The usual way to make string diagrams using rubber bands or yarn on a board with nails does not allow much exploration. Mary Boole meant them as exercises in visualization. Building these diagrams using spreadsheets not only shows their versatility and capability for artistic expression, it helps students get used to using ordered pairs and axes of different sorts and thus builds their graphic sense. There are so many possibilities that you might think of having contests for the most interesting and thought provoking diagrams.
Category: Labs
Enigma Machine
Spreadsheets are great for creating secret codes and for breaking them. During World War II the German military used a machine they called Enigma to send coded messages. In a box about the size of a typewriter, wheels with letters on them were spun around to encode or to decode a message. The story of the breaking of that code by Alan Turing and the British code breakers was made into the movie The Imitation Game. We have used spreadsheets with some of their built-in rules to let you set up your own enigma machine. There are many ways you can use a spreadsheet to generate or to crack codes. It is fun to see if you can make a code your friends can’t break.
Odd Times
How many of the products in a 12 by 12 times table are odd numbers? This is a question we rarely ask in paper-based math classrooms, yet it is an important and a very interesting question. We ask students to explore it, learning to Show and Hide rows and columns in their spreadsheet at the same time. Here again is an interesting pattern in mathematics, one we do not generally expect. Odds and evens often seem to students to be an unimportant distinction, but it is not. Odd and even numbers appear again and again across all of mathematics and in many of our Labs. It is important not only as a pattern, but it tells us to pay attention to odd number products because they are rarer than even number products.
Drawing Triangles
Though spreadsheets lets you put geometric shapes on the screen, those shapes are not connected with the cells and cannot be changed by using different values. We wanted to make geometric shapes that we could control and change by changing parameters. This is our first try. You can learn to use linear functions to create and change a triangle. It is pretty cool. This Lab involves many different aspects of mathematics from geometric shapes to graphing, from slope to linear functions, from perpendicular lines to the definition of function.
Sudoku Challenge
Have you ever played Sudoku? It is fun and challenging. You have to find the numbers from 1 to 9 in each cell so that that all of the numbers appear only once in every row, column, and grid square. Ryan added a sweet wrinkle to the traditional Sudoku game, he gives you the sums so that you not only get to practice addition, you can get some hints about the numbers you should input. Can you use our template to create your own Sudoku challenge?