3-Acts: Linear Inequalities – How much soda?

This student likes to mix Dr. Pepper with Lemonade.  What questions do you have?

Act 1 video

This activity is designed to lead students to connect the graph of a proportional relationship to a linear inequality.  There are two important questions

  1.   If the student fills the cup, what amounts of Dr. Pepper and what amounts of Lemonade are possible?
  2.   If the student does not fill the cup, what amounts of Dr. Pepper and what amounts of Lemonade are possible?”

What information do you need?

Act 2 size of cup

Comments:  Students plot possible combinations of 8 oz. as points on a line.  Students then discover that if the cup is not full, solutions are a region under the line in the first quadrant.

 

Extensions:  What if a third flavor was added to the mix?  How could we graph 3 flavors related to each other (3D graphing).   If the cup overflowed, how would that change the graph? (Solutions would be above the line.)  What is/are the domain(s), range(s)?

Act 3 cup is almost full

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