L5+Doran,+Christopher


 * UNIVERSITY OF MAINE AT FARMINGTON**
 * COLLEGE OF EDUCATION, HEALTH AND REHABILITATION**
 * LESSON PLAN FORMAT**


 * Teacher’s Name:** Mr. Doran
 * Lesson # :** 5
 * Facet:** Analyze
 * Product:** Geogebra
 * Grade Level:** 10th
 * Topic:** Position, Velocity, Acceleration, and Derivatives

__**Objectives**__

 * Student will understand that** all sorts of functions are used in real world problems every day.
 * Student will know** different terminology such as: variable, position, velocity, acceleration, derivative, distributive property, associative property, and commutative property.
 * Student will be able to** analyze real world applications of algebraic functions.

__**Maine Learning Results Alignment**__
Maine Learning Results: Mathematics - D. Algebra Functions and Relations (4) Grades: 9-Diploma Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques


 * Rationale:** In this lesson students will be able to solve position, velocity, and acceleration applications of mathematical scenarios.

__**Assessment**__
Students will complete homework problems from their textbook and complete in class problems dealing with applications of algebraic problems. The homework will be reviewed during the next class period to see what the students understand and don't understand about different mathematical applications and scenarios. Students will be able to ask questions about certain applications and homework problems to clarify any misconceptions they might have. A describing wheel will be used to have students write down different algebraic properties such as the distributive and commutative property, as well as the concept of a derivative. Students will use the Team-Pair-Solo collaborative learning technique to practice using the concept of a derivative to solve position/velocity/acceleration problems. The next class period, I will go over homework problems before students take a quiz on position, velocity, and acceleration, as well as basic derivatives.
 * Formative (Assessment for Learning)**


 * Summative (Assessment of Learning)**

In teams of 2, students will create a position/velocity/acceleration function using Geogebra software. During the presentation, you will need to explain to the class which function is the position function, which is the velocity, and which is the acceleration. In addition, you will also need to explain what each part of the formula represents. Grading will be done by using a checklist. **//(30 points)//**

__**Integration**__

 * Technology:** Students will use Geogebra software to graph position vs. time, velocity vs. time, and acceleration vs. time graphs.


 * Physics:** Position, velocity, and acceleration, which are used a lot in physics classes, will be calculated and graphed by the students.

__Groupings__
Students will use the Think-Pair-Solo activity to practice position, velocity, and acceleration applications as a group, then in a pair before working on them individually. Students will be placed in groups of 4 based on their birth seasons.

__**Differentiated Instruction**__

 * Strategies**


 * Linguistic:** I could use word problems and class discussions to target this learning style.
 * Logical:** Mathematical reasoning and observation could be used and explained on how to solve a word problem.
 * Spatial:** The use of a picture to make it easier to understand what the problem is looking/asking for would help spatial learners.
 * Intrapersonal:** The solo aspect of the Team-Pair-Solo activity will help these students learn the skills and usage of real world applications of algebra.
 * Interpersonal:** The team and pair aspect of the Team-Pair-Solo activity will engage these learners in thinking about different uses for algebra in the real world.
 * Naturalist:** Students will go outside and run on the track to measure their velocity over a certain period of time.
 * Kinesthetic:** Students will be running and getting their times for their position and velocity functions.


 * Modifications/Accommodations**

I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.


 * Absent:** If a student is absent, it will be the student's responsibility to get any work that was missed that day and make a plan with me on how to get caught up. If the student is unable to attend school, yet is well enough to participate, the use of Skype will be possible to get the information. Students will need to email me beforehand to let me know that they will be skyping in so I can plan accordingly.


 * Extensions**

Students will use Geogebra software to graph position, velocity, and acceleration functions.

__**Materials, Resources and Technology**__
Students will need:
 * Pencil
 * Notebook
 * Textbook
 * Graphing Calculator
 * Laptop
 * 3 Ring Binder
 * Geogebra software

I will need:
 * White board markers
 * Laptop
 * Graphing Calculator
 * Describing Wheel handout
 * Pen/Pencil
 * Quiz
 * Stopwatch
 * Checklist for Geogebra project

__Source for Lesson Plan and Research__
[] Used for explaining velocity, acceleration, and position [] Used for explaining the definition of a derivative [] Application of linear equations [] Mythbusters video

__**Maine Standards for Initial Teacher Certification and Rationale**__

 * //Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development.//**


 * Rationale:** Beach Ball ~ Students who are beach ball learners will be interested in this lesson because they will be able to get outside and do an activity. Microscope ~ Students who are microscope learners will be interested in this lesson because they will be able to analyze the concept of a derivative. Clipboard ~ Students who are clipboard learners will have a graphic organizer to keep their thoughts and ideas organized. Puppy ~ Students who are puppy learners will feel safe in a fun environment where students are working together in a group.


 * //Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.//**


 * Rationale:** Students will need to know different terminology such as: variable, position, velocity, acceleration, derivative, distributive property, associative property, and commutative property (Reference content notes at the end of the lesson). //**Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques**//**.** The facet that I chose for this lesson is analyze in hopes that //students will be able// //analyze real world applications of algebraic functions.// I chose this facet because I want my students to look at an application of math and be able to solve it using algebraic techniques that they've learned in the past few lessons.


