Light it Up - Day 1: Modeling with Rational Functions

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Objective

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

Big Idea

Students will investigate a variety of fair games, using graphs and tables they will write the rational equation that models the game.

Introduction: Light it Up

3 minutes

At the start of today's lesson I really need to hook students and try to get them to buy into the challenge of finding the equation to model the Light it Up game. The activity is challenging. It is important to generate student interest in finding the equation. I let students know they will investigate this problem further tomorrow, but first we must make sure they have the prerequisite knowledge.

Someday, I would even like to set up the game in my classroom and have students actually use their equations to win something, I am just not there yet. Pages 3-5 of the Flipchart illustrate the parameters of the Light it Up game.

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.

 

 

Planning and Preparation

I plan to restructure this lesson a bit from the original Illuminations plan. So, I am going to copy the papers as follows:

  1. Light it Up introduction is copied to the investigation part (pg. 1 copied to 11-12)
  2. The Climbing the Wall and the Trip to the Fair (pg. 2-4) problems are back to back and stapled. 
  3. I will put both of the closer looks at the fair trip problems together (pg. 5-8). 
  4. I am going to copy what I plan to be homework on a single sheet of paper (pg. 9-10). Also, before I copy this I plan to write in a #5 on the top of the page with question 8 and write in a NAME line. 
  5. I will not copy the last page as this problem, Cooling Down, is already on their homework.

Many supplies are required for Day 2 of the Lesson:

  • Light It Up Activity Sheet
  • Laser Pointer (or Flashlight)
  • Tape Measures
  • Tape
  • Wooden Block (at least 10 cm thick, or a
    thick book)
  • Graphing Calculator
  • Small, Flat Mirror
  • Markers

Application: Exploring Fair Games

45 minutes

I plan to give students about 10 minutes to complete the first two problems in the Light It Up activity packet:

  • Climbing the Wall (page 2)
  • Trip to the Fair (page 3)

 

Students will be working with their teammates to complete these problems. The goal in this section is that students can identify how the graphs look different and what aspect of the equation is responsible for these differences. Specifically that when the parent function y=1/x is multiplied by a constant, a, that the functions becomes stretched. Before moving on to the next section, I will have a whole class discussion about the graphs for each problem and what effect multiplying by a constant has on this type of function.

Next, once we’ve briefly discussed stretch factors, I will give students the next packet (pg. 5-8 of original Light It Up Activity Sheet). Now I plan to slow things down a bit and give students the rest of the class period to figure these problems out. I am going to ask that students use the  TTTT - Team, Team, then Teacher for questions.

Once students think they have completed this section I am going to ask them to check in with me. I will specifically be checking a few questions here to be sure that students are progressing successfully. I will be looking at questions 4d, 5d, 6c, and 6e to assess students' understandings. If everything looks good I will have students start the homework, if not, I will let students know where they went wrong (not what they did wrong, but where there are issues) and will have them continue working.

As we near the end of this section in the lesson I will start providing more guidance to teams that are falling behind. Possibly even sitting with some teams and doing some small group tutoring if needed.

 

Teaching Note:

  • I have chosen to use the variable a as the ‘constant’ when I discuss this with students even though it is probably more standard to use k, but I think it will help students on their homework tonight… see homework section for more details.

Homework

2 minutes

I plan to assign Question 8 from the Light It Up activity as homework tonight.

I want to hold today’s homework ransom (Yeah… because we all know that all students REALLY WANT that homework!) until students have received feedback on some of those key questions (4d, 5d, 6c, 6e) from the prior section. This helps me to keep track of which students have checked in and which students haven't. 

At the start of this homework, students are expected to write the equation of the rational functions, but they may actually just be writing an equation that is just close to the graph. In the next part of the problem students will be guided in finding that a value to actually make the equation exact. I will let students know this before they leave class today. They need to be writing an equation to the best of their knoweldge in part a, b, c, and d and then they will improve their model later.