Thursday, July 17, 2014

Speed Wheels Track

   Hot Wheels® are the ever popular small cars and trucks that run on sections of plastic track. Each car or truck generally retails for around one dollar. Kids love to play with Hot Wheels® and we keep a box of cars and lengths of track on the Toy Shelf for our grand kids and other visiting kids.
   I’ve written an earlier Hot Wheels post (click on the following link to see Hot Wheels, September 2009).
    In that post I made the observation that Hot Wheels® are all about fun and the force and motion concepts of displacement, speed, velocity, acceleration, gravity, gravitational potential energy, kinetic energy, and force and I promised to explore these concepts in later posts. So here's the next post in the series.
   Kids can explore the above concepts using a Hot Wheels® car or truck, a few lengths of track, and a cardboard box (see Figure 1).
   Consider the car in Figure 1. When given a slight push, gravity powers the car, pulling it down the track. It leaves the curved section at the bottom of the track with its maximum speed. The car will continue to roll along the straight portion of the track until friction reduces its speed to zero.
   Kids soon learn, just through play, that the higher the car is placed on the track (see a, b, c, in Figure 1), the greater the speed of the car as it exits the track. And, the higher up the track, the farther the car rolls along the straight track before coming to a stop. Play provides them with what is called implicit knowledge. This form of knowledge generally differs in detail from the expert knowledge of the physicist.

   With the foregoing in mind, let me share just a bit of the current academic research as to how children learn science. There is a National Research Council document, Taking Science to School – Learning and Teaching Science in Grades K-8, that can be obtained free, in PDF format. Send an email request to and I will email you a copy.

   The document states four conclusions reached by the authors of the book, two of which relate directly to kids making and playing with the Speed Wheels track.

   • Children entering school already have substantial knowledge of the natural world, much of which is implicit.
   • Students learn science by actively engaging in the practices of science.
   As mentioned above, kids playing with a car or truck on the track will discover on their own the relationship between at what point on the track the car or truck is placed and released and its speed at the bottom of the curved section and the distance it will travel along the straight section of track.
   What Taking Science to School – Learning and Teaching Science in Grades K-8 is telling us is that we should talk to kids, let them tell us what they learn from playing in a play environment like Hot Wheels® cars and track, and then build on that implicit knowledge with the goal of helping kids reach the expert knowledge level.
The Expert Knowledge Level
   The car or truck at the top of the ramp has gravitational potential energy (PE). PE is expressed by the formula PE = mgh where m is the mass of the car, h is the release height, and g is the acceleration due to gravity (surely an ‘expert’ piece of knowledge). 
   As the car or truck is pulled down the ramp, PE is converted to kinetic energy (KE), the energy an object has due to its motion. The formula for KE is KE = 0.5mv2 where m is the mass of the vehicle and is the velocity (speed) of the vehicle.
   As the vehicle descends, PE is converted to KE and at the bottom (see b in Figure 2) all of the PE has been converted to KE and the vehicle has reached its maximum speed. The terms PE and KE (not the formulas) and the relationship between the two can be taught to elementary school kids. This is best done by playing with them and teaching them the terms and how the terms apply to the car or truck rolling down the track. Doing so gives them the foundation to build on when they reach middle and high school and the teacher uses these terms. 
If you would like to build the track shown in Figures 1 and 2, follow these instructions.
How to Construct Speed Wheels Track from Card Stock
   Over the years, as the plastic track began to degrade from use, I became frustrated by not being able to easily find and purchase the plastic Hot Wheels® track separate from the expensive themed sets sold at the major retail outlets. So, I designed patterns for both straight and curved pieces of track. The patterns are printed on card stock, scored, cut, folded, and then glued together to form a single seamless track. The patterns make it possible to duplicate the setup shown in Figure 1 with as long a straight track section as required to give the cars or trucks enough track to come to a stop. 
   To get your free copies of the Speed Wheels track, just send an email request to
and I will email you the patterns in PDF format.
   Print each pattern on card stock. You can purchase card stock at almost any office supply retailer.
   Each pattern contains solid lines, dashed lines, and dotted lines.
   • Use a ruler and the opened end of a paper clip to score (trace over) every dashed and dotted line. Scoring makes it easy to fold card stock.
   • Cut along only the solid lines.
   • Use the diagram below to determine if a scored line is a valley fold or a mountain fold.
   • Fold each section of track as shown in the picture following each pattern,
   • Apply white glue to the shaded area to glue together track sections.
   Here’s what the pattern for Speed Wheels track looks like. Note the dashed and dotted lines and the shaded glue here area. Make as many sections of straight track as needed.
   When correctly folded, each section of straight track should look like the one in the following picture.
   The following pattern is for the curved section of track. Note the small, triangular-shaped shaded areas on the pattern.
   Glue the triangular-shaped areas to form the curved track section as shown in the following picture.
   Finally, here’s the Top of the Ramp section of track.
   Tape or glue this section of track to a cardboard box as shown in the following picture. Insert one or more sections of straight track between the top of the ramp and the curved track so that the track matches the height of the box. The bottom of the curved track should transition smoothly to the straight track.

