Monthly Archives: September 2012

Tech Tools for Math Class

Below is a post I wrote for the blog portion of the Siemen’s STEM Academy website.  The site is filled with lots of great, free, STEM resources for educators, including lesson ideas and archived webinars.  I hope you can find a use for this great information in your classroom!

DISCOVER AMAZING TECH TOOLS FOR MATH CLASS:

It’s the new school year.  You have that new projector and touch board, or maybe you have new tablets for your students.  It’s time to get interactive with your math lessons.  So, what to use to get your students to experience mathematics, and move away from worksheet math?

The National Council of Teachers of Mathematics continues to add applets useful for grades K-12 in its NCTM Illuminations resources area.  The applets run on Flash and include:

  • Algebra Tiles – build, manipulate, and evaluate algebraic models
  • Fraction Models – sliders allow you to explore multiple representations for fractions, decimals and percents.
  • Factorize – explore numeric factors and their relationship to length and width

NCTM has also added a new area of downloadable Common Core Math Tools, which require java to run.  Sample lessons and how-to pages are included to get you started.  In the iTunes store, NCTM has also provided free apps geared towards elementary grades:  Pick-a-Path,  Okta’s Rescue, and Math Concentration.

Desmos Online Calculator – a favorite of mine, a tool I have posted about before, and its care-takers continue to seek your feedback to make this graphing utility better!  It has a fast, simple interface, and you can find maximums, minimums, and points of intersection with a single click.  This tool is ideal for class presentations.  A free registration allows you to save your documents.  Runs great on the iPad!

GeoGebra – a simple tool for interactive geometry, constructions, and measurements, but can provide tables and graphs for algebra class as well.  Works as a java applet, but can also be downloaded as a stand-alone program.  The caretakers are working towards an iPad app.

Sketchpad Explorer – an old favorite, the Geometer’s Sketchpad, moves to the iPad with this free app, available through iTunes.  Students can tap, drag and play with interactive sketches which come loaded with the app, or link to your iTunes store account and upload your own creations to share.

Interactivate – from Shodor, this ever-evolving collection of Java-based courseware has something for all math classes.  Learn about estimation through a virtual model of a forest fire, search for patterns in the multiples of Pascal’s Triangle, or investigate the Mandelbrot Set.

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What is Three?

A middle-school teacher’s family emergency pulled me into the classroom last week to teach an honors Geometry class to 8th graders.  Geometry…sigh….the course I always put on my “please do not ask me teach this” list during my time as a high school teacher.  And since it is the start of the year, the class is learning basic terms and definitions, all the great stuff I dreaded as a teacher.  Oh, and I have 10 minutes to plan before the kids walk in.  Ready?  And scene…..

This is the 3rd day of school.  Students have been exposed to the class rules, some algebra review, and textbooks look clean with their grocery-store paper-bag-covered  exteriors.  This is the first real geometry lesson for these kids.  I am their first impression of geometry, and the precision and argument they will experience.  No pressure.  Today’s lesson: basic vocabulary and terms.  Let’s look at the terms we need to understand by the end of today.

  • Undefined Terms: point, line, plane
  • Ray
  • Segment
  • Collinear / Coplanar points

How nice.  I drew the short straw.  Essentials of geometry vocabulary, and I get to be the boring guy.  Not the role I was born to play.

And just what are “undefined terms” anyway?  According to the textbook, these are terms which we understand, but don’t need to define.  Seems a bit hinky to me…

So how to build some discussion, based off previous knowledge, and ease our way into a structure for geometry?  As students entered, I had the following warm-up ready as they prepared to take notes:

DEFINE THE FOLLOWING:

  • Three
  • Line
  • Odd number

After some initial snickering about my strange challenge, the students took to their definitions.  So, how do 8th grade geometry students on the first day of class define “three”.  A similar response was given by a number of students:

It’s the number between 2 and 4

Thankfully, a few students identified the flaws in this definition: that, first, there are an infinite number of “numbers” between 2 and 4, and that in order to understand this definition, you need to understand what 2 and 4 mean, which seems unreasonable if you don’t know what three means.

So, should we consider “three” to be an undefined term?  Are we OK with NOT having a formal definition of “three”?  What do we need to consider?

Do we all understand what three means?

Yes, when asked to represent 3, everyone in the class demonstrated the same understanding of its quantity.

Would we expect any alternate understandings of the term, if we asked others?

Doubtful.

Would having a definition increase our precise understanding of three?

Nah, I think we all get it.  Three is three, and that’s that.

Stooges

This discussion turned out to be a nice opener to the traditional undefined terms in geometry: point, line and plane.  And hopefully a good start as these students begin to experience the logical structure of geometry.

Tomorrow, ask your students to define “Three”.  Would like to hear what they say.

SMART Notebook for iPad

This weekend, I had my first chance to toy around with the SMART Notebook app for the iPad ($6.99).  My colleagues and I have a a nice bank of Notebook files we use, particularly in geometry courses, and I am most interested in utilizing the portability of the iPad to allows students to interact with math lessons.

