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# Parabola Zapper: Beauty in the Misses

One of my favorite parts of my role at Desmos is having the opportunity to engage in math with teachers. Recently, I took one of our new (and free) Algebra 1 lessons, Parabola Zapper, for a spin with several groups of math educators located in various parts of the country. Whenever I’m teaching a new lesson, the unexpected often excites me. The surprises in this lesson came from the variety of responses to the activity. In particular, the missed zaps from the teachers.

#### Connection to the x-axis

Early in the lesson, students (teachers in this case) have to “zap” the parabola by finding points on the graph. However, the incorrect zaps or misses provided just as much insight into student thinking as the correct ones. The equation yields students some clues to the location of the parabola. I observed several students input the value of (1,0) or (-3,0) from looking at the equation. The misses here along the x-axis demonstrate a level of understanding about the connection between the factored form of the equation and the x-intercepts.

#### Finding the Vertex Visually

Similarly, one of the students had a couple of misses surrounding the vertex. The location of the misses are signs that the student used visual understanding of the graph rather than computation to locate the vertex. Building connections, particularly early in the lesson, is more important than finding the exact location of the x-intercepts or vertex on the first try. The beauty of the misses helps shape students’ thinking about a vertex, where it is located, and why it might be potentially significant.

#### Varying Approaches

As a Curriculum Consultant and former teacher myself, I enjoyed seeing multiple approaches to finding the parabola.  While some students focused on the vertex and x-intercepts to light up their parabola, others used the concept of symmetry.  Given the time, it would be interesting to further dive into these two approaches.

What approach will your students take? Click the link to try it out.