Friday, December 24, 2010

A Fluid Christmas Tree

   In the previous post (Fluid Play for Young and Old), you learned that food coloring is heavier than water and falls through water, in a straight line, with little mixing, just like salt and sand falls through air in a stream. A more accurate term than 'heavier' is density.
   Density is the mass per unit volume of a substance and provides a method for directly comparing substances. The volume of a kilogram of marshmallows is much much greater than the volume of a kilogram of lead. Therefore, the density of lead is greater than the density of marshmallows. 
   In this activity, the food coloring is denser than water but salt water is denser than both the food coloring and water.
   Gather the kids and the following materials and let them grow a fluid Christmas tree.  You may want to do the cutting for the kids and let them take over once you have the apparatus ready to go.                         

Glass eyedropper
Green food coloring
Card stock 2-inch square
Plastic margarine or whipped cream top
Two-liter bottle, empty and clean

   Depending upon the ages of your young learner's, you can either prepare the apparatus or supervise their doing the cutting and punching.
• Cut the top from the two-liter just below the curve of the neck
• Trim around the neck so that the neck sits level (see picture)
• Cut a straight line to near the center of the plastic lid
• Punch a 1⁄4-inch hole near the center of the lid
• Cut a two-inch square of card stock or thin cardboard and punch a hole near its center
Now it’s time to setup the apparatus to grow the tree.
Ask the kids to:
•   Pour enough water into the plastic two-liter bottle to so that it is about 1⁄3 full
•   Add table salt, one teaspoon at a time, stirring constantly, until no more will dissolve
•   Let the water sit for about 15 minutes
•   Place one hand, palm up on the surface of the water and carefully pour tap water into the palm, raising the hand to keep it on the water's surface, until the container is almost full (important – do not stir the water!)
•   Slip the glass eyedropper through the hole in the cardboard square
•  Half-fill a teaspoon with red, blue, or green food coloring and use the eyedropper to suction up as much food coloring as possible
•  Place the bottle neck over the hole in the lid and carefully set the eyedropper in the bottle’s neck

   Soon, a thin stream of food coloring starts flowing from the tip of the eyedropper. If there's an air bubble in the tip, gently and slowly  squeeze the rubber bulb until the food coloring starts flowing. 
   For the first few minutes, the green food coloring looks messy, as shown in this picture. Notice that the food coloring is still being contained vertically.
   After an hour or so, the food coloring appears to be collecting in a blob near the bottom of the bottle but is not mixing with the greater volume of fluid.
    Now, everyone can do other things while the tree grows. It takes about four hours for the tree to grow but, as the following picture shows, it's well worth the wait. After an hour or so, the food coloring appears to be collecting in a blob near the bottom of the bottle but is not mixing with the greater volume. As the tree grows, the horizontal branches broaden.
   As Christians, Christmas is the time we celebrate the birth of our savior, Jesus Christ. Grandadscience and grandmother math wish every believer in the the true meaning of Christmas, a very Merry Christmas.

This 'tree' effect was demonstrated by grandadscience and a prominent Los Alamos physicist at a conference of fluid dynamicists. Attending physicists were challenged to offer an explanation but to date, none has been offered. Certainly the collision of the higher density food coloring with the even higher density salt water is at the heart of the effect.

Sunday, December 19, 2010

Fluid Play for Young and Old

   If you’re fortunate enough to spend time with the grand kids (or your kids) this holiday season, here’s a science activity that’s easy to set up, quick to do, and extends the kids scientific knowledge about the states of matter.
   Kids learn that matter exists in one of three states: as a solid, a liquid, or a gas. They are taught a set of characteristics they can use to distinguish one form of matter from another form. For example, a characteristic of a solid is that it holds it shape. It's a characteristic of a liquid that it takes the shape of its container. A gas also takes the shape of its container. Taking the shape of its container becomes a method for distinguishing a solid from a liquid.
   But a solid can exist in many forms. Take a rock, hit it with a hammer to break it into smaller rocks, pound the smaller rocks into sand, and grind the sand into a powder. But sand will fill the shape of its container and also pours, like a liquid! A powder can also take the shape of its container but, unlike sand, does not flow like a liquid! 
   To the scientific eye, there’s much more to learn about the states of matter than just classifying matter as either a solid, a liquid, or a gas. It's time for the kids to explore!
   Ask the kids to fetch the carton of table salt from the cupboard. Tell them to lift the spout and pour a small amount of salt into a cup. 

