Monday, April 27, 2009

Do you believe in ghosts?

By “ghosts” I mean unseen entities that influence the material world, and I certainly do believe in them. I’ve never actually seen any ghosts. But they are there!

Tell the kids you are going to show them how to summon ghosts.

Find a bottle with a narrow neck, like a wine or soft drink bottle. A penny or dime should just sit in the rim of the bottle’s mouth. If it falls through, try another coin or a different bottle. In these photos, a penny sits in the mouth of a wine bottle and a dime in the mouth of a soda bottle.

Show the bottle—without the coin—to the kids and ask if they can see anything in the bottle. Unless whoever had the bottle didn’t finish its contents, their answer should be no, the bottle looks empty. Remember, kids equate air with "nothing". That is they do until they see physical evidence that suggests otherwise. 

Tell the kids it takes time to summon the ghosts and that they require conditions to be very cold (so we know they’re not from That Place) and put the open bottle in the freezer compartment of the refrigerator.

After you’ve had some cookies and milk, have the kids take the bottle out of the freezer. Tell them to set it on the table.

Have them place the coin in the mouth of the bottle, and with an eyedropper or a finger dipped in a cup of water, seal around the rim of the coin with drops of water. And wait. It takes time for ghosts to appear.

When they do appear, their presence will be made known by the coin popping up, and then falling back down into the mouth of the bottle. In this video, note the bead of water around the coin, listen for the "clink" as the coin falls back, and watch the process repeat several times.

The coin seen in the video “popped” continuously for half an hour. The interval between pops lengthens with time. A good measurement activity for the kids to do is to repeat the process and have them measure, record, and graph the data. If you would like a generic data table and graph, email your request to and I will send you a PDF file.

Some science educators will take issue with my framing this activity around something as unscientific as ghosts. But they fool themselves if they think kids believe the stories about atoms and molecules and neutrons and electrons and all of those other invisible particles that fill our elementary science texts. Worse yet, these “atoms” and “molecules” are simply pronounced (with no real evidence) to be “real”. It’s easier to believe in ghosts. Nothing is lost—and much believability might be gained—by calling these invisible particles what they are, unseen entities that influence (and actually make up) the real, material world.

The moral of this story is that something unseen is there, in the bottle, and whatever it is, it can push up the penny. Let the kids talk about what they have just observed and guide the conversation but stay away from technical explanations. If they know and believe that force is a push or a pull on an object, then they have enough to think about trying to figure out what could be invisible and push up the coin.

Later, when the kids are asked to learn about molecules and the kinetic theory of gases, they will remember the "ghosts in a bottle" you showed them and have a real-world experience (other than something read in a book) to build on.

Paula's Puzzle

This puzzle connects to an upcoming post on one set of figurate numbers, named The Triangular Numbers

To build the puzzle, you need a glue gun and twenty plastic practice golf balls. Golfers use these to practice the swing in the backyard without terrorizing the neighborhood. The golf balls cost a couple of buck a dozen and are available at any of the chain stores.

The puzzle was invented during a math workshop I was leading for fourth grade teachers. We were gluing plastic practice golf balls together as part of our study of figurate numbers, Paula, one of the teachers, had glued three golf balls to form a triangle and then glued a fourth on top of the other three to form a pyramid shape. A triangular-based pyramid is called a tetrahedron. So, just as Paula did, you, or the grandkids, glue two, glue three, and then glue the fourth on top of the three, as shown is this picture. This is a good project for teaching the grandkids how to safely use a hot-glue gun.

As Paula was showing her creation to the group, someone wondered out loud if some number of these small tetrahedrons would form a larger tetrahedron.  The group started gluing golf balls together and it was soon discovered that five of the small tetrahedrons would form a larger tetrahedron.

That’s Paula’s Puzzle. Use the five small tetrahedrons to build the larger tetrahedron shown below.

Serendipity is when the unexpected happens. Unplanned, the group had moved from our study of two-dimensional figurate numbers (see the Triangular Numbers post) into a study of three-dimensional figurate numbers. What thrilled me most, as leader, was that the group knew and understood the arithmetic underlying the puzzle. In a later post, I will connect the Triangular numbers to Paula’s Puzzle. For right now, teach the grandkids how to safely use a glue gun, make the puzzle pieces and, as I learned to say teaching in New South Wales, Australia, “give it a go”!

Oh, here’s a short video that shows the solution.

Thursday, April 23, 2009

Educational Computer Games.1

I am one of hundreds of thousands eagerly awaiting the arrival of Machinarium, a game from Amanita, a Czech design team. My interest in the game stems from a preview in PCGamer magazine. The preview contained links to their already published Samorost 1 and Samorost 2 games. Go to where you can view a video preview of Machinarium and also link to Samorost 1 & 2. Samorost 1 is a free download and Chapter 1 of Samorost 2 is also free but Chapter 2 cost $5. It’s worth it. I paid my five bucks and downloaded both games.

