Negative Weather Math

Our family spends a great deal of time in the car.  Like any neurotic mom, I find "car time" to be the perfect place to practice basic facts.  I am always calling out capitals, math facts and spelling words.  Our kids seem to love it and it adds some fun to the tedious task of learning these basics.  

Last week, I had a rare moment alone with our Kindergartner. On our way to soccer practice he asked me to play a math game with him.  Music to my ears!  We began with basic addition and subtraction facts.  After a few minutes, he asked me if we could learn something new.  Again, music to my ears!  So, I thought I would push the envelope, negative numbers.  Here's how the conversation went:

Mom: Andrew, let's pretend we live in Barrow, Alaska.  Okay?

Andrew: Ooooh, it's really cold up there!  I'll need my fuzzy hat.

Mom: Yes, you will!  I am so glad you brought up the weather.  I want to ask you some questions regarding temperature.  Let's pretend the temperature outside is four degrees Fahrenheit.  

Andrew: That is so cold! I bet it's snowing.  I wish it would snow here!

Mom: Me too!  After the sun went down, though, the temperature dropped five degrees.  What is the new temperature?

Andrew: Let's see.  I start at four and go back five places. (Note: I teach addition and subtraction using a number line.)  So, that would be three, two, one, zero.  Zero!  Is it zero?

Mom: Well, let's see. If we start at four and go back to zero that's only four places.  Remember, the temperature dropped five degrees.

Andrew: Oh yeah, that's right.  Well, three, two, one, zero, negative zero.  No, no.  You can't have a negative zero.  Negative one.  Mom, is it negative one?

Mom: Wow, very good!  Yes, it is!  How did you decide on the answer negative one?

Andrew: Well, it can't be zero.  I knew it had to be below zero.  So, I thought about negative one.  Can we do another one? I like this negative weather math game!

Like any good mother we continued to do several more problems.  Andrew was so excited and proud of himself! He knew he was doing "big boy math" and couldn't wait to share the good news with his older brother and sisters.  As a math teacher, I was excited because a door has been opened.  

As I worked through several weather examples with our five year old, I began to wonder why we wait so long to introduce the concept of negative numbers.  Sure, he may not have an expert understanding, however, a foundation as been laid.  During our conversation, he mentioned that he had heard of negative temperatures on television.  When trying to solve the original problem, he was able to draw upon that prior knowledge and apply it to a new situation.  Very exciting!  As someone who works with many Pre Algebra and Algebra students, I know negative numbers can be a stumbling block causing hours of anguish.  With our children, I have chosen to introduce the idea early fending off future fears.  Hopefully, the forecast will be sunny and bright!

PS I am currently creating K-4 materials centered around our "negative weather math."  I'll share when finished.  

Get Moving with Motion Math

Motion Math is a revolutionary, movement-based learning app and winner of the Editor's Choice Award for Excellence in Design from Children's Technology Review.  All I can say is, WOW!  The first game in this series centers around fractions. The learner is asked to equate different representations of fractions by bouncing a sphere to the correct place on the number line.  In order to do this, you must actually tilt your iPad, iPhone, or iPod Touch in the direction where you desire the ball to go.  You must think quickly and accurately to obtain the best outcome!

This game was originally developed by the Stanford School of Education and embodies their research in the area of cognition.  Simply stated, they found that connecting a person's physical body to abstract concepts creates a more positive, successful learning outcome.  Motion Math allows the learner to interact with difficult concepts by connecting learning with game play. 

As a math educator, I know fractions are often a concept many students find difficult to grasp.  This app provides practice in making connections between different representations allowing the learner the opportunity to build a solid foundation.  I highly recommend this as a fun alternative to traditional math drills.  Our third grader said he "wished he could do this for math every day."  Our fifth grader agreed by saying she found the game "addicting" and an "fun way to improve her fraction skills."  Motion Math is an excellent way to integrate technology in the classroom or learning environment while giving students a meaningful, yet fun, math experience.

Ahoy, Matey! Let's Celebrate!

