## Tabs

### Zombies and Math (AAH!!)

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

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

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

Zombie-based Learning

### English to Spanish Math Glossary

Featured in today's post is an elementary school level mathematics glossary for English to Spanish glossary.  This works great for many teachers who teach in a ELL math classroom or in a high population of Hispanic students.  Some of these glossary terms work great in middle and high school math classrooms.

algebraic expression       expresión algebraica
algebraic patterns           patrones algebraicos
algebraic relationship      relación algebraica
algebraic relationships    relaciones algebraicas
algebraically                  algebraicamente

algorithm                       algoritmo
divide                           dividir
dividend                       dividendo

geometric fact              hecho geométrico
geometric figure           figura geométrica
geometric pattern         patrón geométrico
geometric solid            sólido geométrico
geometry                     geometría

line                              línea
line graph                    gráfico lineal
line of symmetry          línea de simetría
line plot                      diagrama lineal
line segment                segmento lineal

See more glossary terms in spanish here: Glossary

### Paper Doll Math

I have recently blogged about Ada Lovelace and her paper doll which could be used as a history piece in a history of mathematics center that students can learn about mathematics and how math was developed back in the day.  Today, are some activities that you can use in your classroom that revolve around paper dolls and mathematics.

Patterns: Figures alternate, for example: right arm up, left arm up, right arm, left arm.

Reflections: Students love that every doll is a flipped copy of the one next to it.  Technically, that's called a reflection, one of three kinds of geometry transformation students study in elementary school, the other two being rotation and translation.

Powers of Two: Fold the paper twice, you get four figures.  Fold the paper three times, you get 8 figures.  Fold four times, you get 16 figures.  Every fold is a power of two of the figures.

Multiplying fractions: Every time you fold, the dolls become half as wide.  That's a visual illustration of what it means to multiply a fraction, in this case x 1/2.  Or, if the first fold divides the paper in half, and the second fold divides it in quarters.

View other activities and information here:
Math Manipulatives
Geometry of Folding
Probability

### Beginning of the Year Survey Questions

I'm trying to piece together a beginning of the year student survey.  What are some questions you ask your students?

Name:

Home Phone:

Parent's Email:

Activities and Hobbies:

Favorite subject in school:

Why do you like math?

Why do you dislike math?

I obviously need more questions, comments are welcome below!

### Math Movies

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

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

Harris says a growing number of public school teachers have been using the series to de-mystify math for their students. The short length of each episode, she says, makes it a good ice-breaker at the beginning of a class.
“I think often times, people feel discouraged or overwhelmed by math and science, and if we can kind of dispel the myth that it’s something that is unattainable or make it somehow more popular or accessible then that’s something I’d like to be able to do.”
You can watch the first webcast below, I recommend subscribing to the channel.

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

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

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

### GIF's that Teach Math

There are many GIF's out there that are of funny cats and of many different movies.  I know that I love the occasional GIF's and especially when they are about math.  Here are some great GIF's that you can include in your classroom to spice up lessons and activities for students.

Find more here: http://www.tumblr.com/tagged/math%20gif

Find other great GIF's here: 7 GIF's for Trigonometry

### Drawing a Circle

Can you draw a perfect circle?

I know that I couldn't, but with help from a SmartBoard game it became easier and my students loved to draw circles on the Smartboard for a great end of the year activity.

I had students put their name with their high score and by the end of the day we had a leaderboard and by the second day students were inching closer to my high score.  (Yes, I did practice for 2 hours to beat some of my students.)

It was a great competition to get students engaged and motivated in the classroom.  I hate to see teachers only using a SmartBoard as a presentation tool, it is there for students to use and manipulate.  I had some students up there for 20 minutes trying to get the tips and tricks down and finally making the leaderboard.

Check out the game here: Circle Drawing

Some of my students didn't know what the cat was there for, but it is a great reminder to tell the students how close they are to 100% like a badge.  If the students do poor enough, they get an angry cat that all the students laughed at.

