How many of the numbers from 1 to 100 are in the times table? All, Most, Less than half? I think you will find in this exploration of the relationship between the multiplication table products and the whole numbers as fascinating as I have. It is one of my favorite Labs because it gives us a chance to explore the patterns of both the times table and the hundreds table. And at the same time it helps us to see the patterns and to practice the multiplication facts.
Spreadsheets can be a great place for you to build your own games. Ryan has built one of his early favorites, Battleship, where you learn graphing as you try to sink your opponent’s battleships. Making your own games can be great fun. Try it.
Strings need not begin and end on axes that are at right angles to each other which we call Cartesian. It is quite interesting that Descartes himself did not use axes at right angles. We consider this a challenge because students have to figure out how to move both the axes and the lines. Once you understand the process there is no end to the beauty of the string diagrams you can make. We suggest you check out the Web and Wikipedia for more ideas.
Scatterplot graphs enable us to build shapes using spreadsheets and to practice transformational geometry. They are surprisingly flexible tools. And since they depend upon a table of value and that table can have both fixed numbers and rules, we can not only build shapes but change them and watch the graph immediately reflect those changes. In this lab we use that capability to get students to explore scaling, reflection, and transposition of a triangle. This is only the beginning and we hope students will take this further exploring symmetries for example.
We take that great old problem of the inventor of chess and the ruler of India and use it to see how powers of 2 grow in size. We start out with a chessboard and look at doubling each successive number. Then we seek a method of representing this doubling in a formula and introduce exponents and powers of 2. We ask you what kind of rule would you suggest that would keep your head and please the ruler?