Thursday, October 10, 2013

Mixing Stuff Together is the Beginning of Chemistry

   Jesse and Salina are the proud parents of three-year old Faith. Salina is a stay-at-home mom and dad is a videographer and video editor for an educational foundation. Salina daily organizes a variety of learning activities for Faith. They recently emailed grandadscience pictures of a mixing activity that Faith had a lot of fun doing and learned a lot about the world she lives in, the stuff in it, and what can happen when stuff is mixed.
   Very young children, children not yet in school, live in the real world full of stuff they are just learning the names for. As they move around in this world—hopefully a world that looks like play)—their five senses are delivering a constant stream of data to their very open and receptive minds. As parents and grandparents out task is to populate this world with as many learning activities as possible.
   Here’s a science-play learning activity Faith and Salina did together that you might want to do with your child or grandchild.
Mixing the stuff of the world together has been going on for thousands of years. In fact, alchemists—the first chemists— tried mixing everything yellow they could find in the hopes of making gold!
   All you need for Faith’s chemical exploration is baking soda, vinegar, food coloring, small bowls or cups, and plenty of paper towels, and a mom, dad, or grandparent.
   Young children are most at home on the floor and that’s a great place for this exploration. A mop will easily and quickly clean up any spilled cups or bowls.  Here, Faith is cleaning up after mixing ingredients.
   Starting with vinegar in a bowl, Faith added food coloring to the vinegar to give the mixture the brownish-orange color.
   In the first picture, Faith has added baking soda to the vinegar in the bowl. In the second picture, fizzing has started. Fizzing indicates a gas is being released and the bubbles due to the fizzing are an indication that a chemical reaction is taking place.
   In the next two pictures the fizzing reaction is spreading and creating a yellowish color to the mixture in the bowl.
   As you can see in the last two pictures the reaction is almost finished.
   In this exploration, a lot of mixing has occurred; food coloring has been mixed with food coloring, food coloring with baking soda, food coloring with vinegar, and baking soda with vinegar. Some of the stuff is liquid, some solid. The liquids have different colors and the solid is in powdered
   Every mixing operation has resulted in a color change but only one mixing, baking soda and vinegar, has resulted in the bubbling and fizzing that is an indication that a chemical reaction occurred.
   No matter the age, it’s always a good idea to have kids record, in whatever way makes sense to them, the steps used in an exploration and the results of the exploration.  After all, If Edison hadn’t kept a list of the 900 plus substances he tried as the filament of his light bulb, he would have waste time by repeating experiments that were known failures. In that spirit, I’ve created a Mixing Stuff Together page for just this purpose. Adapt the form to fit your needs. Here’s a picture of the page.
   For a free PDF file of this page just email a request to
   Thanks to Jesse and Salina for sharing Faith and her exploration with those that drop in to read this blog.
   By the way, I’m sure you are anxious to know that adding baking soda to vinegar creates the compounds sodium acetate, water, and carbon dioxide. The carbon dioxide is the gas bubbling off and the sodium acetate is in solution with the water.

Sunday, August 4, 2013

Joshua's Robotic Arm Project

   Every summer we look forward to the annual week-long visit of  our two oldest grand kids, Joshua and Jordann. We pack as many activities into that week as we can. 
   I planned to teach both kids how to play chess (to be described in a later post) and I selected a construction project for Joshua and grandmothermath did the same for Jordann.
   On the second morning of their visit we drove over to Hobby Lobby and purchased craft kits to work on in the hours between other activities, like going to a movie or watching old Abbot and Costello movies at home.
   Joshua picked out an inexpensive ($20) Robotic Arm kit. And I selected a working model of Leonardo da Vinci's design concept for a helicopter.
   We sat together at a table and each worked on our own project. Both kits contain high-quality wood structural components that are finished to the point of requiring little or no sanding. Even a tube of white glue is included in the kit. The only item not included in the kit is a metric ruler needed to identify the lengths of wood dowels.
   Here is a video of Joshua's completed project. He did all of the work himself and you can imagine his satisfaction when the arm worked as described, the first time!  
   The three-axis arm is actuated using water-filled syringes and therefore models a hydraulic-operated system.
   Here is a picture of the completed helicopter kit. Turning the crank rotates the 'aerial screw' and again, it's a wonderful and easy-to-build working model.