   Ask them:
   “Is salt a solid or a liquid?” [solid]
   “Which is heavier, salt or air?” [They will of course tell you that salt is heavier than air.]
   “Did the salt fall through the air?” [Yes.]
   "Does salt pour like a liquid?" [Yes.]
   "Why do you think the salt fell through the air?" [it's heavier than air]
   Ask them to fetch a small funnel and to put the salt back into the carton.
   Here’s a picture of sand streaming from the tip of a funnel. Salt and sand are called granular solids. To provide the kids another example of how a granular solid flows like a liquid, show this picture.

Glass eyedropper (if you have a plastic eyedropper, wrap thin  wire around the tip end so that it will float vertically)
Food coloring (use red, blue, or green, not yellow)
Two-liter soft drink bottle (remove the wrapper and use a commercial goo remover or citrus juice to clean off the glue)
      Have the kids follow these steps:
1.   Fill the two-liter bottle with cold tap water, all the way to the top.
2.   Half-fill a teaspoon with red, blue, or green food coloring.
3.   Use the eyedropper to suction up as much of the food coloring as possible.
4.   Carefully lower the eyedropper into the neck of the water-filled bottle (see picture) and wait.

5. Soon, the food coloring will flow from the tip of the eyedropper. Have the kids observe the motion of the food coloring.
6. Talk with the kids about what they've just done.
    The food coloring is slightly heavier than water so, like sand falling through air, the food coloring falls, in an almost straight line, through the water until the flow line becomes turbulent and mixing starts.
   In this science experience, food coloring, a liquid, falls through water like salt or  sand falls through air!
   To a scientist, a fluid can be either a liquid or a gas. An important branch of science is called fluid dynamics and fluid dynamicists study the  motion of fluids.
   In the next post, just before Christmas, I’ll show you and the grand kids how to grow a fluid Christmas tree in a bottle of water.

Tuesday, December 7, 2010

Grandmother Math in the Wind Tunnel

   In iFly, the early November 2010 post, grand kids Joshua and Jordan were featured flying in the vertical wind tunnel at iFly South Bay, near San Francisco.
   Our daughter Winona lives in Georgia with her husband, Dr. Gene, and our two wonderful preschool- age grand kids, Asher and Kate. Winona saw the iFly post announcement on the grandadscience Facebook page, viewed the post, and asked to see grandmother Math flying in the wind tunnel.
  Winona, here is the video.

Didn't she fly like a pro!

Saturday, November 27, 2010

Selecting a Microscope for the Kids or Grand kids

   The gift-giving season is here and if, as a grandparent or parent, you intend to purchase a microscope for your kids, then read on. The following information will not only save you money but also keep you from giving the kids a gift that can be the source of more frustration than educational fun.
   Microscopes, especially the ones sold in the major retail outlets, usually tout the high-power of the product. They often look like the microscope shown above. For kids untrained in microscope use, 50 power (50X) is more than enough magnification.
   Don't assume kids are being taught microscope skills in the elementary grades. Until kids have been taught how 'field of view' and 'depth of field' affect what's seen through a microscope, observing at higher powers will simply frustrate the kids. In a school system with a good science program, they may learn these skills in middle school. If they don't, let's hope they have a good biology teacher in high school. 
   When looking through a microscope, the lens near the eye is called the eyepiece lens and the lens at the other end of the tube, near the object being examined, is called the objective lens.