### Angle of Impact

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

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

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

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

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

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

Standards: Apply content to real-world scenarios.

Time: 45 minute class.

Set-up: 10 minutes before class.

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

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

### Student Developed Apps

Who knows apps better than students?

Not too many people, so who is best for creating these apps?

Students, perhaps.

Having students develop apps is a great way of getting students creating when they are young to see if this is a possible career choice for them.  Some great articles include college students developing apps to help with algebra.  The tools assist teachers in diagnosing where students struggle and offer interactive solutions to put them on track.  One app called "Card Clutter" helps students understand the relative value of numbers by arranging cards in order with face values ranging from negative fractions to absolute numbers. Those expressions sometimes stump students when solving algebraic equations.

Others include: Recently a handful of his students tapped the touch screens in rapid fire to solve for x. "Do some 'Alge-Bingo' for me," he told Zack Sheldon, who quickly got to work.  "It makes it fun and easy," Sheldon said.  Jones said it was a great way to use her math skills, teaching skills and computer science skills at the same time.She developed the "Diamond Factor" app, which helps students factor trinomials, an algebraic expression with three terms such as x² + 8x + 16.

One great example that I want to share with you is a student at Elkhorn Public Schools who wants to take his app on the market.  It has many different incorporations in mathematics.  It is called Roll It, and you can check more of it out here: Roll It

Roll It is an app created by a student from Elkhorn Public Schools.  There is an app for it coming soon to iPads and iPhones.  But for now, you can use the online one for your students to use.  http://rollitapp.weebly.com/

Here are a few things Roll It can do:

• Roll It comes with up to 4 possible players.
• Perfect for SMART technologies.
• Comes with a random player selector to decide what player comes next.
• Four random generating dice, perfect for all games.
• Easy to use timer.
You can use any of these technologies for any game and when teachers lose parts to games like I do all the time there is an online place where I can fill in the missing pieces with online parts.  Once the app is up and running in the App Store for iTunes, students could use this at their desks for review games, stations, or even in their homes.  This is a great web 2.0 tool that all teachers can use in their classrooms.

### Forensics in Math

I have been looking for ways to get students to use math that we learn outside of the classroom and I know that some of my students love mystery books and crime scene investigation shows.  So I have obtained some extra activities for my students to do that includes some forensics work.  Here are some ways you can include forensics in math.

• Probability is the chance of something occurring.  It is calculated by dividing the number of favorable outcomes by the number of possible outcomes.  The theoretical probability of how a coin will land after being tossed 100 times is half. 50/50, if you actually flip a coin a 100 times, you will find the experimental probability, which may be 60 heads and 40 tails, whatever your result.
• Ask students to define probability.  How high does the probability occur for a conviction to occur?
• Regardless of their specialty, scientists use mathematics to help describe the world around them.  Forensic investigations use average growth rates of various structures in the human body, such as hair and fingernails, to decode clues left at a crime scene.  When using average growth rates, it is important to pay close attention to the units of measurement being used.
• To illustrate how blood types are inherited, show a cross between a mother who has blood type O and father who has type AB.  The mother can contribute either an A or a B allele.  So this couple could have children of either blood type A or B.  Point out that the child would have a probability of 1 in 2 of having type A blood.
• Explain how the laws of probability are used in determining the probability that a particular person's blood will match the blood found at a crime scene.
There will be more activities included in the future.  Right now these are just a few questions to have your students use forensics in these questions.

How could you incorporate this in to your classroom?

### KUCE Taxonomy and iPad Apps

I recently blogged about the KUCE Taxonomy and what it is all about here: KUCE Taxonomy

Now is the time that I mention some iPad Apps that can be used when using the KUCE Taxonomy.  All of these apps fit great with 21st Century learning in all of the classrooms.

