Many of my students struggle to complete the square in order to transform a quadratic in standard form to vertex form. I like the way this task guides them through this process, first by multiplying square binomials, then by asking them to go in the reverse direction. I also like that students learn to to think through what the vertex form would have to be in order to match (or be equivalent to) the standard form and work to adjust their expressions. I find this approach to be more effective conceptually for students as compared to just showing them how to complete the square.
I begin class by reading through Part 1 of Building the Perfect Square with students and treating questions 1 through 3 as Warm Up problems. Students have recently used area models to multiply binomials, so this work should be a review.
Next, I introduce students to Question #4 where students work towards choosing a value for "c" so that they describe a perfect square (see Building the Perfect Square, page 2). I plan to do Question 4a together as an example and then ask students to continue working on their own (or in small groups).
I will encourage students to pay special attention when they move on to Question 5. Here, they are asked to write about the relationship between "b" and "c." We will also try examples for when b is negative and/or odd. Because this task covers so much material, I usually assign a few problems and then when most students are finished, bring the whole group back together for discussion.
When students get to Part 2 of Building the Perfect Square, they are asked to change y = x^2 - 6x + 9 into a perfect square. From there, students identify the vertex and graph three points on each side of the vertex. Some of my students have trouble seeing where the vertex is when the equation reads y = (x - 3)^2. They sometimes have trouble having seeing that k=0 outside of the more traditional vertex form.
Finally, Question 10 presents an equation that does not fit the pattern for a perfect square. This is about as far as I usually get with this task in class. I often assign this problem for homework. What I like to see when students come back in the next class, is how they adjusted their expressions to include a perfect square AND make the constant fit the original expression.
A lot of today's discussion occurred within the investigation section of the lesson with students working back and forth between the problems and a whole group discussion. I like to provide time at the end of class for student's to reflect on what they have learned so far about moving toward vertex form from standard form.
Exit Ticket: Write about one thing you learned today about converting a standard form quadratic into vertex form. What is one part of the process you are still wondering about?
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