Modelling Notes, Quizzes & Revision

Learning objectives

• Explain what a model is and why we use models in topic_name_replace and subject_replace.
• Identify types of models and choose a suitable one for a simple Kenyan example.
• Follow steps to build a simple model, test it with data, and interpret results.
• Recognise limitations and refine models where necessary.

What is modelling?

A model is a simplified representation of a real situation. It helps us understand, predict or explain parts of the world without dealing with every detail. Models may be drawn (conceptual), built (physical), expressed with equations (mathematical) or run on a computer (computational).

Why modelling matters in Kenya (practical reasons)

• Plan: farmers use simple models to estimate seed and fertilizer needs for maize or tea.
• Predict: local county governments model rainfall or flood risk to prepare early warnings.
• Budget: households and small businesses model monthly cash flow in Kenyan shillings (KSh).
• Test ideas quickly and cheaply before investing time or money.

Types of models (short guide)

Seven easy steps to build a model

1. Define the problem: What question are we answering? (Be specific.)
2. Decide what to include/ignore: choose assumptions to simplify reality.
3. Pick a model type: conceptual, physical, mathematical, or computational.
4. Formulate the model: draw, write equations or sketch a prototype.
5. Collect data and apply the model: plug numbers in or run the model.
6. Check/validate: compare model results with real observations.
7. Refine and communicate: improve assumptions and explain findings clearly.

Worked example (simple mathematical model)

Situation: A small shop in Kisumu wants to model how daily profit depends on the number of customers. Assume average spending per customer is KSh 250 and fixed daily costs are KSh 3,000. Let x = number of customers per day, P(x) = profit.

Model: Revenue = 250x. Profit P(x) = Revenue − Costs = 250x − 3000.

Questions:

• Break-even customers: set P(x)=0 → 250x − 3000 = 0 ⇒ x = 12. So at 12 customers the shop neither gains nor loses.
• If x = 20 customers, P(20)=250(20)−3000=5000−3000=KSh 2,000 profit.

Interpretation: This linear model helps the owner plan promotions to reach the break-even or target profit levels. Remember: the model assumes each customer spends KSh 250; if that changes, the model must change.

Common mistakes and how to avoid them

• Over-complicating: start simple, then add realism as needed.
• Wrong assumptions: always list assumptions and test their realism (e.g., constant spending per customer).
• Ignoring units: track units (KSh, days, mm of rain) to avoid errors.
• Overfitting: a model too closely matched to past data may fail for new situations.

Practice exercises (for age_replace)

1. Farmers in a county estimate that harvest weight (kg) per hectare decreases by 10 kg for every 1% drop in soil moisture below ideal. If ideal yield is 2,500 kg/ha and soil moisture is 8% below ideal, what is the expected yield? (Show steps.)
2. A boda-boda rider notes that fuel cost is KSh 120 per day and earns KSh 700 daily. Create a simple profit model and find profit for 5 working days (assume same numbers each day).
3. Draw a simple conceptual model (a clear labelled sketch) showing how rain leads to river flooding in a town — include at least three components (e.g., rain, soil saturation, river level).

Glossary — quick terms

• Assumption: a simplifying idea you accept to make modelling possible.
• Variable: a quantity that can change (e.g., customers, rainfall, price).
• Parameter: a fixed number in the model (e.g., KSh 250 average spend).
• Validation: checking the model against real-world data.
• Limitations: situations where the model may fail or be inaccurate.

Revision checklist

• Can you state the model and list its assumptions?
• Can you test the model using local Kenyan data or sensible numbers?
• Can you explain what the model predicts and where it may be wrong?