Amanita brings a European fairy-tale quality storyline, graphic style, and problem design to their games. The main character in Samorost 1 lives on a small planet made of wood, rock, and moss, held together by a single nut and bolt. Wisps of smoke and flashing lights indicate that the interior is inhabited. The game is of the point-and-click genre. This means you move the cursor around until it changes to a “hand pointer” and then click to activate what’s under the cursor. Clicking on the metal turret in the upper left corner reveals that the turret is an observatory. A telescope appears, the main character (a little person in a hooded nightshirt) takes the stage, and the game begins.

The game locales the character visits varies from lush woodland scenes ……

to funky industrial sites.

Other characters met along the way are mainly recognizable animals, like the snail pictured above, fantasy creatures, insects, and the occasional hookah-smoking human. Oh, and Samorost 2 is a story about the man and his dog.

To solve each level of these games you have to pay close attention to small details in the graphic environment, be imaginative, understand that what’s possible in the character’s world that may not be possible in your world, listen for sound clues, be persistent, be patient as it may take time for events to unfold in the character’s world, and, most important of all, don’t try to rewrite the story by trying to force your logic onto the character and the character’s world

Other characters met along the way are mainly recognizable animals, like the snail pictured above, fantasy creatures, insects, and the occasional hookah-smoking human. Oh, and Samorost 2 is a story about the man and his dog.

To solve each level of these games you have to pay close attention to small details in the graphic environment, be imaginative, understand that what’s possible in the character’s world that may not be possible in your world, listen for sound clues, be persistent, be patient as it may take time for events to unfold in the character’s world, and, most important of all, don’t try to rewrite the story by forcing your logic onto the character and the character’s world. The little man travels around in a sausage-can rocket ship. Cool. Here, in Samoraost 2, he’s parachuted onto another planet after his rocket ran out of fuel.

Two of our grandkids, Joshua and Jordann, ages nine and eight, played through both games over a recent weekend visit. The computer was always on and they had permission to play when they wanted to. They played casually, sitting down for ten minutes or so and then, like kids do, going off to do another activity (like acting-out Bible stories with grandmother). They wanted to solve each puzzle by themselves but, if they ran out of ideas, they asked for help. I would ask a leading question or give a hint to help them on their way. I was impressed with the percentage of the puzzles they were able to solve on their own.

I look forward to having fun exploring the magical world of Machinarium with the kids in the near future.

Thursday, April 16, 2009


    Games and puzzles provide challenging and interesting opportunities for exercising problem-solving skills. Before looking at the underlying mathematics, the game must be learned to be enjoyed or, the puzzle solved.
    My favorite math puzzle is a seven-piece set of puzzle parts formed by gluing identical cubes face-to-face. Six of the puzzle pieces are made by gluing four cubes. The seventh piece is made of three cubes. The 27 cubes of the 7 puzzle pieces will fit together to form a 3 X 3 X 3 cube. Not counting rotations, there are 240 distinct ways to build the 3 X 3 X 3 cube. Finding just one of them can be a real challenge. The seven pieces are not just chosen at random. They are pieced together according to a precise mathematical rule.

    I first learned of this puzzle from one of Martin Gardner’s Mathematical Games columns in Scientific American magazine. The puzzle is called Soma and he credits its invention to Piet Hein (1905–1996), a Danish architect, poet, and inventor. John Horton Conway, one of our treasured living mathematicians, spent a wet and windy afternoon mapping all of the possible solutions, that are unique, for forming the cube. If you would like to know more about the history of Soma and the rule directing the construction of the seven pieces, just send a request to
In these pictures, Jordann and Joshua concentrate on building the cube. Notice, I made a pink set for Jordann and a blue set for Joshua. If I had it to do over, I would have let the kids glue and paint their own sets.

Check out this video to see one of the possible solutions.

    Building a 3 X 3 X 3 cube is only one of numerous structures that can be built from the seven pieces. Jordann built a castle and Joshua built a tower. Their structures becomes problems for grandad to solve.

    Many of you grandads will simply go to your shop and make a set of 27 cubes. If you prefer, you can order a set of 100 one-inch wooden cubes from EAI Education for $11 plus shipping. Here is the link and phone number 1-800-770-8010.
    In a later post, I will show you how to build a puzzle that explores cannonball numbers, which are 3-dimensional figurate numbers.

Crayon Physics

The first physics-based game I will share with you is a delightful example of the educational games I want my grandkids to play. It’s called Crayon Physics. Visit and download a free demo of the game. Play the demo with your kids and then decide whether or not to buy the Deluxe version.

The playing field in Crayon Physics is a 2-dimensional vertical plane with gravity active. Objects fall and structures tumble if not supported. Wheels rotate around axles and levers lift loads. The goal in every puzzle/problem is the same, pass over a yellow star with a small circle. Each problem has many solutions and can be played over and over.

