boy Rescue where coordinates are flashed and you place the space boy in that location to rescue the alien.  If the rescuer is not placed correctly, the player is told immediately.  In fact, there is immediate feedback of great job or you missed the alien so a student knows immediately if they did it correctly.  The person has 90 seconds to rescue as many aliens as possible.

Another game at Mr Nussbaum's site has a Stock the Shelf game requires students to stock the shelves with 20 drinks in 2 minutes.  A location on the coordinate grid is flashed to the side next to the drink and the student is required to place the drink in that location.  If the student chooses a wrong location, an x appears and the student is told to try again.  This game offers a tablet version for the iPad.

Finally is the Coordinate Jeopardy for those days you want a bit of team actions.  You can set it so you have up to four teams.  There are three topics with four questions each.  If a team answers incorrectly, they loose points but if they answer correctly, they get points.   The three topics are Graphing Points, Quadrants and Axis, Coordinates.  The program automatically flips the coin to determine which team goes first.  The questions are ready to go and this is the type of game you could project to involve the students.

Although these games are listed for upper elementary, lower performing middle and high school students  will enjoy these games.

Cartesian Cartoons

  I was actually looking for one thing and stumbled across this web site instead.  Its called Cartesian Cartoons and is filled with great graphing activities.

All the graphing activities are free and are geared for Pre-Algebra and Algebra classes.  These actually require the student to plot points to create a cartoon image which can be colored in later on to make a hang-able picture.

There are three different sections of graphs available.

1.  Graphs that require only the first quadrant.  The suggested ages for this group is the 3rd to 5th graders.  I suspect these could also be used for low performing students who need extra practice in learning to graph.  Some of the pictures when finished are  bugs, snails, animals and ice cream.  Each of these can easily be colored in when finished.

2.  This group has a variety of tongue in cheek humorous puzzles such as a dinosaur who needs to loose weight, a rocket, a duck and about 32 more puzzles students can have fun with.  These puzzles use all four quadrants of the Cartesian coordinate systems. Check out the titles including Granny's cell and you'll love them.

3.  The last group is the themed one.  You can find puzzles for the first day of school, Halloween, Christmas, Valentines day, and a variety of others.  There is a Valentines one I enjoy that is about loving math.  yeah. 

This site is designed to make graphing fun by having students create these drawings.  In a sense its like those old paint by number kits that my mother tried.  If you follow the numbers correctly, you have a beautiful creation when finished.

The other thing about this site is that you can download either numbered graph paper or unnumbered graph paper to use with your students.  In addition, if you create a cartoon, you can share it with this site.  The material is protected and only to be used by the teacher in the classroom or by home schools.  It cannot be reproduced anywhere else.

So if you are looking for fun graphing activities, check this site out.

Happy Valentines Day

Happy Valentines Day to everyone.  This picture is perfect for me because I woke up to blowing snow and nasty cold weather.  It warmed my heart.

Tomorrow, I"ll share a site with lovely cartesian coordinate graphing for holiday pictures.

Green Highlighter Activity

I stumbled across this activity while researching teaching radicals.  I loved the idea and can see using it any class for anything from warm-ups and bell ringers to daily work to exit tickets.  Everything!  With just a small modification, it can be used with digital devices.

I found it on the Simplify with Me and the author modified it from Square Root of Negative One Math.  The idea is pretty cool.

1.  Assign a few problems.

2.  A student finishes the assigned work.  The work is checked by the teacher.  If it is correct, the student is given a green pen or highlighter.  If not the student tries again.

3.  The student takes the green highlighter or pen and goes around to help other students.

4. As other students get the right answer, they receive a green pen and go help others. 

5.  The teacher only looks for those students who have done the problems correctly. 

6.  It is up to the students to help each other until everyone has it done.

7.  Assign a few more problems and repeat.

This is cool in that the students who finish first are given something to do rather than just giving them more problems to do and they get so far ahead that those who struggle never catch up.  I really like this idea.

As far a doing it on digital devices,  You can pick up stylos for cheap on Amazon.  Get a bunch of those and hand them out to the students instead of green highlighters so they can write on tablets.

This can be used for any topic at any time, easy to implement and its not that expensive to pick up several boxes of green highlighters.  This keeps students occupied who finish first and gives the chance for others to get caught up.  It also implements peer tutoring effectively and shifts learning from teacher driven to student driven.

This is cool.  I am off to order multiple boxes of green highlighters so I can start doing it in March. I also have several stylos around for when we used digital devices. 

