Tools of the Trade: Unit 7: Growing Degree Days

Unit 7: Growing Degree Days: Purpose of Unit:
To learn how GDD and depth of planting affects the time wheat emerges; to give further exercises in computing GDD units; to gather data (or use data gathered by others) from a physical experiment and see how a linear equation predicts the time of emergence; to develop and use an elementary mathematical model for a real world problem.

Note: The information below was created with the assistance of AI.

Level of Mathematics
Target Audience:

Designed for middle to high school students (Grades 7–10).

Adaptable in complexity:

Project I is best for younger or less experienced students.

Project II suits Algebra I and above.

Project III is appropriate when running a physical experiment is not feasible.

Mathematical Content:

Linear equations: Interpreting and using the form 
𝐺 = 𝑎 𝑑 + 𝑏 G=ad+b

Basic arithmetic: Averaging temperatures, computing growing degree days (GDD)

Solving linear equations for one variable

Graphing and modeling: Data plotting, line fitting (subjective and least squares method)

Introduction to mathematical modeling

Application Areas
Real-World Context:

Agricultural science, specifically:

Predicting wheat emergence based on planting depth and temperature.

Connecting biological development with temperature-dependent mathematical models.

Broader Relevance:

Climatology: Use of GDD to match crop types with regional climates.

Environmental science: Investigating growth dynamics under variable conditions.

STEM project-based learning: Combines science experiment, data gathering, and math modeling.

Prerequisites
Essential Skills:

Arithmetic operations (addition, subtraction, division)

Averaging numbers (high and low daily temperatures)

Understanding of linear functions and graphing

Comfort with solving and substituting into linear equations

Preparation:

Completion of Unit 6: Growing Degree Days is strongly recommended, as it introduces GDD computation and temperature interpretation.

Some familiarity with slope-intercept form and interpretation of slope and intercepts helps in deeper understanding.

Subject Matter
Projects Overview:

Project I:

Students are given a linear model (e.g., 
𝐺 = 12 𝑑 + 40 G=12d+40) and use it to estimate depth of planting from emergence time (measured in accumulated GDD).

Includes basic data collection, linear substitution, and interpretation.

Project II:

Students build their own linear model based on measured emergence times from various depths.

Involves graphing (d, G) pairs, selecting or calculating a line of best fit, and using it for prediction.

Encourages conceptual understanding of parameters (slope & intercept).

Project III:

Uses pre-collected experimental data to develop the model.

Ideal for classrooms that can't run the physical experiment.

Includes interpretation of tabular data, line fitting, and predictions for unknown depths.

Scientific Modeling Concepts Introduced:

Definition and purpose of a mathematical model

The use of assumptions in modeling

Role of parameters in defining models

Introduction to least squares method for fitting data

Realism in Modeling:

Students explore model limitations and data deviations.

Discussions on concavity, alternative assumptions, and experimental variability foster critical thinking.

Correlation to Mathematics Standards
Common Core State Standards (CCSS):

8.F.B.4: Construct a function to model a linear relationship between two quantities.

8.SP.A.1–4: Use data to describe relationships and fit lines to scatter plots.

HS.A-CED.2: Create equations in two or more variables to represent relationships.

HS.F-IF.4: Interpret key features of graphs and functions in context.

HS.S-ID.C.7: Interpret linear models and evaluate model fit.

Mathematical Practice Standards:

MP1: Make sense of problems and persevere in solving them.

MP4: Model with mathematics.

MP5: Use appropriate tools strategically.

MP6: Attend to precision.

Cross-Disciplinary Connections (NGSS/Science):

MS-LS1-5: Environmental and genetic influences on plant growth.

HS-LS2-2: Energy flow in ecosystems (related to GDD as energy for growth).

HS-ETS1-2: Design a solution to a real-world problem using models.