| "IRRATIONAL PUZZLE" Math Teaching Tool Description:
This is a puzzle to introduce kids to irrational numbers. This set contains four cubes dissected in four different ways to form a variety of geometric solids.
This puzzle uses the math facts that the face diagonal and space diagonal of a unit cube are square roots of 2 and 3 respectively.
The instructions include seven brain teasers in which different three-dimensional geometric shapes are formed with the pieces.
Three reproducible worksheets cover the history of the square root of 2, the discovery of irrational numbers, and the Pythagorean Theorem.
Cubes measure 2.5" on a side.
Product Specifications:
Grades: 3-12
Product Size: 5.5" x 5" x 2.5"
Product Weight: 0.3 lbs
Product Contents:
11 Geometric Solids, made from soft, durable, and nontoxic foam.
Instruction Manual
Product Warnings & Safety Information:
WARNING: CHOKING HAZARD - SMALL PARTS. This game contains small pieces and is not suitable for children under 3 years of age.
A NOTE FROM LAURI:
Irrational Numbers refresher. For those of you who want a quick refresher about irrational numbers, an irrational number is a number that cannot be expressed as a simple fraction of integers, and cannot be represented as terminating or repeating decimals. The most well known irrational numbers are Pi, e, and square root of 2. All of these numbers are non-repeating decimals, and very smart people and computers love to figure these numbers out to a zillion decimal places.
Pi is the mathematical constant of the ratio of a circle's circumference to its diameter.
"e" is the mathematical constant often defined as the base of the natural logarithm.
Square root of 2, also known as Pythagoras' constant from the Pythagorean theorem, is the length of the hypotenuse of a right triangle with legs of length 1.
A "face diagonal" of a cube is a diagonal from one corner to another on the same face of a cube, and is the square root of 2.
A "space diagonal" of a cube is the diagonal from one corner to another that goes through the interior of a cube, and is the square root of 3.
OK, now that we're done with a definition review, what does that mean? It means that this set of cubes gives kids a tactile learning experience with two irrational numbers (square root of 2 and square root of 3) when trying to understand these weird "irrational number" things that are very basic math constants that they will use often as they progress with math. They also get a tactile view of terminology such as face and space diagonals. Tactile learning can provide a major reinforcement of pictures drawn on white boards. Kids learn better when they can touch it.
In addition, this is one example where the history of math is quite interesting. Although we now have computers as tools to help us figure out a zillion decimal places, long ago there were very smart people that were trying to figure out about these weird math issues. History is woven into the worksheets. This is one instance where your kids may enjoy hearing about tablets from Babylonia (circa 2000-1600 BC), ancient Hindu texts (circa 800-200 BC), Pythagoras and his follower Hippasus (who is generally attributed to the discovery of irrational numbers), and ancient Greek writings of Archimedes. There is even a reference to the Scarecrow in "The Wizard of Oz"! All to make irrational math fun! |