 

We like to have a lot of fun around here and what better way than to celebrate "Talk Like a Pirate Day" on September 19.  Why is this great? 

Check out the top 5 reasons below:

1. Your family can learn a forign language quickly because there isn't an extensive vocabulary or difficult phonetic principles to learn.  Check out Lego.com for a Pirate Dictionary.
2. You get to wear really cool accessories and you can get a jump start on your Halloween costume.
3. You can have family movie night and watch Pirates of the Caribbean - The Curse of the Black Pearl (Two-Disc Collector's Edition)
4. You don't have to wait in long lines at the Hallmark store to purchase a card.  You can simply download one from Flickr.
5. Who doesn't like a good scavenger hunt?

Seriously, this could be a fun, out-of-the-ordinary day to surprise friends, family, and students.  Check out the links below for other great ideas on how to integrate in the classroom or for activities to do at home.

• Geeky T-Shirts
• Pirates in the Classroom
• A Pirate's Life
• Pirate's Theme Page
• Pirate Map Lesson Plan
• Pirate Adventures from National Geographic
• Quest For a Pirate
• Pirates at the National Maritime Museum
• Pirates of Whydah
• Blackbeard the Pirate
• The Mystery of Pirate Ringold's Lost Treasure
• Pirate Classroom Activities
• Place Value Pirates

Have fun!  Fair Winds, Matey!

Hey Dad, How Far Is a Light Year?

After watching an episode of "The Universe" yesterday, the wheels beagn turning inside our fourth-grade daughter's head as she struggled to comprehend the vastness of space.  The conversation went something like this:

Abby: "Mom, how far is a light year?"

 Dad: "It's about 9.46 x 10¹⁵m/sec.  Just round to 9.5"

Abby:  "Okay, what does 10¹⁵ mean?  What is that little number above the ten?"

Mom:  I leave and get a sheet of paper and a pencil and proceed to write down the following:

  10⁰ = 1
  10¹ = 10
  10² = 100
  10³ = 1000
  10⁴ = 10,000

          "Abby, do you see a pattern?"

Abby:  " Hmmm...Well, it looks like the numbers get bigger."  (Abby continues thinking about things.)

Mom:  "What do you notice about the number of zeros in relation to the "floating number thingy?"

Abby:  "Oh, they match.  The number of zeros match the little number.  You're adding, right?"

Mom:  " Good, let's call the "little, floating number" an exponent.  Also, you're not adding.  Look at 10² = 100 and tell me what you think it means." 

Abby:  "Oh, it's 10 x 2.  So, the answer is 20."

Mom:  "No, it can't be 20 because I already told you it was 100.  Keep thinking!"

Abby:  "Okay, it's 10 x 20.  No, that's 200.  I get it!  It means you have a ten, two times."

Mom:  "Good, now you're on to something.  So, 10² = 100.  What does 10³ mean?"

Abby:  "100 x 3.  No, that's 300.  Oh, 10 x 10 x 10.  I get it."

Mom:  "Now, think about this one.  What does 3² mean?"

Abby:  "It's 3 x 2. So, the answer is 6, right?"

Mom:  "Abby, look up at what you discovered earlier.  Keep thinking!"

Abby:  "Oh yeah!  It means you have the number three, two times.  So, it is 3 x 3 or 9, right?"

Mom:  "Yes!  Great job!  Now, let's learn a new word.  The "3" is called the base and what was the "floating number called?"

Abby:  "The exponent."

Mom:  "Right!  So, can you explain how this would work regardless of what number you are using?"

Abby:  "Hmm... Well, the exponent tells you how many bases you have and then you multiply.  So, 4³ means 4 x 4 x 4 or 16 x 4 or 64.  Right?"

Mom:  "YES!!!!!!!"  (Shouts of joy fill the room.)

Abby:  "Dad, so let's go back to the light year problem.  Just how far is it?"

