This graph appeared on one of my favorite websites – Statista.
Given the “breaking news” of the day, that the President wants to impose new tariffs on steel imports, it is fascinating to see from this graph the countries most affected, certainly not the ones we might have thought. It is a perfect example of the power of visualization, of graphs, to tell a story, and the reason we consider them fundamental to our What if Math Labs. Take the Tour to see more.
Art
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.
Spreadsheet math generally focuses on ratio and proportion to develop the concept of fraction. But fractions is such a big problem in today’s curriculum that it seemed only right to use the power of spreadsheets to help students and teachers to gain some fraction-sense. This is a very simple spreadsheet that uses histograms to compare fractions. We expect students to play with this and to put in different fractions and guess which ones will be bigger or smaller and then check their guesses. This Lab only works on Excel Spreadsheets.
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.
We have made a big deal of the times table and of other tables.Now we extend the times table to negative numbers and thus to all 4 quadrants of the real number space. We hope to build student intuition about this space and to gain a spatial sense of graphing as well as of multiplication. So we as usual focus on patternmaking and take students through extending the table first left by rows and then down by columns before we have them build the table as a whole. We moved the axes to the outside so that we do not interfere with the table. There are many things you can do with such a table and we urge you to explore it.
