Corny Equations

Corny Equations With

Computers and Calculators

Mary Lou Silveira

Introduction:

The production of corn is a profitable and dynamic industry attracting the best and brightest individuals. As a person interested in corn production you are being asked to respond to the challenge and take the uses of corn for food, feed, and industrial needs into the 21st century.
But, before you take this challenge you need to know some of the variables that would effect whether you make a profit or not. You will be doing two lessons that will help you decide if you want to grow corn and be a part of the challenge.

Since the majority of Corn Industries use Midwestern terms this lesson will contain terms which are uncommonly used in California. A ton (2,000 pounds) is the unit of measurement that is used in California whereas the bushel (56 pounds) is the unit of measurement the majority of the United States use. For California purposes a ton is 35.17 bushels.

Grade Levels: 9-12

Prior Knowledge:

The lesson is most suitable for the end of the first year of algebra when students have knowledge of using in/out tables, identifying types of lines, and developing lines of best fit, equations, and interpreting graphs.
Navigating the Internet

Knowledge in using a graphing calculator, this lesson was done with the TI-82 graphing calculator. Additional resources are available for the TI-81, TI-83, and TI-85. Other brands of Calculators are suitable as well.

Objective:

Lesson 1:
Students to visit selected Internet sites: a calculator from NK Corn Yield Loss, or a spreadsheet with the same information. They calculate the estimated % Corn Yield Loss, when defoliation occurs, (from frost and hail damage), at different stages of growth. All information is from the National Crop Insurance Service. They will place the information on In/Out tables. They will graph the data, and answer some questions. Then students will use a graphing calculator to analyze the set of data, and derive an equation for a line of best fit for each line.
Lesson 2:
Students will visit a selected Internet site and determine the Economic Returns corn at various yields and various market prices. They will put the data on and In/Out table, graph the data, and answer questions regarding interpreting the graphs. Finally students will use a graphing calculator to determine an equation for a line of best fit for each line.

Resources:

Web Sites:
NK (Novartis Seeds) Corn Yield Loss Calculator (http://www.nk-us.com/toolshed/calculators.asp)
(An excellent source of information about variables effecting corn growth)
NCH-1: Assessing Hail Damage to Corn (http://www.agcom.purdue.edu/AgCom/Pubs/NCH/NCH-1.html

TI-81, TI-82, and TI-83 Graphing Basics (http://www.mathimp.org/#teach)
instructions for Year 1 can be purchased from Key Curriculum Press via Interactive Math Program - Teacher Resource site.

TI-85 Graphing Basics instructions (http://score.kings.k12.ca.us/lessons/curve.fitting.html)

Worksheets:
Lesson 1:

"In/Out tables of Potential Crop Loss from Defoliation due to Frost and Hail at Different Stages of Growth"

HTML or PDF

"Graph - Corn Yield Loss due to Defoliation from Frost and Hail at Different Stages of Growth"

HTML or PDF

Instructions for Plotting Points and Curve Fitting

- TI-82 (see attached)
- TI-85 (http://score.kings.k12.ca.us/lessons/snider/step.by.step.html)
- TI-81, TI-83 (http://www.mathimp.org/#teach)

Lesson 2:

"In/Out Table of Returns of Corn Yields at Various Corn Prices-Yield Combination"

HTML or PDF

"Graph - Returns of Corn Yield at Various Corn Price-Yield Combination"

HTML or PDF

Learning Advice:

Students should be familiar with graphing calculators.
Teachers may use the NK web site and the Purdue University web site or can copy the chart from NCH-1 CLIMATE & WEATHER Table 3: "Estimated percent Corn Yield Loss Due to Defoliation Occurring at Various Stages of Growth" (if a computer is not available for each student:.

Give student copies of the In/Out tables and graph worksheets for each lesson.

Evaluation:

I wasn't sure where this would go and if the lesson could be algebraic but I was extremely surprised at how the lesson supports algebra concepts we are teaching.

Extension:

Instead of using bushels (56 pounds) convert the unit of measurement to tons (2,000 pounds). Do the lesson in tons instead of bushels.
Find out current prices and "your" County Corn Production yields of corn, and find out how accurate this lesson is to real life.

Conclusion:

This was a very interesting lesson to do. I plan on sending copies of "Corny Equations" to the National Corn Growers Association. They have a education program. In addition because I used TI-82 calculator I plan on sending a copy to Texas Instruments.

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California's Mathematics Academic Standards

Grade 8-12:
Algebra I
5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification of each step.
17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.
Probability and Statistics
8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.