## Reflection: Problem-based Approaches Completing the Square of a Quadratic Function - Section 2: Guided Notes

Providing students with an example as an Entry Document instead of a set of problems after the Warm Up increases relevance and interest of the students.  A good real world problem that uses completing the square is a Quadratic Function Problem called Throwing Baseballs.  This problem comes from the following website:

First, hand the problem to the students to problem only to read, making sure to not include the solutions that are listed on the problem above.  Have the students make a know and a need to know list on their paper and then share out with the class.

Some responses of students for the know list are:

• Given two Quadratic Functions
• One function is given as an equation
• One function is given as a graph
• Both boys claim that their baseball went higher than the other

Some responses of students for the need to know list are:

• Find the maximum heights to determine who is right
• How long is each baseball airborne?
• How can we construct a graph of Brett's throw from the equation on the same graph as Andre's throw
• How can we use the graph to confirm our explanations in part a and part b

After students share out with the class and both lists are made, have students generate ideas on Next Steps for a third list.

Some responses for Next Steps include, using the Vertex Formula, Completing the Square to put the function in Vertex Form, Quadratic Formula, and Comparing the Graphs.

Let the students begin working with their table partner using the method of their choice.  Provide students with enough time to work on the problem, about 15 or 20 minutes.  Then select a few students to share out different methods under the document camera.  If none of the students share completing the square, then model this method for them.  It is difficult for students to change from Standard Form to Vertex form without several examples and modeling.  However, Completing the Square is heavily emphasized in Algebra I, and so is Quadratics.

Providing Relevance with Problem Based Learning
Problem-based Approaches: Providing Relevance with Problem Based Learning

# Completing the Square of a Quadratic Function

Unit 8: Quadratic Functions
Lesson 6 of 10

## Big Idea: To use Algebra Tiles to visualize the meaning of Completing the Square and to work through some advanced uses of Completing the Square.

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Standards:
Subject(s):
completing the square, Math, Quadratic Equations, guided notes, algebra tiles, Changing from Standard Form to Vertex Form, Solving a Quadratic Function
50 minutes

### Rhonda Leichliter

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