More On Teaching Radicals

   I am always on the look out for ideas when teaching material.  I ended up at the Math = Love site.  Its actually a unit for radicals and I like the way she reviews primes and composite numbers first before anything else. 

I admit, I've never thought to review this topic because I keep assuming that students will remember this from the last time they had it.  I should know better but it all boils down to "What do I have time to teach?"  I think it would help the unit run smoother if I did this.

She also has a lovely exercise to help students learn more about the parts of a radical. In addition, I like the way she has students prime factor everything on the side and look for groupings that match the index.  Its the same way that PUMAS at NASA recommends teaching it this way so people learn in 5 minutes.  She has all the templates needed that can be downloaded.

Another site I found has a lovely card game for simplifying radicals.  Its modified from another game found on the internet.  The site includes a video showing how the game is played and the author talks about how she would modify it for the next time.

Learn NC has a nice little activity that uses real life examples whose formulas use radicals.  It shows the formula and defines the variables.  In addition there is a real life problem that uses the formula and there is an answer sheet.

I even found a mad minute activity for helping students learn to simplify radicals more easily.  It comes with everything you need.

While looking for ideas, I found a really awesome activity that is easy to implement without tons of preparation or money.  It can be used for a variety of mathematical topics.  I'll be talking about it tomorrow.

Cool Activity for Solving Radicals

  I am teaching solving radicals in my Algebra II classroom.  Due to admin work, I have a substitute in my classroom so I went looking for activities to assign tomorrow.

I came across this cool idea to help students learn to solve equations with radicals.  Miss Calculate's blog has an activity where students use strips to solve an equation.

She wrote the steps for solving a specific problem on strips.  The first step of the problem was marked with a star to show students where to start.  Then they arranged the remaining strips in order till the last strip which is the x = answer.  

Now there is a digital way to do this same activity.  Intel Education has a visual ranking tool which can easily be used to create digital strips.  You simply put in the steps, one step per slip, make sure the steps are not in order and save it.  When the students do this the ranking is not based on importance but on the order of the steps.

This visual ranking tool works on iPads, android devices, iPhones, and Windows computers.  It is nice knowing that it will work on the iPads because they developed a free app you can find in the itunes store.

Think about how this same process would work for solving equations with variables on both sides, solving systems of equations, solving multistep equations with the distributive property, geometry proofs, ranking the most important properties for 3D and 2D figures such as the most important for a square, rectangle, kite, trapezoid, etc.  This offers so many possibilities for use in the classroom.

Math Bits

  I found a nice little site today.  Its called Math Bits notebook (online study notebook) and it is set up as a wonderful digital notebook. Please be aware that all materials are copyrighted and may not be reposted to the internet and is not considered "Fair Use" for educators.

In addition, the material contained in this site go with common core standards.   The site contains material for Algebra, Geometry (90% complete) and some Algebra II. Although the material is set to go with New York State requirements, it is usable anywhere that uses common core. 

When you click on the topic, you go to a clickable table of contents which is referred to as the outline with topics and subtopics.  When you click on the topic, you are taken to another clickable list of lessons, practice, and refreshers.  The practice page has multiple choice questions.  If a student chooses the wrong answer, there is a popup box stating it is incorrect but it does not state why.  They get a popup box if they are correct too.

The lesson are short  at one page but there are lots of examples to check out.  The refresher is actually a reteach with examples or a short quiz that gives immediate feedback.  It is a way to review previous skills.

In addition, there are sister sites for all three topics.  The sister sites provide teacher resources to accompany the notebook but does require a subscription to access all the materials.  There are a few that are free so the instructor gets a taste of the activities and materials available but the majority require the subscription.  The subscription also allows you to access all answer keys, worksheets, activities, puzzles, etc and any new materials.

Both Algebra I  and Geometry have over 600 resources and Algebra II has over 500 resources available to accompany each digital notebook.  The cost is about $40.00 per year for a single subscription and I don't know if you can get a discount if you want all three subscriptions.  You'd have to contact them.

I can honestly say, I like this website as the notebooks are already created and ready to go.  I am thinking about using this to help students learn because I am heading into the testing time of the year and it might make things a bit easier so students can catch up if they are out of the room due to testing or sports.  They can access this if they are out as long as they have internet access.

Is This Wrong?

I've been working on radicals with my Algebra I class.  They've been having a very difficult time with the idea that something squared is a number times itself.  So if I ask them what the square root of 25 is, they give me a totally blank look.

