No solutions in parallel lines: getting it to stick

Like most caring algebra teachers who have been at it for many years, there are very few algebra topics that I have difficulty getting a student to understand.  Teachers who are in tune with the learning process become aware of what makes a topic difficult and systematically remove barriers to understanding.  Getting concepts to stick, though, is not so easy.   Much of  high school math can seem irrelevant to students, which is why I believe there can be difficulty with recall.  I believe part of my job is to convince students otherwise…and least make it relevant enough for them to be able to remember.

Relevance  is a moving target, so I am constantly on the lookout for  memorable connections.  Here’s a quick and captivating lesson about a system of parallel lines.  The “cool factor” video that makes it stick is followed by a two-minute discussion:

Cool Factor video

  1.   Which cab will be cheaper for a 20-mile ride?  Why?

Taxi cab A:                                            c=7+3.50m

Taxi cab B:                                            c=8+3.50m

      2.  Which subway pass is cheaper to commute 20 miles?  Why?

Pass       A:                                                c=10+2.50m

Pass       B:                                                c =10+3.50m

The taxi cab fares run parallel while the subway passes have the same y-intercept.  Students find the contrast almost as interesting as what they learn about haling a taxi…almost.  If a student forgets about parallel lines later, a quick mention of comparing the taxi rates usually takes care of the lapse in memory.  The video provides a memory anchor.

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