## Reflection: Diverse Entry Points Tailgating and Solving Radical Equations - Section 1: Warm Up

In this Warm up, I am modeling a radical equation that police officers can use to measure skid marks and estimate how fast a car was travelling when it began to brake at the scene of an accident. (The phenomena of Tailgating is common and relatively easy for my students to understand.)

During the lesson several of my students understood how to evaluate the radical expression in Number 1.  It refers back to previous lessons on substitution, formulas, and evaluating. Evaluating the radical expression on one side of the equation to determine how fast the car was traveling was not too challenging for my students.

Several students did struggle with solving the equation in Number 2. With the length of the skid mark represented by d, a variable, my students had difficulty reasoning about the problem.  Here are some reflections on two examples of student work:

• Student 1 understood how to evaluate the speed of the car given the distance of the skid marks in number one of the Warm Up, and had the correct answer of approximately 53.5 miles per hour.  On Number 2, this student set up the equation correctly, but did not know how to solve for d, by squaring both sides.
• Student 2 also did number one correctly.  (Some of the students left the radical around the answer and did not evaluate the square root.)  However, this student substituted incorrectly for the variables in Number 2. I think that he had difficulty using the language of algebra problem. This student also did not know how to undo the square root to solve the problem.

Diverse Entry Points: Providing Different Levels of Challenge at the Start of a Lesson

# Tailgating and Solving Radical Equations

Unit 5: Radical Expressions, Equations, and Rational Exponents
Lesson 5 of 11

## Big Idea: The purpose of this lesson is for students to solve radical equations of index 2 by taking the square root and understanding extraneous solutions.

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Standards:
Subject(s):
Math, Algebra, Warm UP, Real world problem, independent practice, guided notes, master teacher project, Skid marks and speed of a car, Solving a radical equation, extraneous solutions, radicals
50 minutes

### Rhonda Leichliter

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