I begin this unit by giving my students a pre-assessment (quadratics_intro). I ask my students to read it individually. Since this is the first day of the quadratics unit, most students will be unsure of what a quadratic function actually looks like. While they have graphed them in other units, we did not spend much time discussing their attributes in depth.
After students have had about two minutes to familiarize themselves with the statements on the pre-assessment I put a picture (quad_pic) of a generic quadratic function on the board. Then I ask students to work through each statement on the pre-assessment with their partner. I tell them to make comments on the side of the paper. For each statement they should either agree or disagree and then explain to their partner why they made their choice (MP3). I want students to eveentually explain their thinking in writing, but not until the next portion of the lesson.
Before letting them get to work, I remind students that my picture is of one quadratic function not all quadratic functions. Others may have a different appearance on a graph.
After my students have work through the pre-assessment, I give them the quadratics_intro_investigation. This resource contains picture of several different quadratic functions. I provide it as evidence that for students to consider as they gather the data they need to successfully agree or disagree with each statement on the pre-assessment.
I plan to move slowly during this portion of the lesson. I intend for my students to make meaning of each statement and then find confirming or contradictory evidence in the pictures. I want students to use repeated reasoning (MP8) to construct a robust mental image as we begin a unit on quadratic equations.
After a suitable amount of time for exploration and partner work, I will bring the class back together to discuss their solutions. I plan to ask several students to provide evidence of their thinking, and to explain their thinking (MP3). As we discuss, I make sure to have the correct pictures displayed, so that students can easily refer to them when providing their evidence.
This portion of the lesson will be very brief and will serve as an introduction to some essential vocabulary. On the first graph of the investigation (quadratics_intro_investigation.pdf). We are going to refer back to the following statements:
1) This graph crosses the x-axis.
- For this statement, explain to students that we are going to call the x-intercepts of a quadratic function (or any function) "zeros" or "roots". Have students circle the x-intercepts and label them with these two terms as well as the coordinates of each point.
2) This graph has a turning point.
-For this statement, explain to students that the turning point of a quadratic function is also called a "vertex." Have students circle this point and label it as well as writing the coordinates. You can also bring up the fact that a vertex can be a maximum or minimum point (highest or lowest point on the graph). In this example, the vertex is a minimum point.
3) This graph has a line of symmetry.
-For this statement, explain to students that for each quadratic function, a vertical line can be drawn through the vertex. This line is called the "axis of symmetry." Have students draw a dotted line that passes through the vertex. They should label the line and write the equation for the line.
For the ticket out of this lesson, I ask my students to follow up on my presentation of vocabulary using Question #1. I ask the students to identify the following attributes of the other five graphs on the quadratics_intro worksheet:
I will encourage my students to label each vocabulary term as well as the coordinates (or equation). Since students have already seen through the investigation that not every quadratic function will cross the x-axis, they should have no roots for graph #5. This exit ticket can be collected as a formative assessment of the day's learning.