In this pic, Joshua is working through the first problem in the demo. The demo contains a short and simple tutorial.

In this pic, Jordann is testing her solution to a problem met towards the end of the demo.

Here is a short video of Jordann's solution to the problem. Notice that the long arm pivots around the small circle.

As grandad, my role is to support the kids as they play. I typically leave the room or sit back quietly and watch. I let them wrestle with every problem but if I think the frustration level is getting too high, I look at their solution and try to offer a suggestion or hint that doesn't solve the problem but let's them continue on to a solution. An important problem-solving skill is to drop a tough problem for a time and let it incubate in the mind. Therefore, if they really hit a brick wall, I have them stop playing and let them return to it at a later time.

In a later post I will feature Samorost I and Chapter 1 of Samorost II, two free problem-solving games with delightful, storybook graphics and imaginative puzzles. The grandkids solved both, with a bit of help from grandad, on a weekend visit.

Wednesday, April 15, 2009

Cartesian Diver

An example of a science-rich activity that helps kids develop intuitions about sinking and floating, it would be hard to find a better one than the Cartesian Diver.

This is all your kids need to make a diver:

• empty 2-liter bottle with cap

• glass eyedropper

• food coloring

Have the kids follow these directions:

• Cut off any label and clean the bottle with warm water and soap.

• Use a goo-remover or citrus juice to clean away the glue residue. 

• Fill the bottle to the brim with cold tap water.• Put four or five drops of food coloring (no yellow) in a quarter-cup of water.

• Draw enough colored water into the barrel of the eyedropper to half-fill it. [If a glass eyedropper is not readily available, any tube closed on one end that will fit through the neck of the bottle will work. Experiment with the amount of water to put in the tube so that it will float vertically. If the tube is made of a buoyant material, wrap wire around the open end until the tube floats vertically.]

• Gently lower the half-filled eyedropper into the neck of the bottle

• Screw the top on tight.

• Squeeze the side of the bottle to make the eyedropper dive, release the pressure to allow the diver to rise.

Joshua demonstrates the action of the Cartesian Diver in this picture and the folllowing short video. He is proud of his ability to apply just the right amount of pressure to keep the diver at a constant level.

The purpose of the food coloring in the barrel of the eyedropper is help the kids focus on observing the rise and fall of the water level in the barrel as the bottle is squeezed and released.

In this picture, Jordann learns to control her dive

Let the experience speak for itself but if you would like a list of the science concepts demonstrated by a Cartesian Diver, email your request to and I will respond immediately.

To illustrate that a Cartesian Diver can be made from almost anything, here’s a shot of my Cartesian Diver collection. The yellow balloon has a lead fishing weight inside.

In my next hands-on activity post I will share a simple method for observing how to lift a dime with only the heat of a hand.

Grandad On Educational Computer Games

My older grandkids (ages seven and eight) enjoy and are very successful playing puzzle-based computer games. These nonviolent games emphasize solving puzzles and problems in dynamic, interactive environments. Because most educators don’t see ‘school curriculum’ in such games, these games are dismissed and are not available to kids at school. Of course, these administrators and teachers have rarely played any of these games. And, the few times I have been able to entice one to play, they quickly become frustrated and quit. This is because school curriculum isn’t readily visible in either the control or goal of the game and they don’t know what to do, which is an uncomfortable situation. They don’t understand that it’s the problem-solving skills that are being exercised, not the student's knowledge of specific curriculum content. What are these problem-solving skills? Curiosity, understanding that you have to start some where if a beginning point isn't clearly defined, being comfortable with the fail, fail, fail, before you succeed characteristic of problem-solving, perseverance, and many others. But the most important outcome of playing these games is the personal sense of achievement experienced when a tough problem is solved.

Grandad On Mathematics

As my grandkids move through the early and formative stages of formal schooling, my biggest fear is that they will leave middle school with a strong dislike for mathematics. There appears to be no known antidote for this malady. I was saved from such a fate not by a schoolteacher, but by Martin Gardner and his monthly Mathematical Games column in Scientific American magazine. In one his columns he tells the story of how he was chastened by his math teacher for analyzing the game of Tic-tac-toe. The fact that he discovered it was a zero-sum game was of no mathematical import at all to the teacher. His monthly columns brought mathematics to life and I eagerly awaited the appearance of each issue on the periodical shelf at our Public Library. It’s true! Mathematics, at every level, is best played as a game.

Grandad On Science

Science is what we call our precise knowledge and understanding of the natural world. Youngsters, as they grow, build a less than precise understanding of nature but the strength they have, often lost as they progress through the stages of formal schooling, is a curiosity about almost anything. Bugs included. Attempts to make knowledge and understanding too precise, too early, can dampen curiosity. The ability to observe nature, and not just look at it, is the first and most important skill for them to learn. Hands-on activities provide the best opportunity for kids to directly observe and think about the wonders of nature. The important language of science (and the math formalizations that come later) works best when added to a rich, experiential base.