   The power of the lens-pair is computed by multiplying the power of the eyepiece lens by the power of the objective lens. These powers are stamped on the barrel of each lens. My favorite microscope, the Brock Magiscope (shown above), has a 10X (10 power) eyepiece lens and a 4X (4 power) objective lens. The magnifying power of the tube is therefore 10X x 4X or 40 power. That’s enough power to see the organisms in a drop of pond water.
   Remember, the higher the power, the smaller the field of view, the thinner the depth of field, and the more difficult it is to find and view an object through the microscope.
   A microscope that kids can actually use will provide lots of enjoyable hours viewing minuscule objects like Abraham Lincoln seated in his Memorial on the back of a penny or the fantastic creatures that swim and live in a drop of water.

   The microscope shown above can be purchased at these web sites.

Wednesday, November 24, 2010

Thanksgiving 2010

   Grandad science and grandmother math received a special Thanksgiving email treat. It’s the above picture of our two oldest grand kids, Joshua and Jordann, with a geometric model they made by sticking pieces of uncooked spaghetti into small marshmallows. During a visit earlier this year, we had made geometric models using toothpicks and raisins that they dipped into a soapy solution to see the surprising shapes formed on the models by the interacting soap films (see the April 2010 post). It’s heartening to know they remember how to make the models!
   Wishing everyone a warm and  happy Thanksgiving with family and friends.

Saturday, November 20, 2010

Image on the Edge

“All physicists use their heads, the best also think with their fingers.”
                    Dr. George Polya   

   In previous posts, we've looked at two ways to establish the fact that the image in a flat mirror appears to be as far into the mirror as the object is in front of the mirror. Here’s a third method and one that kids like to do. Once you've gathered the materials, show the kids or grand kids how to setup and do the investigation (as illustrated and described below) and then let the kids view the video and repeat the investigation.

Plane mirror with binder clip (or anything else to hold the mirror upright)
Two, tall, identical objects
Sheet of paper

   As shown in the picture above, use a ruler to draw a line parallel to the left edge of a sheet of paper. Mark the line in inches. [Send an email to  and I will send you a pdf file of the ruled page as seen in the picture.]
   Attach the binder clip to the right edge of the mirror and place the mirror perpendicular to the ruled line at a point about halfway along the line. Place a tall object (like a AA battery or one of an identical set of salt and pepper shakers) on the ruled line so that half of its image is visible along the left edge of the mirror.
   Set the other object on the ruled line, behind the mirror. Your setup should look something like what’s seen in this picture.
   Observe that the half-image along the left edge of the mirror does not align with the object behind the mirror. The mirror image may appear to be behind or in front of the object.
   Slide the object behind the mirror, along the ruled line, until the image along the left edge of the mirror blends perfectly with the object.
   Compare the distances of the objects from the mirror line. When done accurately, the distances will be equal. As they say, “Seeing is believing.”
     Here is an animation I created that summarizes the on-edge method. It’s a short, 45-second video.

    With the holidays fast approaching. in the next post I will recommend the right microscope to purchase for your kids or grand kids.

Saturday, November 6, 2010

We Fly at iFly

   Joshua, our oldest grandson was born on Halloween. This year, for his tenth birthday, he wanted to go skydiving in a vertical wind tunnel.  There happens to be, within an hour from his home, a vertical wind tunnel. 
   Joshua’s mom and dad met at a drop zone where they both skydived. Dad was a skydiving instructor and mom ran the manifest where she kept the airplanes loaded with skydivers, and, when the paying customers were taken care of, went skydiving.
   Joshua’s dad arranged for all of us, grandadscience, grandmother math, and he and his family, to visit the iFly vertical wind tunnel near their home.
   The scientific principle used in the vertical wind tunnel is simple. Instead of a person falling through the air at 120 miles per hour, a big fan blows high-speed air upwards at and around a person.
   A ping-pong ball and your hair dryer will quickly demonstrate to you the feasibility of this method. Hold the hair dryer upright in one hand, turn it on to the highest setting, and drop the ping-pong ball it on the air stream. The ball, contained in the air stream, will float above the open end of the dryer. Watch this short, 20-second video to see how this works (with no one around to help me, I had to put the hair dryer in a stand so that I could take the video).
   The hair dryer video demonstrates two scientific principles; first, Bernoulli’s principle tells us that the pressure in an air stream is lower than the pressure outside of the stream. That’s what keeps the ping-pong ball centered. Second, the weight of the ball equals the force due to upward air flow. That keeps the ball suspended in the airflow.
   Watch this video to see Joshua take the place of the ping-pong ball in the iFly vertical wind tunnel. Towards the end of the video, his instructor takes him up to the top of the chamber.
   Well done Joshua! Now here’s Jordann, his sister, flying in the tunnel. 

