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.  

Enjoy a Slice of Pi!

Happy Pi Day! Happy Birthday Einstein!

We are taking a break from the math books today and exploring "pi."  The following activity is simple enough that elementary students can begin to understand the magic of this number.  Please add your calculations to our spreadsheet. I would love to keep collecting data! 

Materials: 

• string
• ruler
• circular objects (at least 5)
• spreadsheet

 Activity

1. Have students collect circular objects of various sizes and shapes.
2. Take a piece of string and place it around each circular object.  Mark it and measure the length on a ruler.  This represents the circumference. Record your data on the spreadsheet.
3. Next, use the string to measure across the widest part of the circle.  Again, mark it and measure the length on a ruler.  This represents the diameter.  Record this information on the spreadsheet.
4. Have students calculate the ratio of circumference/diameter.  They should quickly see this is our magical number, 3.14!

As our children quickly found out, measure carefully! Try to be as EXACT as possible.  As an added bonus, I created a "slope" cell that will change as more data is collected.  If you were to plot diameter versus circumference, the slope of the "line of best fit" should approximate pi.  Let's see how close we can get! 

Online Resources 

• http://www.exploratorium.edu/pi/pi_activities/index.html
• http://www.onlineschooling.net/visualizing-pi
• http://www.mathgoodies.com/webquests/pi_day/
• http://www.joyofpi.com/
• http://www2.scholastic.com/browse/article.jsp?id=3749138
• http://www.eveandersson.com/pi/

Math Girl Games- The Fun Keeps Adding Up!

Math Girl Games, created by Lynn and Molly Rasmussen, recently launched Addition House adding to their popular series aimed directly at young girls.  Addition House builds on the skills explored in Number Garden allowing girls to gain confidence in math.  The beauty of this app is that it syncs with Number Garden allowing you to view both your house and your garden. 

Continuing with the right-brain approach to learning, Addition House possesses all the things you love about Number Garden.  Through game play, girls count patterns of flowers to develop visual representations of basic addition skills.  Through this method of pattern recognition, they are able to quickly move away from counting individual items to counting groups of items laying a foundation for multiplication concepts.

If that's not enough, there are opportunities for the more advanced to challenge themselves in timed play and develop fluency of their basic facts.  With each success, the player is awarded virtual "money" in which they can go shopping and decorate their house.  What girl wouldn't love that!  The shopping experience actually serves as a surprise bonus.  As the child buys and sells items for their house, they develop money skills as well. 

As with all of the apps I review, they are field tested on our children, the gymnastics team, the soccer kids and the kids I tutor.  The overwhelming response was "This is fun! I wish I could do this for math homework."  Our second grader was quoted as saying it was "addicting."  Imagine that, being addicted to learning math!  That is every educators dream!  The team at Math Girl has found a winning combination by creating a platform where young girls can develop math skills using a visually interesting and engaging game. 

Check out this series for an exciting alternative to flash cards and the traditional "drill-n-kill" approach to learning.  This is an inexpensive way for young girls to gain confidence, develop fluency and see that math is fun!

Carpe Diem! Problem Solving on a Morning Bike Ride

This weekend, I took our 6 year old for a bike ride around SELU’s campus.  Along the way, something interesting began to happen: a spontaneous, math discussion.  Let me explain!  As we were running/riding, we each pretended to do “tricks” as if we were part of the latest Mario Wii game.  60 points if mom “jumps” the curb!  50 points if Ellie “pops” her front wheel!  You get the idea.  Then, the conversation shifted from video gaming fun to a lesson in critical thinking and problem solving.  Check out our dialogue.

Mom: How many points would you score if you “popped” your wheel twice?
Ellie: 100 points.  
Mom: Great!  How did you know that?
Ellie: Well, two 50’s make 100.
Mom: Great!  Can you make an addition sentence out of this?
Ellie: 50 + 50 = 100.
Mom: Fantastic!  can you tell me the corresponding multiplication sentence?
Ellie: Easy! 50 x 2 = 100.
Mom: Super cool!  Way to go!  What if you “popped” your wheel 4 times?  How many points would you score?
Ellie: Let me think.  Well, 50 + 50 = 100 and another 50 + 50 = 100 and two 100”s are 200.  So, I would score 200 points. Right?
Mom: Wow! Great thinking!  So, 50 + 50 + 50 + 50 = 200.  What would be the matching multiplication sentence?
Ellie: Easy! 50 x 4.
Mom: Now, for the bonus round!  What if you want to score 400 points?  How many times would you have to “pop” your wheel?
Ellie: Let me see... I would just double the number of times because 200 and 200 make 400.  So, I would need to “pop” 8 times.
Mom: Wow!  I am so proud off you!  Great thinking!  You’re awesome!  What would be the multiplication sentence?
Ellie: 50 x 8 = 400.  

