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Understanding Rate of Change in Mathematical Functions

On Monday, August 29, 2011, students will have 2 minutes after the bell to answer the clicker question regarding distance/time graphs showing their journey from school to home. The lesson focuses on determining which graph indicates walking at a constant rate of change. The agenda includes exploring how to compare rates of change in parent functions, reviewing previous activities, and understanding the concept of "rate of change." Students will engage in examples to identify and compute rates of change for various functions, enhancing their analytical skills in mathematics.

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Understanding Rate of Change in Mathematical Functions

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  1. Monday, August 29, 2011

  2. You will have 2 minutes after the bell rings each day to answer the clicker question …STARTING TODAY!!! If the distance/time graphs drawn on the board show your journey from school to your house (where a distance of zero corresponds to you arriving at your front door), which graph shows you WALKING at a constant rate of change?

  3. Daily Agenda8/29/11; MATH 1 • MM1A1g: Rate of Change • EQ: How can we compare the rates of change of our parent functions? • Notes: Handout FYI: You are not required to write anything contained within a cloud.

  4. Let’s think about what “rate of change” means!

  5. REVIEW: From our activity Friday… How did we find the rate of change for the first 50 seconds of Jin’s journey? Was this rate of change constant? Does the entire graph of Jin’s journey have a constant rate of change? Why or why not? Distance (in 100’s of yards) Time (in seconds) America’s Choice, Unit 1 Lesson 5

  6. EXAMPLE 1: Find the rate of change for the following function. *What information do we need before we can find the rate of change? *What family does this function belong to? *For this family, what do we usually call the rate of change?

  7. EXAMPLE 2: Try one more like the last one…

  8. EXAMPLE 3: Can you find the rate of change for this function? f(x) = x2 *What information do we need to start? *f(x) belongs to what function family? *How is this rate of change different from the previous example?

  9. EXAMPLE 4: Try one more like the last one… *Pick two pairs of points*

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