Day 2 of 30
Average rate of change
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Learning Objective
Students will explore average rate of change through guided practice and application.
This lesson focuses on average rate of change. Mathematics provides tools for modeling and analyzing complex systems.
Rates compare two different quantities. A unit rate expresses the comparison per one unit: 60 miles per hour, $3.50 per pound. To find a unit rate, divide: 120 miles in 3 hours → 120 ÷ 3 = 40 miles per hour. Percentages are rates per 100: 10% = 10 per 100 = 0.10. Finding 10% is easy: move the decimal point one place left. Finding 1%: move it two places. Scale drawings use a ratio to represent real dimensions: a map at 1 inch = 50 miles means distances on the map are divided by the scale to find real distances. Rates and ratios appear in cooking, construction, science, and everyday comparisons.
As you engage with this material, consider both the theoretical foundations and practical applications. Think critically about how this concept builds on prior knowledge and where you might apply it beyond the classroom.
Challenge yourself to go beyond memorization—seek to understand the "why" behind the processes and principles.
A mathematical question requiring analysis and solution
The result obtained by solving a problem
Instructions
Materials Needed
- Notebook
- Calculator (if needed)
- Graph paper
Practice Problem 1: Apply what you learned today.
Practice Problem 2: Try a similar problem on your own.
Challenge: Can you create your own problem like the ones we practiced?
Teaching Tip
For advanced learners: Encourage deeper analysis and real-world connections. Consider extension activities that allow students to apply average rate of change to novel situations.