Land Conservation and The Mathematics of Area

The problem – We have a field that currently uses gravity fed irrigation (the lighter colored field in the center of the picture).  This mode of irrigation is very wasteful, and so a more efficient center pivot irrigation system needs to be put in place.  Design a center pivot irrigation system for the field below.  Your design must utilize exactly the amount of irrigated acres available.  Additional irrigated acres are not allowed and utilizing less than is currently there will loose you money!!

Once the designs are completed we will do a cost analysis of their designs.  Prices to consider.  Each Center pivot costs approximately $50,000.  Running electricity and water pipe from the well to the center point $7.00 per linear foot.

Transferring dry land to irrigated acres costs $50 per acre.   Transferring pasture to irrigated costs $500 per acre.

Consultant fee for asking the teacher a math related question- $1,000 per question answered. (an idea to make it more lifelike).

When we are done with this project I will post some of their plans after Christmas.

Factor by Grouping with a Negative GCF

A harder example of factor by grouping.

What is a Function? In Five Minutes

After about 5 takes, I was able to almost get what I wanted to say in this video.  The mathematical concept of a function is hard to convey in less than 5 minutes.  Had to keep it pretty basic, and I hope there are not many errors.

Estimating Slope Take One

In this silent video I show how a group of Ag and math students estimate slope in order to calculate how erodible the newly planted field will be.   I just wanted the video up fast.  I will spend some more time later refining it and adding some other explanations.

A major question I had as a math teacher, after hearing this is how the Ag class estimates slope at a range management competition.

How is it possible to use the hypotenuse to calculate a fairly accurate estimate?

Finding the Interesection of a Parabola and a Line

Sketch the graphs of the line 2x – y = -2 and the parabola y = -x² – 4x + 1.  Find the coordinates of any points of intersection with technology and with algebra methods.  As student was requesting a video on how to do this, and I couldn’t find one already made online so here goes.

Construction of a Perpendicular Line Through a Given Point and Line

Using a compass and straight edge construct this theorem.   Through a point outside a line, there is exactly one line perpendicular  to the given line.

Construction of a Parallel Line Through a Point

Here is the construction of corresponding angles to create a parallel line through a point and parallel to a given line.

Finding the Equation of a Line Through a Point and Perpendicular to a Line

Find the equation of a line through the point (5,-2) and perpendicular to the line 2x + 5y = 7

In the video at the end I changed all of my signs by multiplying both sides of the equation by -1.  The signs can’t just magically change.

Orienteering – Where am I? Find My Location in Southwest Nebraska

Watch the video and then using the piece of the sectional Jepsen Aviation map for southwest Nebraska find my approximate location on the map using the coordinates I give you in the video.  I am using a very imprecise tool, so do not expect perfection.