 Dad:  "Well, it's 9.46 x 10¹⁵ m/sec.  So, we have this:

1 light year = (3 x 10⁸ m/sec)(365 days)(24 hr/1 day)(60 min/ 1 hr) (60 sec/ 1 min)

Abby:  "What exactly am I supposed to do with this?  You want me to multiply all of that out?  How?"

 Dad:  He proceeds to explain the dimensional analysis and how things simplify to 9.4608 x 10¹⁵ m/sec.

Abby:  "So, that would be 9.4608 x 1,000,000,000,000,000.  Right?  Wow!  That's pretty a huge number!"

After this, I continued giving her a few problems to simplify.  She was really excited and thought it was actually "fun."  Wow!  I proceeded to tell her it does get more complicated when you start talking about negative exponents.  In true "mom fashion", I just had to show her an easy example.  So, I wrote 3^-1 = 1/3.  Again, her curiosity was sparked and we did a few more.  All in all, I feel really happy.  An educational moment presented itself and we ceased the opportunity to explore.  Carpe Diem!  I seem to be saying this a great deal lately. 

 Anyway, I feel whether you are homeschooling or in a regular classroom.  It is important to not veer away from a learning opportunity.  Did I ever imagine I would be discussing exponents with our fourth grader?  No, well, maybe.  As teachers, we should be aware of teachable moments and capitalize on them.  So what, if it deviates away from the "current lesson" or topic.  Take a chance and go with it!  Everyone may benefit in the end.

"The Secret Key" to Learning

"Good Afternoon, Alderbash School! ..... I am here today to give a talk.  The title of my talk is My Secret Key to the Universe."

What is the "secret key?"  According to George it is.... PHYSICS!  I can just see my husband doing backflips in his office right now!!  Physics is a word that comes from the Greek, physis, and means nature.  Quite simply, physics is the analysis of nature in an attempt to make sense of the world, or more correctly, the universe in which we all live.  Being one of the oldest disciplines, physics is often intertwined with an understanding of mathematics, chemistry and even philosophy.  Advances in physics often serve to benefit other disciplines and technologies.  In other words, it appears that George was right!  Physics is a secret key to the universe explained through our models and fostered by an atmosphere of inquiry.

While most of us can safely say we lack the ability to space travel via a supercomputer named Cosmos, we do have other opportunities in which we can challenge our students, our children, and ourselves.  His mentor, Eric, actively engages George and Annie in his research.  He is not afraid to tackle the big issues and finds no need to "dumb down" the material.  He provides them opportunities to have real discussions, real experiences, and construct real models.  In other words, Eric facilities their learning by allowing them to actually "do" science.  

This is exactly the situation our brave hero, George, finds himself.  Throughout the book, George is presented opportunities to experience science.  He is doing more than just reading about it in a textbook.  He is actually living it, feeling it, and actively engaged.  He hurls through space on the head of a comet.  He touches the origins of our solar system as he drifts through the rings of Saturn.  He feels the gravitational pull as he and Annie fly past Jupiter.  He feels the bombardment of the asteroids as he passes through the asteroid belt heading home towards earth.  His experiences not only inspire but provide a foundation upon which he is able to construct knowledge.  

As teachers, we need to breathe life into our teaching so that students can have similar opportunities.  Think about it!  How can you make math come alive?  How can students relive the Middle Ages or explore New Worlds?  What can you do to stimulate interest and create an atmosphere of inquiry?  There are those who are already striving to break through the barriers and revolutionize teaching.  Check out dy/dan and his method of WCYDWT.  There are more resources available to us now than ever before and it is truly exciting!  

In the beginning of the book, Eric sparks George's curiosity in science by performing a simple experiment in which he uses static electricity to bend water.  It was not expensive and the materials were right in his own kitchen.  He just took the time to cease a learning opportunity.  Carpe Diem!  Whether you choose to stream live podcasts into the classroom (or home in our case) or perform a simple experiment in your kitchen, educators must find a way to stimulate creative thinking and get kids excited about learning.  How exciting it would be to create a "living classroom" where teaching and learning are organic and always evolving.  The "secret key" to the universe may be physics, but I think the "secret key" to learning is curiosity.