For a quick review session:

K: Know

U: Use

C: Create

E: Evaluate

These are the quick steps that let me know that a student is proficient for a particular concept or section I am teaching in the math course.  If a student can successfully go through each step the know the content, how to apply it, and be able to create with it as well.

Featured below are some shots of apps, I will briefly mention and move along.  I am a math teacher so most of these apps are based on the math classroom, there will be more apps later for elementary and middle school.

Know

These are the few knowing apps where students can gain knowledge through these apps.  The first on the left is Britannica Kids on Volcanoes where students can learn and watch videos about Volcanoes.  The next two are math related which are Khan Academy and DragonBox where students can learn more about math.  Next is Gooru where students can learn bits of sections that lead them to learning an entire amount.

Use

This next app is Maps and History where students can use their knowledge of maps and keys to put their knowledge to the use of getting familiar with maps.  The next two are also math related, in both of these students use their knowledge that they gained to practice problems all the way to finding real-world problems that they can solve.  (MyScript Calculator and WolframAlpha)

Create

This is one of my favorite sections where students use the knowledge they gained and create.  Students can use these apps to produce and send via the web on apps like EduCreations and ShowMe in video form for anyone to watch.  The next app is Aurasma where students can create augmented reality videos in format with the camera on the iPad and watch their videos in a 3D environment.

Evaluate

This last section is evaluate where students can evaluate each others work on the web.  Using apps like Linoit where students can post what they liked and disliked.  Socrative, where students can vote on their favorite creations.  YouTube where uploaded videos can be watched and evaluated by other students.  Lastly, KidBlogs has an app where students can blog and have their teachers, peers, and family members evaluate their work.

This is just a few of the apps that fit in these niches, if you have any apps that you use and where they would be placed on the KUCE Taxonomy please feel free to comment below.

### Dueling with Math Snowballs

A great lesson idea stems from Jenna Krambeck at Elkhorn Ridge Middle School in Elkhorn, NE.  (You can visit her site here: http://elkhornbltf.wikispaces.com/ )

Dueling with Math Snowballs, now she is a reading teacher at Elkhorn so I have adapted this lesson from her.  You start with a simple snowball fight.  Students write down math problems on a half sheet or full sheet of paper and students fling their paper across the room.  For more math snowball information check it out here.

To put this in perspective, students are in groups and it is their job to solve the problem.  First team with 5 points wins.

The game proceeds as a student from a particular group walks up and picks up a piece of paper and challenges a group to solve a particular problem.  If they get the problem correct they get a point, if they guess incorrectly the team who selected the problem has a chance to steal.

This is dueling, because the student has the choice of selecting a group to send a problem to battle.

Could you use this small review game in your classroom?  What could you change to better adapt it to your students?

### Design your Lesson around a Game

I was in a global math department "hangout" the other day.  One of the teachers presenting provided a great professional development opportunity for teachers to take to their teams and get feedback from students on how their lesson went.

The professional development looks like this:

go to a charity shop, find a game, design a lesson around it.

The teacher who presented found a game at a charity shop that was Marble Run.  A marble takes turns round and round and the students had to find the plot the graph for distance vs. time.  This is a great graphing stories, an extension of this activity is having students create posters with the plots.

This shows that any teacher can go out and design a lesson around a game they find for cheap.  I have found many other teachers using these same ideas for using games around the classroom.

What games do you use in the classroom?  Do you think you could use a game around a lesson next week?  Could you do this with the faculty you work with?

Check out global math department videos here: https://www.bigmarker.com/GlobalMathDept

### Forgetting Proofs

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

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

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

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

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

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

### Using Instagram in Math Class

Instagram is a free, fun, and simple way to make and share photos on the iPhone and iPad.  Students pick from one of several filtered effects to breathe new life into mobile photos.  Students can transform everyday moments in the classroom in see and to works of art.  Students can show photos in a simple photo stream with friends, classmates, teachers, and family.