  It was a great family outing and we are all excited to go again. In case you are curious, children as young as five, if genuinely eager to do so, are allowed to fly in the wind tunnel.
   As shown in the video, a qualified instructor is with you at all times. You may have noticed the instructor giving hand signals to the fliers. Two outspread fingers means drop your legs. Two curled fingers, lift your legs. Spread legs drive the flyer forwards and curled legs causes the flyer to back up. The basic tunnel flying skill is learning the correct leg and arm positions so as to stay centered in the airflow. Thumbs up means the body position of the flyer is correct.
   Joshua and Jordann, Here’s a Thumbs Up from mom and dad, grandadscience, and grandmother math!

Thursday, October 21, 2010

Water-grow Animals – Part 2

   In an earlier grandadscience post (July,2009), I shared how grandson Joshua and granddaughter Jordann observed, measured, and graphed the increase in length of two toy animals made of polyacrylamide, the water-absorbing polymer used in diapers. These animals will dramatically increase in size when immersed in water for several days. I call these toys, water-grow animals. The alligator pictured above will fill a bathtub. We know, because the kids kept one in grandmother math's bathtub for two weeks!
   The kids had a lot of fun with the activity and, during a late August visit, were eager to repeat it. Grandmother math keeps a menagerie of these animals and the kids agreed to use a gray rat for the new activity.
   Jordann is eager to get started and begins by measuring the length of the rat.
   Grandmother math decided to add mass-measurement to the activity so Jordann is shown below using a balance to measure the mass of the rat. Notice that the rat sits snugly in the red bucket of the balance, That smile comes from adding the right number of mass units to the yellow bucket to balance the rat.
  The rat was then placed in a bucket of water. Every morning, grandmother math made time for the kids to observe, measure, record, and graph, the length and mass of the rat.
   After a few days, the rat had grown to an ominous size (for a rat)!
   The rat had also grown to the point it would barely fit in the bucket on the balance! Notice the number and size of the mass units in the red bucket needed to balance the rat!
  After a day or two, the mass of the rat exceeded the range of the balance so Joshua improvised what problem-solvers and engineers call a work-around. The following day the kids had to return home and they took the rat, wrapped in a towel, with them.
     Joshua starts the fifth grade next year and Jordann will be in the fourth grade. If the kids are interested, they will do the activity one more time, measuring and recording the mass and length, as in past activities, but adding width, and height measurements. Doing so will allow grandmother math to talk about proportional growth which explains why the animals maintain their shape and don't become distorted.
   Water-grow animals can be purchased at most large retail outlets. If, like grandadscience, you like the convenience of ordering online, the following link has a large selection and good prices for water-grow animals.

