## Reflection: Connection to Prior Knowledge Quadratic Functions and Roots - Section 2: Investigation

I am glad I included the Teaching Note in my narrative for this section.  Today, it was really crucial, so I have included it again below.  And, in general it is really important to know how well your students can evaluate functions numerically for all values of x. Today's investigation hinges on fluency with this skill.  If students struggle with numerically evaluating a function they will not be able to make connections in the investigation.

I found myself having to sit with several groups of students (for longer periods of time than I would have liked) to walk them through the arithmetic needed to successfully evaluate each function.  All was not lost, because these students did get to make a lot of connections with what the zeros of a function are from a graphical standpoint.   These students, did not however, have the big "aha" moment that others had when they could see that each function would be zero when evaluated at its roots.

Teaching Note: I sometimes find it is necessary to review how to evaluate x^2 when x is a negative integer (for example -4).  In some of my classes, students will evaluate (-4)^2 and get -16.  This will obviously introduce bad data into their investigation. It is important to keep in mind that technology can contribute to this error. If a students types -4^2 into a calculator, they will get the incorrect answer of -16. This is one of the famed "Lies my calculator told me!"

Connection to Prior Knowledge: Know Your Students Background Knowledge

Lesson 2 of 21

## Big Idea: Students will learn the meaning of roots (zeros) by numerically and graphically inspecting quadratic functions.

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### James Bialasik

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