Reflection: Connection to Prior Knowledge Graphing & Modeling with Exponents - Section 3: An Exponential Model

 

My students had WAY more trouble writing an explicit formula for this problem than they should have.  I found that while many could complete the data table fairly quickly, they couldn't move past a recursive formula for h(n).  You can see what I'm talking about in this student's work. It is typical of 90% of the class.

After a few relatively simple suggestions failed to help them, I decided it was time for a deeper and more direct intervention.  I decided to use an example of linear data to simplify the problem and connect to their prior knowledge.  They all quickly recognized the constant difference from term to term, we formulated a recursive formula, and then explained how the explicit formula is developed out of it.  (See the whiteboard here.)

Next, we moved back to our exponential data.  This time we have a constant ratio, rather than a constant difference.  By carefully and continually referring back to the linear data, I was able to help them see that in this case we have repeated multiplication from an initial value rather than repeated addition.  At this point most were able to see that our formula would be exponential.  (See the whiteboard here.)

Once they had the formula, the rest was pretty easy.  Check out this student's work for a good example of exactly what I was hoping for from everyone.

  Connection to Prior Knowledge: Making the function explicit
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Graphing & Modeling with Exponents

Unit 6: Exponents & Logarithms
Lesson 5 of 14

Objective: SWBAT graph simple exponential functions with integer bases. SWBAT use an exponential model to analyze a real-world situation.

Big Idea: How high will the basketball bounce and will it ever stop? An exponential model sheds light on the question!

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calc exponential
 
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