Tuesday, October 12, 2010

Quest of the Questionaut

   Readers know that I am a big fan of the computer games created by the team at Amanita Design ( I like playing their games because of the creative problem-solving scenarios that float within the frame of a story. And so do my grand kids. In earlier posts, I've reviewed three of their games, Samarost I (free), Samarost II, and Machinarium. The creativity at Amanita Design is even reflected in how you navigate through their web site. The home page is blank except for a curious object in the lower right corner. Click on one of the white buds and it blossoms to a new stem with more white buds. Click on the indicated buds to get to the Flash Games screen. All of Amanita's games can be reached from this screen but for this post, click on Questionaut.
   This short, one-minute video starts the story. An unnamed character, sitting on a cactus at the top of screen, has its hat blown off, sending the Questionaut on a quest to retrieve it.
   At each of the eight levels, the Questionaut has to correctly answer questions in order to collect and store enough helium to float up to the next level. Answering a question correctly adds a bubble of helium to the collection canister at the left side of the screen. Answering a question incorrectly pops one of the bubbles already in the canister. The questions keep coming until you get a total of five gas bubbles. Then, away you (the Questionaut) float to the next level. The first level shows grand dad reading a book as grandmother types away on her antique Remington. 
   For myself, and probably kids, the most fun comes from solving the point-and-click problem that starts each level. For example, to get the questions at level 1, you have to shift grandad's attention away from his book. If you get stuck, send an email and I'll give you a hint. Not  the answer—a hint!
   Consider the question, When reading an illustrated book (a book with pictures and diagrams), asked in the following level 1 graphic. If you were to answer with c, ‘look at all the information on the page’, you would be correct and the fifth bubble would fill the canister and be transferred to the balloon for enough lift to get to the next level.
   The game has eight levels. The levels were designed to cover basic school topics. The topics covered are, in order:
Level 1:         Writing Skills
Level 2:         Arithmetic
Level 3:         Plant and Flower Facts
Level 4:         Geometry
Level 5:         Science
Level 6:         Graphs/Probability/Statistics – [28p means 28 pence]
Level 7:         More Science
Level 8:         Grammar
   There has to be a large number of questions in the data bank. I've played through the game four times with very few repeat questions.
   It took Amanita two years to give us Machinarium. I hope I don't have to wait that long before I can play their next major product.

Friday, September 17, 2010

Second Scratch

   In an earlier post (see June 2010) I announced a forthcoming series of posts on Scratch, the programming language especially designed for (but not limited to) kids. 
   Scratch asks its users to imagine, program, and share. As an example of this three-step sequence, I’ll describe a project of mine that I imagined, programmed, and shared (uploaded) to the Scratch homepage.
   Imagine four motionless ants sitting at the corners of a square, all facing in the counterclockwise direction.

   At a given signal, each ant moves towards the ant ahead of it. What will the paths of the ants look like? Decades ago, I saw this questioned posed in a book. This was long before we had programming languages like Scratch to provide a wordless, dynamic, answer.
   The script (program) that answers the question is not an entry-level program but Scratch contains two commands that greatly simplifies the programming; point towards and move 5 steps. Since the ants are numbered, it's easy to point each ant towards the ant in front.
   To view what happens when the ants are turned loose, click on the following short, one-minute video. What’s not visible in the video are the scripts that create the ant’s motion.
   As can be seen in the video, the ants trace a spiral path and the straight lines connecting the ants always form a square. 
   I uploaded the working Scratch file to the Scratch web site for any user to look at and any registered user to download. If interested, Scratchers can modify the program to make it do what they would like it to do. For example, what if three ants are at the corners of a triangle? To view my Scratch projects, go to and search on grandadscience.
  The Scratch homepage contains data as to the age and numbers of registered Scratch users. Tens of thousands, at each of the ages 11 through 16, form the bulk of Scratch users. Few are getting instruction in public schools. It would appear that kids are learning how to program in Scratch from each other! Also, girls are as well represented as boys.
   I'm not suggesting that all kids need to learn to program in Scratch. I am saying that all kids should know about Scratch and make the decision for themselves. The math and science (particularly the math) they learn in school then has an outlet. 
   To help you and your kids or grand kids get started with Scratch, I've made several short videos. Instead of loading this post with the videos, below are the links to the seven How to Scratch videos I uploaded to Youtube. Every video is short (two minutes or less), builds on the previous video, and asks the viewer to duplicate (with their downloaded version of Scratch) what's just been viewed.
   The first video shows how easy it is to download the Windows or Mac version of Scratch. Be sure to bookmark the homepage. By the seventh video (15 instructional minutes later), the user has written a script that draws a square with any side length.
   I will be here to answer questions about Scratch and I will occasionally post a Scratch update or project.
Scratch A1.1 – How to Download Scratch
Scratch A1.2 – The Move and Turn Blocks
Scratch A1.3 – Pen Commands: pen down, pen color, pen size
Scratch A1.4 – The Repeat and wait blocks
Scratch A1.5 – How to edit the Scratch the cat sprite to add a pen
Scratch A1.6 – The 'Click on the Green Flag' block and the Presentation Mode
Scratch A1.7 – Defining the variable 'distance' for use in the Square Script