There are some examples below where you can use Instagram in the classroom:

Problem Solving
Turn a dry subject with numbers and formulas, and connect it to art through visual expression. Younger students can capture mathematical concepts through visual problem solving re-enactments (like word problems) or even snapping photos of complex formulas designed on poster board.

Classroom Account
Every month, take a few photos of the student’s progress. Families can follow the classroom account and keep up with what their child is learning and doing.

Teacher Photos
Parents and community members love to know about the teachers who work in the schools. Have the kids interview all the teachers in a school, writing up a bio of each instructor and tagging a photo of them on Instagram. The filters make even the poorest photos look professional! You can take pictures of homework questions or even some of the answers to the problems.

Math in the Real World
Similar to digital storytelling, this would allow students to explore issues in their world through a visual medium. I want them to engage in citizen journalism. Students can use the mobile devices to express their social voice and find math in the real world by tying together photos of math concepts and definitions.

Math Prompts
Last year, I found photographs and created writing prompts. Sometimes, they were geared toward poetry or narrative while other times they were persuasive or informational. I will encourage students to develop their own photo prompts using Instagram.  Having photos where students come up with their own math story problems by a photo.

Metaphors in Math
I will give students concepts from any of the subject areas and ask students to find a metaphor that fits the concept. They will use Instagram to find the metaphor and then describe it in the comments section.

What ways can you think of where you could use Instagram in your classroom?  What other types of iPad applications do you use in the math classroom?

Check out two sites that offer educational ways of incorporating Instagram into the classroom below:
10 Instagram Ideas
Creative Ways of using Instagram

### KUCE Taxonomy

I was trying to think of ways of implementing more Bloom's Taxonomy in my classroom and I had an epiphany.  Bloom's Taxonomy is dated for 21st Century learners and does not give students the freedoms of a classroom atmosphere for the real-world.  So I came up with my own taxonomy: KUCE Taxonomy.  It takes bits and pieces from Bloom's along with some adaptations of my own.

K: Know
In Bloom's Taxonomy the first two base stages of the pyramid are remember and understand and if you combine these two bases together you get know. Students remembering and understanding the material is normally done in one or two days depending on the material.  Students in most classrooms listen to lectures and either understand or don't.  In my classroom I want students to know the material and be able to get to the next step in the learning process as quickly as possible.  I believe that knowing something is just the first step in the process of learning.

U: Use
Again in Bloom's Taxonomy the next two steps in the pyramid are Apply and Analyze, in my understanding this is using the material that you know.  After students know and understand the material, I want them to use the material in my classroom, in the picture below of the actual taxonomy it is semi-broken down into two different parts: examples and real world.  I put a wavy line between the two, because you can use different ways of using the material and sometimes it may not be examples or going as far to the real world, but the line is blurred and in my classroom I want to have students come up with examples and once they have mastered using examples I want them to learn how to use this information in the real-world.

C: Create
Once students know the material and can use the material, the next logical step is create and in Bloom's Taxonomy this changes a little bit (Bloom has it at the pinnacle of the pyramid).  Once again I have semi-broken down the creative stage in to two parts: local/community and global.  For 21st Century learners, students need to be able to apply their knowledge in their community and globally, students need to be informed citizens and care about the world they live in.  The arrows are in their, because students need to be moving in the direction of global learning and thinking about others outside of their local bubbles.  In my classroom for example, students might create a presentation for the classroom then students set up either a website to take their use of knowledge to the next level the global web.  In other classrooms it might be researching tyrannies in other parts of the world, not just their own backyard.

E: Evaluate
At this point, in my classroom, students have mastered the material.  They have become small masters of the material and once they have completed something on the global scale they can evaluate others work.  This might be in the sense that they can evaluate a math website for mistakes or in other classrooms students are able to evaluate other governments for flaws and successes other than their own.  Students become well-rounded and are able to make decisions on their own from the previous sections of knowledge.  They know the material, use it, created their own projects, and are now prepared for the real world.