IMPORTING FILES:  One of the issues I have with my iPad is how difficult it can be to work with files.  But using DropBox along with the Notebook app worked quite well.  I saved a few files I use from my desktop computer into DropBox.  Choosing one of these files in DropBox on my iPad, they were recognized, and I was given the option of opening them in Notebook.  Clean and seamless.

dropbox

The instructions file included with the app also gives you guidance on how to save and open files directly from the SMART Exchange.

WHAT TOOLS DO WE HAVE?  Once a file is opened, you have a “lite” version of the SMART Notebook software.  Available tools are pen, eraser, text tool,and  photo import.  Some of the more popular and creativity-inducing features, like screen shade and the magic pen, are not available.  No drawing tools either.  Essentially, it seems easier to prepare a document on your desktop, then move them to the iPad.

Tree

Like any iPad app, Flash animations will not run, which is a bit of a downer here.  If I am thinking about ways I would like students to interact using the iPad,the manipulatives like category sort, vortex, and pairs would be most useful.  But we can still make good use of drags and movement.

angles

Protractor

WRITING NOTES:  If you are like me, then writing on the iPad is a new experience.  For small groups, my fat fingers may be fine to communicate ideas.  But the idea of the infinite page we have come to know from Notebook does not seem to be a feature here.

Fat Fingers

Equation

In the end, this app is really SMART Notebook “lite”, with the ability to look at files you have already created, edit and share them.  I see this as a nice formative assessment tool for classroom.  Imagine a Notebook file with a number of practice problems or challenges, and passing the iPad around to have students contribute their ideas.  Connecting to a projector, a class discussion of student work could then be held, as students appraise each other’s work.  I’m excited to try this with a class and observe their response to this tool.

Here are some other reviews of the Notebook app:

Tall Tales for Probability Class

Probability is fun.

Nothing drives me nuttier than boring probability units.  Endless worksheets filled with tales of balls in urns and cards being drawn from decks.  Nothing screams for fun and games more than a probability unit.  Here’s some ideas for you to try:

DRAW THE CUBES, WIN A JOLLY RANCHER!

This is a good opener for teaching dependent events.  Take a brown paper lunch bag, and place inside 20 colored cubes.  In the past, I have used 10 white, 6 red and 4 blue.  Do NOT let the students know what chips are in the bag.  Shake the bag, and travel from student to student, having each student draw 3 cubes from the bag (without replacement, or all 3 at once, doesn’t matter).  If they are able to draw exactly 2 whites and a red from the bag, they receive a Jolly Rancher reward.

Chips

After every student has had a chance to play, I add an additional challenge to the game.  Letting the class know that there are exactly 20 cubes in the bag, can they predict the distribution of colors in the bag, using the information gathered from the pulls they observed as evidence?  Students who can guess the exact distribution also win the coveted Jolly Ranchers.

Next, dump out the cubes to show the true distribution.  Was the 2 white, 1 red game “winnable”?  Was it possible to win?  Was it plausible that one would win?  I usually try to rig the color distribution so that one can win about 25% of the time.  The 10 white, 6 red, 4 blue configuration will provide a 23.6% probability of winning.

STATISTICAL TALES OF THE IMPROBABLE

Always remind your students that probability is a long-term ratio.  The 1/6 probability of rolling a five on a die does not mean that every 6th roll will be a five.  In the short term, strange things can happen.

The CBS show “The Amazing Race” provided a great probability teaching moment in its 6th season.  In a “Pit Stop”, teams must complete a challenge in order to earn a clue and move on in the race.  Here’s a summary of the challenge:

In a field are 270 large hay bales.  20 of the bales contain clues.  You must continue to roll out hay bales until you locate one with a clue, at which time you can move on.

Think about these openers:

  • What is the probability you select a bale with a clue on your first attempt?
  • What is the probability you select a bale with a clue on your second attempt?  Third attempt?
  • What is the probability it takes you 5 or more bales to locate a clue?
  • What is the probability you roll out 20 bales, and do not find a clue?

The clip from this show appears below.  You’ll love the reactions of your students!

One last example tale comes from the world of gambling.  While I try to stay away from too much gambling talk in classes, this die-rolling activity leads to a neat backstory.  Have your students roll pairs of dice, and record the number of rolls needed to roll a sum of 7.  After a 7 is rolled, start a new count.  Plotting the results in a class dotplot gives a nice example of a skewed-right distribution, which is often a new shape for our students.

In class, what was the most number of rolls needed?  I have had students get into the 20’s or 30’s.  Is it possible that it could take 50 rolls to get a sum of 7?  Is it plausible?  Note the subtle language lesson happening.

Now, on to craps.  Craps is a fairly complex game, which boils down to this for our example:  once a player rolls, they continue winning until a sum of 7 is rolled, at which point the round ends.

Meet Pat DeMauro:

Craps winner

Pat visited the Borgata casino in Atlantic City in May, 2009 and set the world record for a game of caps, by tossing the dice 154 times without rolling a 7!

Pat’s winning streak was featured in Time Magazine, and features some of the details of the record run.

Probability is exciting!  Make it so!