Wednesday, May 21, 2014

Algodoo Tutorials

   In the last post I introduced Algodoo, the physics sandbox for the PC, Mac, and iPad.
   I made a point of stressing the importance of working through the tutorials and lessons built into Algodoo to acquire the knowledge and skills needed to have a enjoyable experience building working machines and contraptions in Algodoo.
   I've decided to start building a library of Algodoo tutorials because I want learners of all ages to have the opportunity to take advantage of all of the features built into Algodoo.
   For example, to test the accuracy of the physics modeling in Algodoo, I decided to model a simple pendulum with a length of three meters. I would then measure the period of the Algodoo pendulum by timing (with my cell phone) 10 back-and-forth cycles and dividing that time by 10 to get the time (period) for one cycle.
   Watch this tutorial to learn how simple it is to model a pendulum in Algodoo.
   When I viewed many of the Algodoo YouTube videos I was impressed with the wide variety of shapes modelers used in building their contraptions. Watch this short tutorial to learn how easy it is to build a circular track for a marble to roll in.
   One of the mechanisms I saw on YouTube was a piston moving back and forth between two blocks. In this tutorial you will learn how to motorize an axle and how to use the add tool to make a connecting rod.
     There is a gear tool in Algodoo and it it used to build a train of three gears. View this video to learn how it's done.
      Like you, I too am learning how to play in the Algodoo sandbox. Every time I have an idea for a new mechanism I have to figure out how to do it given the tools available in the program. For example, it's easy enough to understand how I used the gear tool to draw the rust-colored gear in the following picture.
   But how did I construct the bottom straight gear? 
  To find out, click on the link below and go to a special site on Vimeo where all of the above tutorials and the tutorials done to date are  stored, and click on the Rack and Pinion tutorial.

   A big thank you to the AIMS Education Foundation for hosting the Algodoo tutorials on Vimeo. Visit often to view the latest tutorials.

Thursday, May 8, 2014


   Several years ago I downloaded and played with a physics sandbox called Phun. I was impressed with the physics modeling but thought the user interface a bit too difficult for younger kids (grades 3 – 6) to learn. I am cautious about recommending science-based, educational computer programs to youngsters because a frustrating experience can be counterproductive.
   Phun has now morphed into Algodoo and I was excited to download and play with this new, redesigned version. Just understand that Algodoo is not a casual game but a simulation that requires an investment of time to learn.
   The Algodoo download for the PC and Macintosh platforms is free at (  There is an option to pay a small, $5, support fee that I happily paid to download my Mac version of Algodoo.
    An iPad version of Algodoo is available from the Apple App store but costs $4.99 (still a bargain).
   I made the following video to illustrate how easy it is to simulate a simple physical process, like floating and sinking, with a few clicks of the mouse (or swipe of the finger).

   It is important that you, your kids, or your grand kids, work through the built-in Tutorials and Lessons listed in the menu option that appears on the opening screen.
   Also, be sure to spend time in the Help menu. I did and I found it very useful, especially the second menu item labeled Tools.
   I found a video on YouTube of an incredible Rube Goldberg-style machine built in Algodoo. I captured a short, one minute section of the video just to show you what the simple machines that can be constructed in Algodoo.
   If you would like to view the complete, four-minute video on YouTube, click on the following link.
   I will be posting short, tutorial-style videos to help speed interested contraption builders along the learning curve.

Wednesday, April 16, 2014

Grandadscience Loves to Program!

   Did you know that grandadscience also blogs about computer programming or, as it's now called, coding?
  Since the introduction in the 1980s of the Apple IIe, powered by the BASIC programming language, I have had a strong interest in helping learners of any age learn the basic fundamentals of computer programming .
   I have taught learners to program in BASIC, Logo, Starlogo, the Texas Instruments version of BASIC, and now, I'm using Scratch, a new language designed for beginners (and skilled coders too). To  understand the attraction of Scratch as a coding language, watch this short video from the producers of Scratch.