Now that you have most of the information the KUCE Taxonomy is built for life-long learners in a pluralistic society, students are well-rounded and prepared for anything.  This system of learning in schools is not adopted yet, but I hope to think that master teachers and reformists in education are built towards this style of learning.  I believe that children are built for learning new things, just not in the classroom but on their own.

The last thing I want to include is the shape I built in for the taxonomy.  The trapezoid shape is developed not only for time students should be spending on each stage, but learning increases as you go up the ladder.  In Bloom's Taxonomy it is a pyramid with a point top, for me this is where learning stops.  In the KUCE Taxonomy it has a open top, learning never stops.  As teachers, we know this all too well.

If you have any comments or suggestions about changes to the taxonomy, please post them below.  How do you think learning would change with these steps instead of Bloom's?  How do you think you could shape your curriculum to fit these stages?

### Calculating Weather Probability

When multiplying decimals or percentages in your classroom a great way to incorporate real-world scenarios is how weatherman get their predictions of a percentage of rain in your area.  Take for example the 7 day forecast located to the right.

There is a 30% chance of rain on Saturday, how did they come up with that percentage.

Forecasts issued by the National Weather Service routinely include a "PoP" (probability of precipitation) statement, which is often expressed as the "chance of rain" or "chance of precipitation".

An example of this
ZONE FORECASTS FOR NORTH AND CENTRAL GEORGIA NATIONAL WEATHER SERVICE PEACHTREE CITY GA 119 PM EDT THU MAY 8 2008

GAZ021-022-032034-044046-055-057-090815-CHEROKEE-CLAYTON-COBB-DEKALB-FORSYTH-GWINNETT-HENRY-NORTH FULTON-ROCKDALE-SOUTH FULTON-INCLUDING THE CITIES OF...ATLANTA...CONYERS...DECATUR...
EAST POINT...LAWRENCEVILLE...MARIETTA 119 PM EDT THU MAY x 2008

.THIS AFTERNOON...MOSTLY CLOUDY WITH A 40 PERCENT CHANCE OF SHOWERS AND THUNDERSTORMS. WINDY. HIGHS IN THE LOWER 80S. NEAR STEADY TEMPERATURE IN THE LOWER 80S. SOUTH WINDS 15 TO 25 MPH. .TONIGHT...MOSTLY CLOUDY WITH A CHANCE OF SHOWERS AND THUNDERSTORMS IN THE EVENING...THEN A SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS AFTER MIDNIGHT. LOWS IN THE MID 60S. SOUTHWEST WINDS 5 TO 15 MPH. CHANCE OF RAIN 40 PERCENT.

What does this "40 percent" mean? ...will it rain 40 percent of of the time? ...will it rain over 40 percent of the area?
The "Probability of Precipitation" (PoP) describes the chance of precipitation occurring at any point you select in the area.
How do forecasters arrive at this value?
Mathematically, PoP is defined as follows:
PoP = C x A where "C" = the confidence that precipitation will occur somewhere in the forecast area, and where "A" = the percent of the area that will receive measureable precipitation, if it occurs at all.
So... in the case of the forecast above, if the forecaster knows precipitation is sure to occur ( confidence is 100% ), he/she is expressing how much of the area will receive measurable rain. ( PoP = "C" x "A" or "1" times ".4" which equals .4 or 40%.)
But, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that, if it does occur, it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. )
In either event, the correct way to interpret the forecast is: there is a 40 percent chance that rain will occur at any given point in the area.

Explaining "Probability of Precipitation": http://www.srh.noaa.gov/ffc/?n=pop

You can have your students multiple percentages and come up with their own weather forecast for the surrounding area for the next couple of days and see if the weatherman in your area are more accurate at predicting than you are.

Other ways of incorporating weather into the math classroom are below:

Do you think you could put more real-world scenarios in your classroom?  Is this a good example to start with in your room?