Thursday, September 9, 2010

Behind the Mirror

   In the first mirror post (see The Two of You, August 2010) we looked into a mirror and observed that our image was reversed, left-to-right. We also observed that our image appeared to be behind the mirror's surface. Somehow, our image had moved behind the wall! Also, when trying to touch the nose on our mirror image, we could get no closer than than surface of the mirror.
   Over a series of posts, I will share three simple investigations that explore the relationship between an object and its mirror image. The first investigation is to have the kids simply put a mirror on top of a ruler. In the photo below, a mirror is set on top of a see-through plastic ruler and aligned at right angles to the ruler so that the ruler appears to extend straight into the mirror.
   Place a small object (I used a green pushpin) on the ruler at a point three inches in front of the mirror. Ask the kids to report how many inches the mirror image’s position on the ruler appears to be into the mirror. Now have them move the pushpin, along the ruler, and tell them to watch its mirror image mimic the position of the object. Kids like color so instead of an inch-ruler, I used my graphics program to make a series of colored circles, spaced an inch apart. If you would like a copy of this page, shown below, just shoot an email to and I will send you a pdf.
   Use the same procedure for observing object-image distances with the color bar as used for the ruler. This is how the color bar looks in the mirror.
   Now is a good time to talk to the kids about forming a hypothesis as to the relationship between the distance an object is placed in front of a flat mirror and the distance the object appears to be behind the mirror. It’s important that kid’s understand that the hypothesis (idea to be tested) comes from observation and experiment and is just not a wild guess or prediction.
   A good hypothesis, easily tested is,
The distance an object is placed in front of a flat mirror
 is equal to the distance the mirror image appears
 to be located behind the mirror.
   Distance is a quantity that can be measured so in the next mirror post we will discover how two pushpins and a ruler are used to test the hypothesis.
   This post motivated me to read again Lewis Carroll's Through the Looking Glass in which Alice, of Wonderland fame, steps into and behind a mirror. The best version of both tales is found in The Annotated Alice, by Martin Gardner. Gardner's notes to the text illuminates the math and science (Carroll was a mathematician) that fill the background in the stories. A game of Chess directs the action in Through the looking Glass and Alice confronts a host of marvelous characters like the mirror-image twins, Tweedledee and Tweedledum. I recommend adding Through the Looking Glass to the kid's library as it is literature, and, if you get Gardner's annotated version, learning the math and science connections makes a classic even better.
   Here's a short animation I made that will summarize the object-image relation in mirror reflection.

Tuesday, August 31, 2010

Moonbase Alpha Computer Game - Free

   Moonbase Alpha is a FREE, NASA-funded, computer game set on a hypothetical lunar outpost. A wayward asteroid hits and knocks out critical life-support systems. The player (or group of 2-6 players) has to analyze the situation and restore the systems before emergency supplies are exhausted.  To do so, the astronaut must use a variety of tools including a remote-controlled robot.
   During a recent visit, grandson Joshua (he starts the fourth grade this year) played through Moonbase Alpha in about 45 minutes. After a brief time experimenting with the mouse and keyboard controls, Joshua went on to successfully play through the game to the end. He then challenged me to better his time!  In the following picture, Joshua is controlling the astronaut as the astronaut sets up a repair station.
   In this photo, Joshua, from the perspective of the controlling astronaut, sends a repair robot into an area too dangerous for the astronaut to enter to replace a damaged life support system component.
  As adults, we can help kids by understanding that even though we may feel uncomfortable playing a video game, our kids do not. Why not put quality gaming experiences in our kid's environment and simply out of the way. By the way, I have not bettered Joshua's time. Yet.
   Here's the link to the NASA web site where you can learn more about Moonbase Alpha. The site will also direct you to the Steam home page where you can search on Moonbase Alpha and download the game (PC only). If you don't already have the free Steam client software, you will have to download and install it before Steam will download the game to your computer.

