Lesson 13 of 19
Objective: SWBAT write a function defined by a quadratic expression in a different but equivalent form to reveal and explain different properties of the function.
Set the Stage
I begin this lesson activating students' prior knowledge of factoring and completing the square as methods for rewriting quadratic functions. The twist I put on this is that instead of demonstrating these skills myself, I ask for student volunteers to work through a few examples on the board. (MP1) I explain the value of this in my video.
With the examples and solutions posted I ask my students what the solutions mean in terms of some real-world problem like a baseball hit in the air or the arc of a swimmer diving into the water. (MP7) I am hoping that someone will mention the connection between roots and zeros, using roots to understand symmetry, but if they don't I ask leading questions like "What part of the graph do these solutions (roots) represent?" and "What is the shape of the graph based on the original equation and solution?"
Put It Into Action
For this lesson I tell my students they will be working independently and without using calculators using factoring to rewrite quadratic functions. I explain that there are only five problems because I want them to factor each equation and then use both forms of the equation, standard and factored, to help identify and describe key features including zeroes, maximum and minimum points, and lines of symmetry. I distribute the Rewriting Functions worksheet, ask if there are any questions, and then tell them they have about 20 minutes for this assignment. (MP1, MP2)
This exercise may be very challenging for some students who still struggle with basic factoring, often because they don't see the factors as another way to write the equation. For these students I give the analogy of breaking a large number into smaller parts. For example, 2525 is a large number but they can easily see how to factor out at least a 5. This gives us 505x5, which shows another 5 to factor out. This is usually enough to get some of my reluctant learners moving in the right direction with factoring.
As students all are working I walk around offering encouragement and assistance as needed. When everyone is done or after about 20 minutes I ask my students to exchange papers with their front partner for checking. I remind them that as I go over the answers they have two responsibilities; first to make corrections for their partner, and second to challenge any of my answers they think are incomplete or incorrect. (MP6)
Wrap It Up
I close this lesson with a closing challenge. I give each student a notecard and ask them to write what ways they've found factoring helps them understand key features of quadratic functions. If you need more specific questions you might try:
- What is one key feature you can identify immediately using the factored form rather than the standard form.
- Describe how you can identify the feature you listed in question one.
This kind of closing activity gives my students the opportunity to reflect on the lesson and focus on what they've learned/gained and it gives me a snapshot of what my students are thinking.