Out of desperation, I drew a square on the board, labeled the area inside 16 square units and labeled each side as 4.  I told them the number under the square root is the area found inside a square.  We know the area is length times width or side times side.  The square root sign is asking for the length of any side.  Because its a square, the sides are all the same length and you only have to write down one side.

This is the first time I've taught it this way but it made it easier for students to visualize and find the square root of a number.  For cubed roots, I drew a 3 dimensional cube with a volume of 8 and showed how the height, width, and length were each 2 inches.  I only needed the 2 written once because each length was the same.

It actually worked quite well.  My students often drew a small square on the side of the page, filled in the area, and found the side length much faster than teaching it the traditional way.  So when I moved to simplifying I talked about perfect squares (relating them to area again) and a square that is not perfect.

I have a story I use to help students remember which value is taken out.  There are two sisters who share a house.  One sister is perfect.  Her hair is always done perfectly, her make up is perfect, even her clothing is just perfect.  The other sister is comfortable, doesn't worry about looking perfect all the time.  The perfect sister goes out to the front porch to flirt with the boys while the not so perfect sister stays inside to read a book or play a game.

If a student asks me if they got the problem right, I simply ask "Did the perfect sister leave the house?".  They can easily figure out if they did it right.

Now the question I have for everyone.  "Do you think its fine to teach square roots this way?"  Thanks in advance for your input.

fishing

 

Hopefully this works the way its supposed.  It was done in Keynote.  I added the image of a fish, animated it and saved it as a quick time movie.  The final step was to upload it as a video.  It worked earlier so we'll see if I got it uploaded properly.

 I don't think is working right.  Please let me know!

Gone Fishing!

Created using Keynote.  I copied a picture, pasted on a slide, added the text and exported as an image.

My Favorite Program/App.

  I have one app, I use all the time when I need something.  I use it for making recordings, animation, posters, videos, and anything else I can think of.  I can create a multi slide presentation or use just one slide.  What is this elixir of presentations?

It is keynote.   I absolutely adore Keynote because it does all those things and more.  I can do so much with it for my math class.


1.  Using My Script Math pad, I can create any and all math equations and then send them to dropbox or google and then bring it into keynote.  This is an app for my iPad that allows me to use my finger to write equations and it automatically turns the handwriting into text.  It is beautiful and so easy to use.

2.  Keynote itself allows me to create animated slides so I can show movement of numbers or of shapes. I made an animated slide showing congruence explained through translations.  I've put sound to it and it was cool.

3. I've imported short stop motion animation of nets that change from flat 2 dimensional to 3 dimensional shapes.

4.  I've imported pictures and put text onto the picture to make a poster with math terms.  I had fun exploring it.

5.  I can show how to solve equation step by step using bullets and special effects.

This is only a short list of what I can do with Keynote.  I'm using a different computer right now but I'm hoping to post an entry with examples of all of these things plus more.

Digital Interactive Notebooks

  Right now, I'm trying to use interactive notebooks using composition books.  They are nice but they also take quite a bit of space and the kids don't always keep up.  Since we have iPads in the classrooms, I need to learn how to create digital notebooks.

One article recommends using Book Creator because it allows a person to add audio, video, images and text to create an interactive notebook.  Although there is a free version of Book Creator, it only allows one book to be created.  If you have one to one iPads, that works but if you have a shared set of classroom iPads, you might want to buy the app so multiple books can be produced.

The same article suggested using Google with power point, keynote or google slide. Google allows you to set up a template so all the students have to do is fill in the appropriate information.  This article gives more information on doing it and has some nice information on creating interactive math notebooks using Ever Note.

This site starts with producing the material on the laptops before moving it to Book Creator.  They recommend using KeyNote to produce the slides complete with color and everything you want.  Once the slides are done, you move the material into Book Creator.  The instructions are really quite nice.

Finally, I looked at Holtthink for additional information on digital interactive notebooks.  This article looks at the typical hand written notebook and then provides step by step instructions for creating the notebook on iPads.  I like the over all picture it provides. 

Now off to figure out how to do it myself so I can start doing it in class.

Math in Film Making

  As long as I've been exploring math in music, I thought I'd check out information for film making.  Most of us have a student who love filming everything and turning it into the epic adventure. 

I'm not talking about the student who is always making selfie video to post on their site but the one who has  vision they create on film.  It turns out film making uses so much math.

