3-Acts Absolute Value on the construction site

As a stay-at-home mom, the price tag of $17,000 to put siding on my old house that was peeling toxic paint was not in the budget. What’s a mother to do?  The building supply store quoted $3,000 if I did it myself.  That day I learned about Algebra from a couple of guys on a construction site.  I know if I had asked them to work a few problems they would likely have said, “Ma’am, I don’t know nothing about that stuff.”  But they were doing Algebra!  Anyone can snap long pieces into place and nail them down.  Making cutouts to fit around outlets, windows, and fixtures, however, presents many mathematical challenges because of all the constraints.  The goal is to help students develop a sense of “tolerance range” for measurement which is related to absolute value.  Cutting siding is also a simple example of metrology (not to be confused with meteorology.  Metrology is a lesser-known STEM field.

Act 1 – How should it fit?  Will it fit?  What does he have to think about to make it fit?  video

The siding must fit closely enough around the cut-out so that insulation is well covered, but not too tight or it will buckle as it expands in the summer heat.  A single piece of siding and a single strip of j-channel can be cut into pieces so that student groups will have a piece of each to see how they fit together.  The main questions are, “Within what range of values must the width of the cutout be to fit properly?  How can we write the answer as an absolute value inequality?”

Act 2 – Information you might need:      download  

The piece must be cut such that the cut edge is covered by the J-channel (about 1/4″) but leaves about 1/4″ for expansion.  The J-channel is 1″ wide.  That means the perfect cut would place the piece approximately 1/2″ into the J-channel, with a tolerance range of +/- 1/4″.

Hints download

Act 3 – Snapping the cutout in place download

For the cutout to fit properly, it must be within 10″ +/- 1/2″  As an absolute value, we write |x-10| =1/2 as an inequality |x-10|< 1/2

 

Standards and learning extensions  download  This activity can be extended to 10 or more Common Core State Standards.

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