This complete high school teaching concept provides a clear and structured instructional framework for analysing and comparing linear, exponential, and logarithmic models.

Rather than teaching function types separately, students learn to compare models directly, evaluate rates of change and long-term behaviour, and make justified modelling decisions based on real-world contexts.

Instructional Approach

The unit follows a comparison-based and modelling-focused approach.

Students explore:

• constant vs. accelerating vs. decelerating growth
  
• graphical, algebraic, and numerical representations
  
• criteria for choosing appropriate models
  
• common misconceptions (especially linear thinking)
  
• limitations and assumptions of mathematical models
  

What This Teaching Concept Includes

• a fully structured unit plan
  
• lesson progression with clear learning goals
  
• modelling and comparison tasks
  
• discussion prompts and reflection questions
  
• differentiation and assessment guidance
  
• flexible use in regular, honours, or advanced classes
  

Students will be able to:

• analyse and compare different growth models
  
• interpret graphs and data critically
  
• justify model selection mathematically
  
• evaluate predictions and limitations
  
• apply modelling skills to real-world situations
  

Best for

• high school algebra and functions
  
• modelling and applied mathematics units
  
• instruction focused on reasoning and interpretation
  

Keywords
function analysis teaching concept, model comparison math, linear exponential logarithmic, high school modelling, applied mathematics instruction