   Both kits are marketed by the same company and can be purchased at Hobby Lobby stores or online. Here's the link to the pathfinders web site.
   We will be purchasing and building many of the other pathfinder kits.
   Once Joshua returned home he showed the robot arm to friends. In the following video his friend Mitchell is operating the arm to deliver a spoonful of ice cream to Joshua.

   Well done Joshua!

Saturday, June 22, 2013

Teaching Kids to Program in Scratch

      Our son Patrick is a computer professional holding a high-level IT position. He's responsible for keeping a large, distributed network of computers that handle important documents, up and running and secure. 
   His first computer experience was in the early 1980s when I brought home a Commodore PET (Personal Electronic Transactor) with a whopping 8K of memory! It had a tiny keyboard and a cassette tape player for saving and loading programs. There weren’t many programs so we wrote our own and copied others from magazines.
   The school that his two children (our grand kids) now attend has a computer lab. He checked with the instructor and found out that the software they use is limited to a typing-tutor and Microsoft Word. There, in the heart of the Silicon Valley, the kids were learning no more about the creative applications of computers than native children, living deep in a tropical rain forest, that have never seen electricity much less a computer.
   After numerous conversations with school staff it became apparent that there was not any interest in providing a creative computer curriculum for the kids.

   Never one to be held back, Pat located an area where he could set up tables, roundup computers, and open a classroom.

   Copies of the excellent introductory book, Super Scratch Programming Adventure!, available from the No Starch Press, Inc, were ordered and received.
   I can not improve on this description of the book, as taken from its back cover.
   “ In Super Scratch Programming Adventure!  kids learn programming fundamentals as they make their very own playable video games. They’ll create projects inspired by classic arcade games that can be programmed (and played!) in an afternoon. The book’s patient, step-by-step explanations of the code and fun programming challenges will have kids creating their on games in no time. This full-color comic book makes programming concepts like flow control, subroutines, and data types effortless to absorb. Packed with ideas for games that kids will be proud to show off, Super Scratch Programming Adventure! is the perfect first step for the budding programmer.
   Scratch 1.4 has been updated to Scratch 2.0 but all Scratch 1.4 programs run in Scratch 2.0 so I still recommend the book.
   I call grandson Joshua first attempt to create his own program outside of the class The Spider and the Pesky Fly. In the Paint Editor, Joshua drew a spider web for the background. He also drew a fly and a spider. Both are sprites, programmable characters that move over the background. Sprites (and the programming blocks that control them) are what makes writing games, science simulations, art projects, animated stories, etc. so much fun.
   In his program, the spider chases the fly around the web. Sound can be recorded directly into Scratch using the microphone in the computer or uploaded from music and sound files.
  What makes all the action happen are the programs that control the sprites. Here are the the two scripts Joshua wrote for his project. One for the spider and one for the fly.
   The point missed by the majority of educators is that you can't program, in any language, without math! In his scripts, Joshua used the Cartesian plane (x-y coordinate system), [turn x degrees] blocks, [move forward x steps] blocks and event reporters.
   Much was learned by the kids in Pat's class and he is already planning the direction for the next series of meetings.
   Over 4 million projects have been uploaded to the Scratch web site. Scratch is located at MIT. What better recommendation do you need?
   If you would like to explore Scratch, here's the link.
   If you would like to download Scratch 1.4, here's the link.
   I also have a blog devoted to Scratch. View it at
where I also provide free PDF files for most of my projects. The files discuss in detail the mathematics and programming contained in the project.
   You can also view My Stuff on the Scratch home page by searching on popswilson.

Wednesday, May 22, 2013

Gillian Solves the Soma Cube Puzzle!

   The smile on her face, the gleam in her eyes, and the thumbs-up tells us that seven-year old Gillian has just successfully put the seven pieces of the Soma puzzle back into a cube. The personal joy achieved by solving a difficult problem is, in my opinion, best expressed by Danish polymath Piet Hein, in his famous aphorism,
   Well done Gillian!
   There is nothing better for bolstering a person’s self-esteem than for that person to solve a difficult problem. Self-esteem is earned, not awarded
   Engaging with three-dimensional puzzles helps develop persistence and exercises the spatial visualization and problem-solving skills so important in the arts and sciences.
   Those are reasons enough for us to be sure that our kids and grand kids have puzzles like the Soma cube to learn from and enjoy.
   The Soma puzzle is available on the Internet or you can glue wood cubes together to make each of the seven pieces as shown in this diagram.

