## 04 Dec 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.