   Scratch is a product of the Multimedia Lab at the Massachusetts Institute of Technology (MIT). Coding in Scratch is a very popular activity with over five million Scratch programs (called projects) uploaded to the Scratch community web site. To the best of my knowledge, Scratch is by far, the largest educational online community anywhere in the world. To learn more about Scratch, and hopefully join the throng, click on this link.
   You can visit my Scratch programming blog by clicking on this link.
   My posts represent math and science projects that I programmed because I wanted to explore the topic that forms the core of the program and are too advanced for beginners but I have posted a number of projects designed for the beginner.
  For example,  I have written three Getting Started with Scratch  documents.
   The first document guides the reader through the steps of building a script (program) that draws a square with a side length of 100 steps. This introduces the blocks menu and the mechanics of connecting blocks together to build a script.  Think of this level as the arithmetic level.
   The second document describes how to create variables, sliders, and how to set the minimum and maximum values in a slider. The size of the square is now under variable control. Think of this level as the algebraic level.
  The third document helps the reader build a script that will draw any regular polygon. In a regular polygon the side lengths are equal. A slider controls the number of sides and again, the side length is controlled by a slider. 
   The relationship between the number of sides and the turn angle for a regular polygon of n sides requires a bit of mathematical analysis but how to get to the relationship is described in the document. Think of this level as the generalized algebraic level.
   You may request any or all of these documents—in PDF format— by sending an email to:           
            Getting Started with Scratch – Part 1
            Getting Started with Scratch – Part 2
            Getting Started with Scratch – Part 3

Monday, March 31, 2014

Persistence of Vision

   We recently visited with our oldest son and his family. They are a military family and had just moved to a new duty station here in the United States. 
   Grandmother math always travels with activities to do with the grand kids. In the following video you can see one of the grand sons demonstrate the Woodpecker Illusion

    Both boys made an illusion by cutting and gluing two sheets of paper and then they used crayons to add color to the two patterns that make the illusion. Andrew added apples falling from his tree.
   The illusion is made by gluing one picture with the woodpecker's head back from the trunk of the tree over a second picture with the head of the woodpecker on the trunk.
   The top picture is curled around a pencil. 

   As is seen in the video, the illusion is created by rapidly unrolling and rolling the top picture.
   The best use of this simple activity is to stimulate students to create their own two-picture illusion
  A free cop (PDF) of the Woodpecker Illusion can be had by simply emailing a request to 

Saturday, January 18, 2014

The Cartesian Diver - Revisited

   When grandmother math recently retired as a school teacher (for the third time) she found among the mountain of math manipulatives and hands-on science materials that she had accumulated, a bag of Cartesian divers dressed up as squids.
   One of my first blog posts featured grand kids Joshua and Jordann making and using Cartesian divers made  from glass eyedroppers (see Blog Archives, 2009, April or click on this link
to view the first Cartesian diver post.
   I gave of couple of the squids to friends Jesse and Salina to show to Faith, their three-year old daughter (see previous post, Mixing Stuff Together is the Beginning of Chemistry, October 2013).
   They put the squid in a 2-liter bottle filled with water to find out if Faith could squeeze the bottle with enough force to make the squid dive for the bottom! As shown in this picture, she can!
   Watch this short video of Faith interacting with the Cartesian diver.
     Faith's small hands makes it easier for her to apply pressure to the bottle by placing her hands on its dome-shaped top. Note that when she tries to sink the diver by pressing on the sides it is harder for her but, after several tries, she is still successful in sinking the diver.

   The sensitivity of the diver to the force exerted on the bottle can be controlled by the initial amount of water in the barrel of the diver. Remove the rubber cap from the dropper, plug the small end with a finger, and use a second eyedropper to add water to the barrel. Test the buoyancy of the diver in a tall glass of water. Add enough water to the diver so that it just floats. 
   I have not been able to find a source for the squid seen in Faith's video but I have made a squid-like Cartesian diver by gluing colored yard to the barrel of a glass eyedropper and then wrapping the barrel with yarn of a different color. The yarn traps small air bubbles so you have to swish the diver back and forth in water to release the bubbles.
   The modern super-glues make it easy to attach yarn and small figures to the barrel of the eyedropper.
   Glass eyedroppers have been largely replaced by plastic droppers but  I much prefer the glass.  Six glass droppers can be purchased for three dollars from this science supply retailer.
  You can use a plastic eyedropper but you will have to weight the end by wrapping wire around the barrel to get the dropper to float vertically.
   If you would like to view a wide variety of Cartesian divers click on the following link. Also, when you visit the link, be sure to download the free colorful PDF document that describes the science concepts you can teach older children (or learn yourself) using a Cartesian diver.

   The Cartesian diver is an interesting object that children like Faith enjoy because they can control its action. It's so important that we as parents and grandparents continually nurture the curiosity about the natural world that children are born with.
    Thanks again to Jesse, Salina, and Faith for sharing the video and pictures.