Day 14 of 30
Rate of change concept
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Learning Objective
Students will understand rate of change concept through guided practice and application.
In this lesson, we'll explore rate of change concept. Mathematical thinking develops logical reasoning and problem-solving abilities.
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 work through today's material, pay attention to the examples and try to identify the patterns or strategies being used. This will help you apply these concepts to new problems.
Take notes on key points and make connections to what you've already learned in previous lessons.
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 rate of change concept to novel situations.