We rode on for a few minutes.  Along the way, I have to admit, I was beaming with delight!  She actually got it!  She clearly understands the relationship between addition and multiplication and was able to apply that knowledge to find solutions.  Yea!  My enthusiastic thoughts were then interrupted by Ellie.  

Ellie: Mom, let’s do more math.  That was really fun!  Now, I am going to do this trick for 25 points.  (She was standing up while riding her bike.  So, we called this cool move the “stand!”)
Mom: Okay, great! Cool move!  How many “stands” would you have to do to reach 100 points?
Ellie: Well, each “stand” is 25 points.  That’s like a quarter, right?  So, it takes 4 quarters to make a dollar.  So, I would need to do 4 “stands.”
Mom: Totally correct!  Now, what if you wanted to earn 200 points?
Ellie: Well, 200 is just 100 doubled.  So, I would double the 4 and get 8.  I would have to do 8 “stands.”
Mom: Super thinking!  Are you ready for the bonus round?
Ellie: Yes!
Mom: What if you wanted to score 150 points?  How many “stands” would you have to perform?
Ellie: Let me think...this one is harder.  I think I would need 7 “stands.”  No,  that’s not right.  I know it has to be less than 8.
Mom: True, but how do you know that?  
Ellie: Because 150 is between 100 and 200.  So, I have to do between 4 and 8 “stands.”
Mom: Great! Let’s think about it this way.  You said it takes 4 “stands” to make 100 and you need to get to 150.  So, how many more points do you need to add to 100 to make it to your goal of 15o points?
Ellie: Hmm...I need 50 more points.
Mom: Great!  So how many “stands” do you need to do to score 50 points?
Ellie: Oh, I get it.  I need to do 2 stands to make 50 points because they are each 25 points.  Right?
Mom: Now, you’re getting it!  So, how many “stands” do you need to perform to score 150 points?
Ellie: Let’s see.  I need 4 to get 100 points and 2 more to get 50 points.  So, that gives me 4 + 2, which is 6.  I need to do 6 “stands.”  Wow!  That one was the hardest.  
Mom: Yes, but great thinking!

At this point, she asked me what grade she would be in to do problems like that.  I told her probably third grade.  Of course, this made her smile because we are “officially” homeschooling second grade this fall.  I told her it doesn’t really matter, though.  The important thing was to focus on what she was understanding in math and that I was super proud!  We rode on for a few more minutes in silence.  Then, Ellie told me this had been so much fun.  She said she loved bike riding with me, but also loved doing math.

As a mom and educator, this really made me smile!  She LOVED doing math!  Did you catch that?  There is a great deal of conversation buzzing around about the need for schools to meet the ever-changing demands of today’s students.  One of the most essential, I feel, is to help students develop their critical thinking skills.  I love that I was afforded the opportunity to have a spontaneous, meaningful math lesson with our daughter.  Unfortunately, these moments don’t come along too often or do they?  As parents and teachers, we need to seize every opportunity to promote critical thinking among children.  Carpe Diem!  Sometimes these “moments” are designed and planned in formal learning situations.  Other times, they may simply arise when taking your child for a bike ride, on field trips or waiting with students for their bus to come.  Regardless, we should tap into the power of their imagination (and ours), establish meaningful dialogue, and create learning opportunities wherever they may arise.

Growing Number Sense with MathGirl Number Garden

The team at Icanology has done it again! After great success with their engaging math app, Arithmaroo, Lynn and Molly Rasmussen are launching a new app aimed directly at girls.  On July 16, MathGirl Number Garden will be released on iTunes.  In addition, there will be a Lite version available for free showcasing the first 4 of 12 levels. 

The format is similar to Arithmaroo in that it takes a right-brain approach to developing number sense.  The game consists of moving through 12 progressively harder levels.  The early levels of the game are geared towards preschool and kindergarten but can challenge even adults at the higher levels.  Along the way, girls will have the chance to earn stars that can be exchanged for exciting rewards like virtual bunnies, rainbows, flowers and many other objects.  These can be used to add personal flair to individual gardens! 

Also like Arithmaroo, this app takes an organic approach to learning mathematical concepts.  Colorful, everyday objects are used to represent numerical values creating visual interest for young learners.  As children interact with the game (Yes, I said game!), they are easily able to make connections between numerical symbols and the values they represent.  This provides a firm foundation upon which future concepts can grow.  Before your eyes, you will begin to see the concepts of addition and multiplication take root.  More importantly, with each success, the "I can't do math" attitude transforms into an "I can" as confidence blooms in young learners.

As a homeschooling mom of four, as well as, math educator, I can feel good about letting our children explore this new app.  MathGirl Number Garden provides a fun, educational alternative to the usual video gaming options.  This app is the perfect illustration of meaningful technology integration into the learning process.  So, go ahead, let the kids borrow your iPod.  Then, sit back and watch as they begin to cultivate a love of learning and grow in their knowledge of math.  By the way, they might have a little bit of fun!