# Speeding up the mechanics to slow down the thinking

Heading into my math 8 unit on linear relationships, I knew that I wanted students to use electronic tools like Google Sheets, Excel or Numbers to generate and manipulate graphs. The students got a bit of a preview when we did a “live graphing” activity at the end of the unit on area and volume. Then, when the new unit began, I had each student make a copy of a Graphing Spreadsheet I had created using Google Sheets*.

After a brief tutorial about how to get the spreadsheet to do calculations, students were able to generate graphs quickly by changing the x-values and/or by changing the equation used to generate the corresponding y-values.

Students had some time to play around the graphing tool and practice generating graphs. I then asked them to use the graphing spreadsheet to determine how different values of m and b affect the shape of graphs in the form y = mx + b.

While I will still require that my students practice plotting graphs by hand, I like giving them the option of doing it electronically so that they can focus the bigger picture. Because students can generate several graphs in just a few minutes, they can see how different values of m affect the shape of the graph, without getting bogged down in the process of generating a table of values, drawing axes, labelling axes and plotting points. By speeding up the mechanics, students can think about questions that get at a more conceptual understanding of linear relationships.

For example:

• What happens to the shape of the graph if the value of m (or b) is increased (or decreased)?
• Do negative values of m (or b) have the same effect as positive values?
• Why does multiplying x by a number change the slope, while adding (or subtracting) a number to (or from) x change its position?

As it turned out, this was just the beginning. Having students look at specific graphs to come up with general rules evolved in to some really rich discussion. Stay tuned for the next post to hear how this all played out…

*You can make your own copy too! Simply follow the link to open the spreadsheet. Under the “File” menu, select “Make a copy”. Give the file a new name and it’s yours to play with!