Friday, August 13, 2010

The Two Of You

"The world is full of obvious things which nobody by any chance ever observes." So said Sherlock Holmes in "The Hound of the Baskervilles".

   One of those 'obvious thing's' found in everyone’s world is a flat mirror. There's probably one hanging on your living room wall and for sure there is at least one where you shave or comb your hair.
   Ask your kids or grand kids to stand in front of a mirror and tell you what they see. They will see a lot of things like their own image, objects in the room, their hair is uncombed, etc., but they will not observe that their image appears to be behind the mirror
   Ask them to touch the nose of their mirror image. In trying to comply with your request, they should observe that instead of the finger touching the nose, it touches the surface of the mirror!
   When looking into a flat, plane mirror, there is the real you, in front of the mirror, and then there is a virtual you, an image of you (cleverly called mirror image), as seen in the mirror! The two are not exactly identical.
   To observe a difference between the two images, ask the kids to look into a mirror, close their right eye, and observe which eye the mirror image closes. It comes as a shock to most that the mirror image closes its left eye!
   The word AMBULANCE is often painted in its reversed form,

on the front of the vehicle. A driver, looking into the rear-view mirror, sees


and correctly identifies the vehicle as an emergency vehicle and pulls to the side of the road. 

   To demonstrate, I've printed a page with the word AMBULANCE reversed on the page (I have graphics software that reverses text). When viewed in a plane mirror, the mirror left-right reverses the word so that it reads correctly, just as you would see it spelled correctly in your rear-view mirror.

  Besides the left-right reversal, there are several interesting mathematical and scientific relationships to be discovered exploring mirror reflection. Here's a good question to ask. Since a plane mirror reverses left and right, why doesn't the mirror reverse up and down?
   In the next mirror post, I will explore the relationship between the distance an object is in front of a mirror, and the distance the image appears to be behind the mirror. I know several ways to demonstrate this relationship so I'll start with the simplest and most intuitive method.

Tuesday, August 3, 2010

The Adventures of Little Wheel

   Grandsons John and Andrew love stories and games that feature robots. We’ve played through Machinarium, a great computer game about a city of robots. Machinarium (see the November 2009 post) is long enough to tell a good story, full of fun problems-to-solve, but can hold the rapt attention of a four and five-year old when played with an adult (like a grandfather or grandmother). Every night, for two weeks, I played through Machinarium as John and Andrew's bedtime story.
   There are hundreds of web-based games and I keep my eye out for those that I would like all of our grand kids to know about and, if they choose, play. I recently found a game that features a robot so this post is especially for John and Andrew (and any other grandparents, parents, or teachers) that appreciate good interactive stories).
   Little Wheel is a sentry robot living in a city populated only by robots. Watch this brief introduction as it sets the story and calls Little Wheel to the stage. [When you play the game online, you can skip this intro by clicking on 'Skip' in the lower right corner of the screen.]
   The bolt of lightning that struck Patrol Tower #2 provided Little Wheel with enough juice to get moving on solving the problem of restoring electrical power to all of the robots in the city.
   The problems Little Wheel has to solve to restore electrical power are not difficult but do require the player to pay 'attention to detail', which is an important problem-solving skill. As a new level is reached, a series of white circles appear that identify where on the screen an action is required to move the story forward. The white circles eliminate the need to click all over the screen to find 'hot points'.
   In the following short, one-minute video, I show how to use the white circles to solve Little Wheel's first problem, calling an elevator.
   Little Wheel is a short game and is designed to be played through in a single session. There is not a 'SAVE GAME' button so don't look for one.
   To play the game, go to either of these sites. Have fun. 

