The connected machine is a single function that takes an input, runs it through the network inside and produces an output. You control a network of function machines along with the input and the operation performed by each machine to solve problems.
To find the area of a shape, surround the shape with a rectangle, determine the areas of the rectangle and subtract the pieces of the rectangle that are outside the original shape. Use this geoboard to create shapes and determine their areas.
The colors listed in the boxes represent different parts of speech: noun, verb, adjective, adverb, etc. Figure out which colors represent which part of speech and then use the colors to create proper sentences.
To find a hidden treasure use taxicab geometry, a special kind of geometry that counts in city blocks. Pick an intersection, ask the computer how far it is to the treasure and get the distance using taxicab geometry.
Build as many different looking towers as is possible, each exactly four cubes high using two colors of Unifix® Cubes. Convince yourself and others that you have found all possible towers four cubes high and that you have no duplicates.
You can find the areas of different polygons by dissecting the polygons and rearranging the pieces into a recognizable simpler shape. Cut a circle into wedges and fit them together to form a crude parallelogram.
Which hexomino net wastes the least amount of paper and yields the most boxes per sheet? Comment on how concepts such as area, spatial visualization and relationships among geometric shapes are all involved in solving this problem.