##
* *Reflection: Accountability
Light it Up – Day 2: Modeling with Rational Functions - Section 2: Investigation: Light it Up

My students struggled a bit with what exactly this activity was wanting them to do. They were confused on what the variables were in the problems and which measurements should remain fixed. In the future, I will be sure to emphasize to students that the measurements in part a and b should remain fixed. The only variable in which they will be changing is the distance the person stands from the wall. They will also be measuring how the height of the reflection changes as they move.

As my students moved on to writing their equation in part e and f of this activity, I was sure to check in on them. Their b value in the equation should match the distance from the wall to the center of the mirror (first question in part b). Their c value should match the distance from the floor to the mirror (their answer to the third question in part b of this activity). It was easy for me to tell which teams were on the right track and which were not by checking these. However, it was much more difficult for me to diagnose where they went wrong if their answers didn’t match. Where I think some of my students were making mistakes was not fixing the height of the laser pointer. It is essential that the student holding the pointer is always holding it at the same height. It is also important that students always point the laser to the center of the mirror. I think this activity would almost work better with smaller mirrors. I used dollar store compact make-up mirrors that were circular and that worked pretty well. Also, I think there was just simple human error in measurements that were making some of my student’s data off.

My students had fun with this activity once they realized what they needed to do. However, if you are pressed for time, don’t have the supplies, don’t have the classroom space, or simply don’t trust your students to stay focused when collecting data, I would recommend using the Light Bounce APP on the NCTM website. Students can collect the same data using this APP and I am guessing it would actually be more accurate. However, the downfall of course would be that they would not be engaging in as many mathematical practices.

*Post Teaching: How the activity acutally went!*

*Accountability: Post Teaching: How the activity acutally went!*

# Light it Up – Day 2: Modeling with Rational Functions

Lesson 8 of 12

## Objective: SWBAT write rational functions that model problem situations and use these equations to solve problems.

## Big Idea: Students will investigate the Light it Up game and find a rational equation that will help Bart and Lisa to win this game every time!

*40 minutes*

#### Warm-up: Review Homework

*5 min*

As we begin Day 2 of this lesson, it is essential that students are able to write the equation for a rational function by interpreting a graph where a clear shift is evident. Some students will also be able to write an equation for a graph involving a stretch factor. In order to assess students' status with respect to these issues, I will begin today's class by reviewing last night’s homework (Question 8 on the Light It Up worksheet).

To facilitate homework review, I am going to divide the whiteboard into four sections labeled A-D and ask students to write the equation they found for each graph in the appropriate section. I don't want duplicates, but I will ask students to keep writing equations as long as their equation is not already posted. I want this to happen as students are entering the classroom, which will provide some measure of anonymity.

Once all of the students arrive, I will lead a class discussion in which we identify the correct equations as a class. I am hoping that by looking at some incorrect answers, as well as correct answers, the conversation will address both misconceptions and correct mathematical work.

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#### Investigation: Light it Up

*30 min*

After the Warm-up students will spend the rest of the period collecting data for the Light it Up game and finding the equation that models this situation (pg. 11-12 of original Light It Up activity sheet).

**Teaching Notes:**

- Today's lesson was adapted from the lesson
*Light It Up*on the National Council of Teachers of Mathematics Illuminations website. The lesson can be found here (accessed March 6 2014) - Check out Light it up, video narrative for an overview of my plans for the lesson over the next two days. In the video I also discuss the mathematical practices I expect students to engage in during the lesson.

#### Resources

*expand content*

#### Closure

*5 min*

As a closure to today’s lesson, I am going to have teams text in their answers to part f, the equation that models the light it up game. This closure will have two purposes. First, it will hold students accountable to get to the equation before the end of the class period. And secondly, students’ responses will help lead a class discussion about the correct equation. I plan to keep teams’ responses anonymous so we can discuss what is correct and what is incorrect about each answer without putting kids on the spot. I think it is important for students to verify they have the correct answers before they leave class today. If mistakes were make, it will be a good learning opportunity for students.

*expand content*

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Rational Approaches to Solving Rational Equations
- LESSON 2: Speed Dating Rationally
- LESSON 3: Another Rational Approach to Solving: Graphing
- LESSON 4: Ahoy again! What can you see now? Building Rational Functions
- LESSON 5: Evolving Rational Functions
- LESSON 6: Rationalized Transformations: Shifting Rational Functions
- LESSON 7: Light it Up - Day 1: Modeling with Rational Functions
- LESSON 8: Light it Up – Day 2: Modeling with Rational Functions
- LESSON 9: You can’t Get There from Here: Finding the Asymptotes
- LESSON 10: Rational Functions Review Day
- LESSON 11: Rational Functions Test Review
- LESSON 12: Rational Functions and Equations Test