Number Lines introduce students to functional thinking and the use of formulas in spreadsheets. For younger students we call these formulas “rules” and ask students to build a variety of number lines using rules. For example they can build a whole number line by creating a rule that adds 1 to the number in the previous cell (=J9+1) and then copy that rule across the numberline cells. They build numberlines with only odd numbers, even numbers, and starting with different numbers. We encourage them to explore a variety of rules to make different numberlines.
Author: Ryan McQuade
Introducing Spreadsheets
In introducing Spreadsheets we want you to learn to build a numberline by using a rule (a formula). We begin with a simple rule that you can copy and paste into the entire numberline. Then we want to add an input from another cell into the rule to give you a chance to change the numberline. And finally you build a rule that lets you change not only the input number but the operation so that you can build any numberline you want. Remember that you have three ideas in functional thinking, an input, an output, and a rule to change the input into the output.
Fibonacci’s Sequence
Fibonacci, the nickname given the great medieval mathematician Leonardo of Pisa, is connected in most of our minds with the Fibonacci sequence. Spreadsheets make wonderful tools for creating such sequences. This one is amazingly simple. Just select a cell, any cell and write a formula in that cell that adds together the two cells above it. Now copy that cell down the spreadsheet and seed it with 1 in the first cell. The Fibonacci sequence is a pattern that this action shows very well. This sequence has surprising attributes, and we explore some of them as well.
Triangular Numbers
1, 3, 6, 10… are called the triangular numbers because they can be stacked up to form a triangle. They are very interesting numbers, and they form a very interesting pattern when graphed.
Can you guess the next triangular number? Can you guess the shape of the graph of the triangular numbers? Can you explain that graph?
String Diagrams
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.