Foundations of Agricultural Education · 5 min read
Scientific Inquiry, Mathematics, Data, and Maps in Agriculture
Scientific Inquiry
The scientific method answers a testable question with a controlled, repeatable experiment. A hypothesis is a testable prediction for one investigation; a theory is a broad explanation supported by evidence from many investigations. Results support or fail to support a hypothesis; they do not prove it.
| Term | Definition | In the example |
|---|---|---|
| Independent variable | Factor the researcher changes | Nitrogen rate per acre |
| Dependent variable | Response that is measured | Grain yield |
| Controlled variables | Factors held the same for all groups | Hybrid, planting date, irrigation, soil |
| Control group | Untreated group; the baseline | Plots with zero nitrogen |
| Replication | Repeating each treatment on several units | Four plots per nitrogen rate |
| Randomization | Assigning treatments by chance | Rates drawn at random for each plot |
| Sample size | Number of units observed; larger is more reliable | Total plots harvested |
Data, Statistics, and Graphs
| Measure | How to find it | Result |
|---|---|---|
| Mean | Sum of values divided by number of values | 2,550 ÷ 5 = 510 lb |
| Median | Middle value when ranked | 500 lb |
| Mode | Most frequent value | 500 lb |
| Range | Highest minus lowest | 550 − 480 = 70 lb |
| Graph | Best use | Example |
|---|---|---|
| Line graph | Change in a variable over time | Daily milk production across a lactation |
| Bar graph | Comparing separate categories | Yield of five wheat varieties |
| Pie chart | Parts of a whole that total 100% | Share of farm expenses by category |
| Scatter plot | Relationship between two measured variables | Rainfall versus forage yield |
Random error comes from chance variation and is reduced by replication and larger samples. Systematic error shifts every measurement in one direction, as with an uncalibrated scale. Bias enters when samples or treatments are not chosen randomly or an observer expects a result. Accuracy is closeness to the true value; precision is agreement among repeated measurements. Correlation does not show causation.
Agricultural Mathematics
- 1 acre = 43,560 square feet; 640 acres = 1 square mile = 1 section
- Standard bushel weights: corn 56 lb; wheat 60 lb; soybeans 60 lb
- 1 hundredweight (cwt) = 100 lb; 1 ton = 2,000 lb
- 1 gallon of water weighs about 8.34 lb
- 1 mile = 5,280 feet; 1 kilogram = 2.2 lb; 1 hectare = 2.47 acres
| Calculation | Formula | Example |
|---|---|---|
| Acreage | Length (ft) × width (ft) ÷ 43,560 | 660 × 1,320 = 871,200 sq ft; 871,200 ÷ 43,560 = 20 acres |
| Fertilizer nutrient | Bag weight × percent analysis | 50 lb of 13-13-13 holds 6.5 lb each of N, P₂O₅, and K₂O |
| Ratio mix | Total × part ÷ sum of parts | 2,000 lb at 3:1 corn to soybean meal = 1,500 lb corn, 500 lb meal |
| Average daily gain | (Final weight − starting weight) ÷ days | (1,270 − 550) ÷ 240 = 3.0 lb per day |
| Board feet | Thickness (in) × width (in) × length (ft) ÷ 12 | 2 × 6 × 12 ÷ 12 = 12 board feet |
| Percent slope | Rise ÷ run × 100 | 6 ft rise over 200 ft = 3% |
- Yield per acre: 420,000 lb of corn is harvested from 50 acres. 420,000 ÷ 56 lb per bushel = 7,500 bushels; 7,500 ÷ 50 acres = 150 bushels per acre.
- Fertilizer rate: a recommendation calls for 100 lb of nitrogen per acre from urea (46-0-0). 100 ÷ 0.46 = about 217 lb of urea per acre.
Maps and Land Description
| Map or tool | What it shows | Typical use |
|---|---|---|
| Topographic map | Elevation by contour lines | Planning terraces, ponds, drainage |
| Soil survey map | Soil map units and their properties | Crop suitability and site limits (NRCS Web Soil Survey) |
| Plat map | Property boundaries and ownership | Locating tracts and easements |
| Aerial or satellite image | Land cover seen from above | Field boundaries, crop condition |
| GIS | Stacked layers of location-referenced data | Overlaying soil, yield, and elevation layers |
Contour lines connect points of equal elevation, and the contour interval is the elevation change between adjacent lines. Closely spaced lines mean steep slope; widely spaced lines mean gentle slope. Contour lines never cross, and they form a V pointing upstream at a drainage. A legend explains map symbols, and the scale relates map distance to ground distance.
The rectangular survey system describes land by township (36 square miles), range, and section (640 acres). Metes and bounds descriptions trace a boundary by bearings and distances from a point of beginning. Texas kept its public lands at statehood and is not part of the federal rectangular survey; most Texas tracts are identified by original survey name and abstract number with a metes and bounds description.
- Independent variable = what is changed; dependent variable = what is measured.
- The control group receives no treatment; replication and randomization reduce error and bias.
- 43,560 sq ft per acre; 640 acres per section; bushel weights of 56 lb (corn) and 60 lb (wheat, soybeans).
- Line graphs show change over time; bar graphs compare categories; scatter plots show relationships.
- Close contour lines indicate steep slopes; Texas land descriptions rely on surveys, abstracts, and metes and bounds.
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