   If you would like drawings of more Soma structures (other than the cube) to build, send an email request to
and request one or both of these pdf files:

Soma Structures I and
Soma Structures II.
   Also, check out the previous blog posts that tell about three other youngsters, Malachi, Asher, and John, and the problems they explored using the seven Soma pieces.
• May 2009 – Malchi’s Soma Cube
• June 2009 – Asher’s Soma Pieces
• April 2010 – John’s Soma Towers

Sunday, March 10, 2013

Fly to Learn!

   Our two oldest grand kids, Joshua in grade 6 and Jordann in grade 5, have just had their first in-flight, flying lesson. Along with friends Tyler and Bryan, they successfully completed an aviation program, called Fly to Learn, developed and taught by Pat, Jordann and Joshua’s dad The culminating event of the program was for each of the four, to have their first flying lesson, one at a time, with a  CFI (Certified Flight Instructor). Here is an aerial shot of the school they attend.
   When Pat (our son), was in third grade, a teacher we knew took him flying in a Piper Archer. That experience eventually led to Pat getting his private pilot license. The husband and wife flight instructor team that soloed Pat and led him to getting his Private Pilot License, are among the most influential teachers Pat ever had.
   As grandparents, it is a special thrill to know your son and his wife are motivated to provide exciting learning opportunities for their kids. Joshua and Jordann will most likely have goals in life other than becoming professional pilots but the experience of flying with a flight instructor gives them the opportunity to spend time in the adult world and to apply the mathematics and science learned in the classroom.
   In naming the program, Pat reversed the invitation, ‘learn to fly’, to the education-focused Fly to Learn!. He had the kids use the popular computer flight simulator X-Plane X (for the PC and Mac) to learn the basics of flying a virtual airplane. Using a joystick to control a virtual airplane in flight, the kids learned that the rudder pedals control yaw (nose left-nose right), the elevator and throttle controls pitch (nose up-nose down), and the ailerons control roll (roll right-roll left). 
   After learning the basic flight controls and before ever getting into the left seat of the real airplane, they also learned the names and functions of the six instruments that make up the primary instrument group.  They practiced at the computer reading these instruments and observing how the instrument readings changed as they flew the virtual airplane..
   Here is a picture of Joshua in the air, in the real airplane, flying the airplane with the primary instrument group outlined in red, in his direct line of vision.
   Starting in the upper left corner of the red box and moving clockwise is the airspeed indicator, artificial horizon, altimeter, vertical speed indicator, heading indicator, and bank and turn indicator. The kids know that theses instruments (during a phone conversation I asked Joshua to name them for me and he did) tell them the orientation of the airplane and the direction the airplane is heading.
   In this picture Jordann is finding the horizon visually and clearing the airspace for a coordinated aileron and rudder turn to the right. Along with straight and level flight, mastering coordinated turns are first on the skill list. 
  The flight instructor, also named Pat, is in the right seat. The airplane has dual controls so he is always there to assist the student pilot.
   If a youngster is big enough to sit in the seat and reach the rudder pedals he or she can take flying lessons. But you have to be 18 years old to skydive. Joshua and Jordann’s mom and dad are also skydivers. Will the kids ever get a pilot’s license? That’s a few years in the future but who knows, they may not only want to fly airplanes but also want to learn how to jump out of perfectly good airplanes!
   Now it’s Joshua’s turn to do a coordinated right turn. Learning to fly the airplane by visual inputs provided by looking out the window comes before building instrument flying skills.
   Bryan is buckled in with the engine running and ready for his flight lesson. He and instructor Patrick check for traffic to the right as part of preparation for takeoff. Next, Bryan in the air, at the controls, soon after takeoff.

   Tyler getting ready to taxi out for his flight of the day. Unfortunately I do not have any in-flight photos of Tyler.
   The kids received a framed ‘diploma’ after completing the computer training, ground school, and the first flight lesson. Jordann must have taken the picture because she received a framed diploma too! Pat is with the kids in the photo.
   And, what better way is there to end the day and the learning by having a piece of well earned cake!
[Joshua is a huge fan of Portal, the computer problem-solving game that’s always promising the player, but never delivering,  a slice of cake. Here he finally gets cake.]
    Below, Joshua, Jordann, and flight instructor Patrick pose for diploma pictures under the Pacific States Aviation sign.
   Word of the Fly to Learn! program got around to someone affiliated with the Aircraft Owners and Pilots Association (AOPA) and they plan to do a feature article on the kids and the program in an upcoming issue of the member magazine. As the kids say, “Cool.”