The math goes from the producer keeping track of the budget to making sets, costumes, filming, and so much more  I found several sites that have wonderful information on the topic. 

A student online newspaper has a wonderful article on math in film making. The author discusses how the producer uses math in the cost of the film while the cinematographer must calculate the best angles for a shot.  We are told not to forget the sets and the costumes both of which involve quite a bit of math.  In addition, the author comments that animators use the most math and several types of math.

The Mathematical Association of America has a lovely piece on film making and math. They actually reference a paper about math and animation that goes into quite a bit of detail.

No Film School goes into specific detail about the golden ratio, the Fibonacci sequence, perspectives, the rule of thirds, and there are accompanying videos to show many of these. 

Plus Maths has a very technical article on mathematics and animation. This article takes the reader through the process step by step so the get an idea of how creatures and items are created.  There is talk about matricies, vetices and so many other mathematical material.  It is such a cool article.

Eveltio has a list of several articles with links, all dealing with math in film making.

To make it even more relevant, I found a few places that talk about the cost of making a movie from start to finish.  This puts the information of the previous articles into context. 

Investopedia has a great piece on the cost of making films.  They include information on the cost of marketing films.  Something many people don't think about.

Quora has a summary of a 75 page budget used for the movie the Village.  The final cost was over 71 Million for making it.  You see how much costumes, sets, lighting, visual effects, etc.  This ties in with what the producer keeps track of.

Digital Films has sample budgets for independent films to give approximate costs. 

Slide Share has a whole piece on when a film starts making money and many of the misconceptions involved in that process.  The article uses Spiderman 2 as its example.  I found out that there are huge costs involved in printing and distributing the film.  Something in the neighborhood of 50 to 100 million!

Just think what type of eye opener this kind of unit would make for our students!

The Math in Music

  We often hear that music and math are related but did you ever wonder how?  I always have that one student who is so into music that their lives revolve around it.  So I went and found information on this topic so I can snare one more student into the "Math is all around us" group.

Math Central out of Canada has a lovely article that talks about fractions used in music as time signatures.  Rather than being "part of the whole"  it tells how many notes per bar and the value of each note. It also explains where the Fibonacci sequence fits in. I learned something new today.

Plus Maths explores frequencies and pitches which are extremely important in music.  It even explains why certain notes work together while others do not.  This article is great for the mathematics involved in the notes.

Arts Edge from the Kennedy Center for Performing Arts has a short piece on ratios, fractions, counting and patterns found in music, all of which are math.  This is a great introduction to the topic and the pieces are short.

The Math Forum goes into detail about frequencies, ratios, etc and includes a connection to geometry in one part of the piece.

Finally, the American Mathematical Association has several videos that deal with this topic.  The videos range from "Music + Math: Symmetry" to "Geometry in Music" to "Symphonic Waves".  In addition there are lots of links and reference materials to help students learn how music uses math.

Math in the Music Industry?

  How many of us has someone who is going to be the next big name rapper like Eminem, or is going to be the next big record producer?  You know the one!  So know the question for them is "Do you know how math is used in the music industry besides making sure your manager is not ripping you off" when they tell you they don't need the math.

It turns out there is a fair amount of math contained in the music industry.  There are so many ways to make money with in the field.

There is a great article on Quartz that addresses some of the issues with radio vs spotify and the royalties involved.

This article from NPR which looks at what it costs to produce a record album for a singer such as Rihanna.  It starts with the cost of writing the songs all the way to the finished album and includes the studio time, the musicians, the backup vocalists.  Everything!  This is quite an eye opener for anyone who thinks it takes just a couple dollars to produce and market the song.  I was amazed!

The Wall Street Journal has a great explanations on how much royalty is payed every time a song is played.  It turns out it is very very little so most people are not going to make much on it.  Its a really good piece.

Then New York Entertainment has a wonderful piece showing the amount of money various bands are going to take home pay for three different bands.  The information includes the amount made off a CD, Itunes, spotify, merchandising, film, video, and other sources of income.  This can provide a real eye opener as to  what the costs are.

The Tech Dirt site has a wonderful infographic on how the money is split and it turns out the band makes the smallest chunk.  Apparently for every $1000 of music sold, the average musician makes only $23.40. That isn't much, is it?

Just think what kind of project kids can do with this information.  They could even follow up on the song mentioned in the NPR article to determine how many albums were sold, downloaded, etc to get a better idea of how much she makes in royalties for the song.  This is a topic the kids should enjoy exploring.