Friday, July 23, 2010

Flower Festival - Part 3

Jordann, our oldest granddaughter, will be in the third grade next year. Soon after our return from Belgium last March, she and her brother Joshua spent a few days with us. She decided she wanted to do a science experiment and plant the same flower variety in two pots, keep one indoors, one outdoors, and then observe, over time, the flowers grow. Jordann had learned in school that plants need light to live and grow but had never taken the time to conduct her own test.
Weeks later,Jordann and Joshua returned to spend a week with us. We had lots of fun. We spent one night at a very nice hotel with a great restaurant and a beautiful swimming pool.
Later the next day, after a huge breakfast, we drove to the mountains to a spot just south of Yosemite National Park, and rode the Sugar Pine Railroad. The SPR was a logging railroad and one of the steam engines used to haul logs out of the forest is stiff huffing and puffing away. Here’s a picture of  Joshua and Jordann in front of Old Number 10. 
The conductor announced over the PA system that Number 10 was built in 1934. That’s just four years before I was born and I’m stiff huffing and puffing too!
Here is Jordann with her indoor flower.
This is Jordann's outdoor flower.
Jordann was amazed at the difference in the leaf growth between the plants and the indoor plants' lack of flower blossoms. She will continue to check the plants on subsequent visits.
After Jordann and Joshua left for home, I was watering the yard and noticed this blue flower growing from the intersection of a stucco wall and concrete slab at the front of our house. 
We planted this type of flower as groundcover in the planters that separate the sidewalks from the street in front of our house. Apparently the wind (or possibly a bird) deposited a seed on the slab and the wind wedged it in the crack at the wall.
The front of our house faces West so the little blue flower receives plenty of light. But where does it get water and nourishment? I’ll ask Jordannn that question when she and Joshua return next month. The little blue flower suggests that perhaps it is time to read with Jordannn, The Little Prince, by Antoine de Saint-ExupĂ©ry. The story tells how the Little Prince learns to care for a flower.

Sunday, July 11, 2010

Flower Festival - Part 2

Not long after our return from visiting the flower garden at Keukenhof, Holland, the boys and I were playing outdoors. John found a small, white flower in some loose soil and pulled it up, roots and all. I suggested we put the flower in a glass of water, set it on a windowsill, and see what happens. 
John found the roots interesting and we talked about how the flower sends its roots in all directions to find water and other nutrients. I said that since the roots were not damaged, the flower could live for several days in the glass of water.
Here is a close-up of the flower’s roots.
Several days passed. The flower even added new blossoms. John decided to return it to the ground so that it would live through the Spring and Summer. Our son and his family have since returned to the United States and a new Air Force assignment. I’m sure the little flower has survived and is adding its glory to the Belgium summer.
Where’s the math and science in John’s flower experience?  Besides the more complex botany and biology, there’s a simple and structurally important symmetrical form to be seen in leaves, stems, and roots. It’s a structure that helps a five-year connect what’s above the ground and what’s below the ground when they see a planted tree or flower.
Trunk, limb, twig is a branching structure much studied by scientists and mathematicians. Branching is a highly efficient way to collect or distribute something.
In a planted tree or flower, the top endpoints of the branching system are called leaves. Branching maximizes the number of leaves (nature’s solar panels) available for collecting the sunlight necessary for photosynthesis. The roots maximize the collection volume for finding water and subsurface nutrients.
Branching is a highly efficient way to collect or distribute things like sunlight, corn flakes, and taxes. Not all branching systems are like the one shown above that has branches at both ends. Many branching systems are two-way systems. Corn flakes are made at a factory, shipped to a wholesaler, transshipped to a retailer, and purchased by a customer. Money flows in the opposite direction, from customer to corn flake maker.
Branching is an important idea to teach our kids and grand kids and is one of those science and math ‘themes’ we can look for throughout all of nature.

John will be starting Kindergarten soon. With the push to get kids reading and doing ‘math’ from day one in school, I wonder if the first school year wouldn’t be better spent teaching kids a reverence for living things.