Saturday, January 26, 2013

One of a Kind

   As a struggling high school student, I credit Martin Gardner for instilling in me a life-long passion for learning mathematics and science that eventually led to my earning a B.Sc. in Mathematics and Physics, even though I have no special ability in either subject. I have been a math and science educator since 1964 and one of my goals has been to share my love of both subjects with students and teachers. The current educational system, with its heavy emphasis on testing, makes doing so more difficult than it was in the past but not impossible. I learned what I know about these subjects the hard way so I have a lot of sympathy for students that try, but struggle, with either or both subjects.
   No, Martin Gardner was not one of my teachers. I never met him or even saw him at a distance. He didn’t actually know me, but he visited me every month from 1956 to 1981. During those years he wrote the Mathematical Games column for Scientific American magazine.  I never missed a column and copied and collected them for years until they were republished in book form.
   You can imagine how excited I was to find a web site devoted to the problems and puzzles of Martin Gardner. There are 63 puzzles and problems in the Gardner section of the web site.
   Each puzzle or problem is presented in the form of a full-color graphic with text. You can play in your web browser or download  every puzzles as a Print ‘n’ Play pdf file. A solution or explanation is also available for every puzzle or problem.

   Before I provide the link to the Gardner site, here is a simple math experience (for kids and adults) that combines geometry and number, and makes a nice segue to  one of the problems on the Gardner site.

   A simple closed curve is a curve drawn on a flat surface that starts and stops at the same point and doesn’t cross itself (see the diagram below). A simple closed curve divides the plane into an inside and an outside. And, staying within the dimension of the paper, you can’t get from the inside to the outside (or the outside to the inside) without crossing the curve.
   The orange curve in the diagram below is an example of a simple closed curve I’ve labeled the inside and the outside of the plane (flat surface) the curve is drawn on. The curve drawn in green is not a simple closed curve because it intersects itself at point A. 
   I’m sure you understand that you could color the inside of the orange simple closed curve one color and the outside another color and the two colors would not mix because they are separated by the orange boundary.

    For a long time the obvious fact that a simple closed curve drawn in the plane creates an inside and an outside was considered so obvious that mathematicians never bothered to state the theorem, let alone prove it. The result was first stated as a theorem in Camille Jordan's textbook, "Cours d'Analyze de l'École Polytechnique" in 1887, and hence bears his name. Jordan found that proving this theorem is by no means easy, and in fact the proof he gave in his textbook is completely wrong. I will simply state his theorem and leave the proof to the professional mathematicians.

Jordan Curve Theorem: Any continuous simple closed curve in the plane, separates the plane into two disjoint regions, the inside and the outside.
   Now, let's play with the theorem. I've done the following activity with second graders and above so don't let the word theorem scare you off.
  Take a sheet of paper and draw a simple closed curve. Make it as squiggly as you can but don’t let the curve cross (intersect) itself ant any point. Here’s an example of a simple closed curve drawn in blue.
   Carefully draw a second simple closed curve, in a different color, over the first simple closed curve. The following picture shows how I've overlaid an orange curve over the blue curve.
     When I taught this to second graders, I was actually wanting to do an odd/even number activity and I knew kids liked to draw and color so I combined a bit of geometry with number. For reasons unknown to myself or the classroom teacher, odd and even numbers were listed in the second grade curriculum. The math workbook defined odd and even numbers but students had only to identify whether a number was odd or even. Students were never asked the sum of two odd numbers (an even number), the sum of an odd and even (odd), or the sum of two even numbers (even). The kids were justly mystified as to why anyone would care to know about odd and even numbers.
   Now, circle every point the orange curve intersects the blue curve.
   Count the number of intersections. In the above example, there are 18 intersections. And 18 is an even number. How many intersections did your example have? Is there a pattern? If you pick a point outside a simple closed curve and then draw a line to any point inside the simple closed curve and then again to any point outside the simple closed curve, how many times did you cross the simple closed curve?
   The answers to all of the above questions will help you quickly solve the In ‘n’ Out puzzle on the Gardner web site. Here's the link.
   Here's the link to all 63 of the Martin Gardner puzzles.
   Pick the puzzles and problems that interest you and ignore the rest.