Teaching Resources for Mathematical Analysis

Light It Up- In this cooperative learning activity, students are presented with a real-world problem: Given a mirror and laser pointer, determine the position where one should stand so that a reflected light image will hit a designated target. This investigation allows students to develop several rational functions that models three specific forms of a rational function. Students explore the relationship between the graph, the equation, and problem context.

Title Light It Up

URL http://illuminations.nctm.org/LessonDetail.aspx?id=L606

Materials needed
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
Carousel Cards
Markers
Overhead Projector
Blank Paper
Timer
Scissors

Learning Objectives
Students will:

State the domain, range and end behavior of rational functions.

Write rational functions that model problem situations

Use rational functions to solve problems

Grade Levels Algebra I, Mathematical Analysis

CA 97 Standards Algebra I: 13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques

Mathematical Analysis 6.0: Students find the roots and poles of a rational function and can graph the function and locate its asymptotes.

CA Common Core State Standards
Standards for Mathematical Practice:

1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning

Algebra-APR 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials, and divide polynomials by monomials. Solve problems in and out of context.

Functions-IF.7d; Graph rational functions, identifying zeros and asymptotes
when suitable factorizations are available, and showing end behavior.

How could you use this resource? Students can use this resource in a lab to discover how rational functions are used in the real world as well as practice graphing data and drawing conclusions from data. Teachers can use this resource as a lab or a lesson as an introduction to rational functions.

EL and Special Needs Does not use vocabulary in a way that makes the lesson hard to follow. Uses manipulatives to get the students involved and to physically see what is going on and where the data is coming from.

Lesson Plans
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See other teachers' lesson plans on MERLOT.

Teacher Comments
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Cost Free

Copyright (c)2008 NCTM

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Title	Light It Up
URL	http://illuminations.nctm.org/LessonDetail.aspx?id=L606
Materials needed	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 Carousel Cards Markers Overhead Projector Blank Paper Timer Scissors
Learning Objectives	Students will: State the domain, range and end behavior of rational functions. Write rational functions that model problem situations Use rational functions to solve problems
Grade Levels	Algebra I, Mathematical Analysis
CA 97 Standards	Algebra I: 13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques
CA 97 Standards	Mathematical Analysis 6.0: Students find the roots and poles of a rational function and can graph the function and locate its asymptotes.
CA Common Core State Standards	Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning
	Algebra-APR 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials, and divide polynomials by monomials. Solve problems in and out of context.
	Functions-IF.7d; Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
How could you use this resource?	Students can use this resource in a lab to discover how rational functions are used in the real world as well as practice graphing data and drawing conclusions from data. Teachers can use this resource as a lab or a lesson as an introduction to rational functions.
EL and Special Needs	Does not use vocabulary in a way that makes the lesson hard to follow. Uses manipulatives to get the students involved and to physically see what is going on and where the data is coming from.
Lesson Plans	Share your lesson plan on MERLOT! See other teachers' lesson plans on MERLOT.
Teacher Comments	Share your comments on MERLOT! See other teacher comments on MERLOT.
Cost	Free
Copyright	(c)2008 NCTM