Saturday, February 21, 2015

Robot Turtles – A Board game that Teaches Programming

    I was excited to recently find a board game that claims to teach fundamental programming concepts to very young children. It’s called Robot Turtles. The feature that I found most attractive and perhaps unique in the game is that Robot Turtles is designed for adults to play with kids. Sure, Robot Turtles could be an APP, but touching and swiping an APP is a solitary experience.
    The idea of a ‘turtle’ as a programmable object originated with Dr. Seymour Papert in the early 1970s. At that time he was a researcher working in the Artificial Intelligence Lab at the Massachusetts Institute of Technology. You can trace the evolution of Logo from Papert’s original mainframe LISP version to Apple and Atari Logo in 1980s to Starlogo in the 1990s and to Scratch (, its latest incarnation.
    A grownup is the Turtle Mover and controls the movement of the game pieces. This keeps the game moving and removes the errors youngsters might make in counting positions on the board.
Each youngster is a Turtle Master and controls the action cards.
The goal is for each Turtle Master to use their set of action cards to get their turtle from the start position to the colored gem that matches the color of their turtle.
    The path between the Start position and the jewel can be blocked by walls of ice, stone, or even wooden crates. Fortunately, each turtle can carry a laser to blast through these walls.
    Here’s what a typical game board looks like.
   Robot Turtles is a great introduction to Scratch Jr 
a free programming language for five to seven year-olds.
   Check Amazon for the latest price.

Tuesday, February 17, 2015

Figurate Numbers

Note: This post originally appeared in May of 2009. Technical issues required that I delete the original post and repost it.

  Isn't it wonderful when the grand kids first show off their ability to count?  For the most part, kids learn to count on their own! That's why the set of numbers, 1, 2, 3, 4, 5, … are known as the natural numbers. They just come naturally.
   Kids connect numbers with real objects. Two cookies are better than one cookie. Abstract ideas such as "number" are best met in the form of "real" objects. The ancient Greeks understood this. They used pebbles to form geometric shapes, discovered number patterns in these shapes, and laid the foundation of mathematics.
    Early Greek mathematicians used the visual simplicity of geometric shape to discover and think about abstract number relationships.
    Why shouldn’t our kids and grand kids do the same?
    Fish fifteen pennies out of your piggy bank, gather the kids around the kitchen table, and let’s explore figurate numbers.
   The place to start is, naturally, with the set of natural numbers.
    Lay a single penny on the table. Ask one of the kids to use pennies to lay the next number, two, in a line, under the single coin as shown in the diagram below. Have the kids use pennies to construct the third, fourth, and fifth rows. 
   Now this is so simple and obvious that my grand kids might take it as an early sign that I am beginning to see profundity in the simplest of situations. But, ah! It stays simple, but gets better.
   Ask one of the kids to move the row of two pennies up and under the single penny so that they snuggle together, as can be seen at the top of this diagram.
   Ask them to identify what shape the three coins form when nudged close together (it helps to lay toothpicks or matches along the edges).
   As the Greeks observed, the three coins (pebbles) form a triangle. The natural number three is called a triangular number.
   The natural numbers four and five are not triangular numbers because no matter how hard you try to arrange five pennies in a snug, triangular form, there's always a hole (see above picture) and we won't allow a hole to spoil our pattern.
   Have the kids fit the third row of pennies under the second row and observe that the 6 pennies do form a triangular pattern with no holes. The natural number 6 is a triangular number.
   Now ask them to move the fourth row under the third row, count the pennies in the four rows, and tell you if the sum is or is not a triangular number (it is). Why? (The ten pennies fit snugly together to form a triangle).

   Finish by having them move the fifth row up, count the pennies, and decide if the sum is or is not a triangular number.
   Now for the mathematics. Ask the kids to predict the next triangular number (21) and explain how they got answer (15 + 6 in the sixth row = 21). If they want to keep going, let them. If not, that’s OK too.

   A good way to summarize the activity is to have the kids write down the natural numbers from 1 through 21 and to draw a triangle around those natural numbers that are also triangular numbers.
   If you would like a free PDF file that let’s the kids color and record the triangular numbers through row ten, simply email

   There are so many directions we can go with this activity but let me just choose one other property of the triangular numbers. The Greeks quickly found that any two consecutive triangular numbers form another class of figurate numbers, the square numbers.
   Watch this video to see the transformation of the two consecutive triangular numbers, three and six.

   The second figurate number post can be found by clicking on the following link.

Sunday, February 15, 2015

The Old Tree

   Our grand kids have loved the computer adventure stories that are strong on colorful storybook graphics, tinkling sound effects, simple controls, and do not have any voice or text narration. This style of story telling allows the player’s imagination to take a role in developing the details of the story.  I’ve reviewed several of these games and a list appears at the end of this post. Now, on to The Old Tree.
   First, since there is no narrative other than the action on the screen, when you click on the red light on the opening screen, a creature is revealed. It’s a light-green bulb with four legs (or tentacles). Some have called the creature a space alien but I perceived it as a seed that is looking for a fertile place to grow. That’s the power of these types of computer games. You decide the details!
    One of the first challenges our hero meets is a caterpillar that parks itself over the hole that is the entrance to the tree. A bee, drops of water, and a flexible flower stem are the tools available to our hero. The clever use of these tools (by clicking on them) will chase away the caterpillar.
   After successfully solving a few problems, our hero, upon leaving the previous room clinging to the ceiling, enters a kitchen where another unnamed character is boiling water for a stew. Unfortunately, the ingredients for the stew aren’t there. Ah! There’s a button on the wall.
   Press it and a carrot is transported into the room. But look out, if you are not quick, a critter will steal it!            
   Unlike the other creative games I’ve reviewed, this one is short. After about thirty minutes of play, you reach the end of the tale and wave goodbye to the hero.
   And here’s the best part. The Old Tree is free! The Old Tree is a free download on Steam (go to or can be played in your browser on the Red Dwarf Games web site at

   Here’s a list of creative computer games with great stories that kids will enjoy.

Quest of the Questionaut

Tiny Bang Story


Samorost 1 and 2