What do cantilevers and pulling nails have in common?

Math Standard:

A.CED.1 Create equations in one variable and use them to solve problems.

G.CO.2 Represent transformations. 

CTE Standard:

            Students will understand how levers and fulcrums are used in construction.

Teacher Notes/Materials Needed:

Ruler, cups, fulcrum, fun size candy bars, 2 x 10 x 10, 

CTE Situation (opener):

What principle is involved in deciding how far you can cantilever a deck or 2^nd floor, or how big a hammer or crow bar is needed to pull a nail?  Why is holding a hammer close to the head less efficient than holding it close to the end of the handle? 

Lesson Sequence:  Can 1 candy bar lift 6 candy bars?

1.     Show a visual demonstration of the lever/fulcrum principle by using a ruler, pen (fulcrum), 2 plastic cups, fun size candy bars.  Model this with the fulcrum at the center of the ruler with a cup containing 1 candy bar placed on one end of the ruler and a cup containing 6 candy bars on the other end (note it does not balance).

a.     Discuss and experiment with ruler lever/fulcrum so that 1 candy lifts 6 candies.

b.     An extension, using a 2 X 10 x 10, have a lightweight student lift a larger (football player type) student.

c.      Process with students using the photos above, where is the fulcrum and lever located?  This is a great place to talk about the “center of rotation” and “translation” of the fulcrum.

2.     Transition into developing a math expression/equation to represent the lever scenario

longer distance X lighter person = shorter distance X heavier person

or express as a proportion

Thanks to John Gregory & Steven Davis of Norwich, NY for letting this problem be reprinted.