Solving Systems By Graphing

I had the pleasure to be in a MTH1W class that was working on solving systems of equations with tables and by graphing.

In small random groups students tackled the problem with many strategies. Some made equations, then graphed directly. Some groups rewrote 1.5 as 3/2 to show the slope in a fraction form to help graph more easily.

Some made tables and equations and graphs which all showed that there’s a cross over point, or point of intersection at 4km and $11.

A follow up question was regarding the planning of a birthday party. At Tony’s Pizza they charge $150 for the party room and $12 per guest, and at Joey’s Hamburger it costs $180 for the party room and $10 per guest.

Some groups made equations, then used tables and calculated values until they could see a cross over point.

Groups that tried to graph directly from equations had a struggle with the scales, and plotting rise and run accurately. Lines started to look almost parallel, even though we know that the rates are not the same. The point of intersection would be way off the graph in this case.

Student are getting confident applying their skills to solve problems with linear equations, and to work together in groups and communicate their learning.