 * //Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.//**


 * Rationale:**


 * Strategies**


 * Linguistic:** I could use word problems and class discussions to target this learning style.
 * Logical:** Mathematical reasoning and observation could be used and explained on how to solve a word problem.
 * Spatial:** The use of a picture to make it easier to understand what the problem is looking/asking for would help spatial learners.
 * Intrapersonal:** The solo aspect of the Team-Pair-Solo activity will help these students learn the skills and usage of real world applications of algebra.
 * Interpersonal:** The team and pair aspect of the Team-Pair-Solo activity will engage these learners in thinking about different uses for algebra in the real world.
 * Naturalist:** Students will go outside and run on the track to measure their velocity over a certain period of time.
 * Kinesthetic:** Students will be running and getting their times for their position and velocity functions.


 * Technology:** Students will use Geogebra software to graph position vs. time, velocity vs. time, and acceleration vs. time graphs.


 * //Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.//**


 * Rationale:** This is how I plan on assessing student learning

Students will complete homework problems from their textbook and complete in class problems dealing with applications of algebraic problems. The homework will be reviewed during the next class period to see what the students understand and don't understand about different mathematical applications and scenarios. Students will be able to ask questions about certain applications and homework problems to clarify any misconceptions they might have. A describing wheel will be used to have students write down different algebraic properties such as the distributive and commutative property, as well as the concept of a derivative. Students will use the Team-Pair-Solo collaborative learning technique to practice using the concept of a derivative to solve position/velocity/acceleration problems. The next class period, I will go over homework problems before students take a quiz on position, velocity, and acceleration, as well as basic derivatives.
 * Formative (Assessment for Learning)**


 * Summative (Assessment of Learning)**

In teams of 2, students will create a position/velocity/acceleration function using Geogebra software. During the presentation, you will need to explain to the class which function is the position function, which is the velocity, and which is the acceleration. In addition, you will also need to explain what each part of the formula represents. Grading will be done by using a checklist. **//(30 points)//**

__Teaching and Learning Sequence__
Day 1: (80 minutes)


 * [|Hook video]
 * Have a class discussion asking why we learn math and what uses does it have in our lives (10 minutes).
 * Hand out graphic organizer and review or reteach the distributive, associative, and commutative properties (15 minutes).
 * Introduce position, velocity, and acceleration and the relationship between the three (15 minutes).
 * Introduce the concept and idea of a derivative, keeping the explanation as simple as possible (15 minutes).
 * Separate students into groups of 4 based on birth season and have them work on practice problems on position/velocity/acceleration and derivatives (20 minutes)
 * Briefly inform students of their Geogebra project that they will gather data for next class. I will give them their checklist before class is over (5 minutes).

Day 2: (80 minutes)


 * Review homework problems, allowing students to ask any questions they may have regarding it (10 minutes).
 * Students will take a quiz on position, velocity, and acceleration, as well as the basic concept of a derivative (15 minutes).
 * After the quiz, the entire class will go outside to the track. Once at the track, I will explain their next project in more detail which will involve them gathering data (10 minutes).
 * Students will separate into their groups of 4 from last class and walk or run a set distance of 5 meters and will record the time it took for them to travel that distance (multiple trials will be used and the average of those trials will be used for calculation purposes) (30 minutes).
 * Students will head back into the classroom and will plot their position vs time graph using Geogebra. The other two graphs should be completed for homework and should be ready to present next class. (15 minutes)

Day 3: (80 minutes)


 * Time devoted at the beginning of class to those who need it to finish up their Geogebra projects. I will pass back quizzes that the students took during this time (15 minutes).
 * I will go over the quiz with the students, answering any questions they may have on it (10 minutes).
 * Presentation of Geogebra projects (40 minutes).
 * Students will give feedback to me on what they liked and didn't like about this lesson, as well as what improvements should be considered for the future (10 minutes)
 * Brief overview of what the next lesson will be about and what the students' final project for the unit will be (5 minutes).

Students will understand that all sorts of functions are used in real world problems every day. Math is used in real world applications and these are just some of the ways in which algebra is incorporated into life. //Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques//. At the beginning of class, I will show a mythbusters clip and after there will be a class discussion where I will ask students the question "What relevance is math, specifically algebra, in the real world?" This discussion will lead into talking about position, velocity, and acceleration. **Where, What, Why, Hook, Tailors: Intrapersonal, Interpersonal, Logical, Visual**.

Students will need to know different terminology such as: variable, position, velocity, acceleration, derivative, distributive property, associative property, and commutative property. They will use a describing wheel to write down the definition of these terms and any formulas associated with them. Students will respond to the question: "How will real world situations use the functions in their applications?" By doing so, students will be able to relate what they're learning in the classroom to some applications outside of the classroom. **Equip, Explore, Rethink, Tailors: Logical, Visual, Interpersonal, Intrapersonal**

Students will be able to analyze real world applications of algebraic functions. To get into groups composed of no more than 4, students will seek out others who have the same birth season that they were born in. In their groups, students will use the Team-Pair-Solo collaborative learning technique to practice position/velocity/acceleration and derivative problems from the textbook. The following class, I will go over the homework with the students, giving them time to revise their answers and refine their skills before taking a quiz on the same material. The next day I will go over the quiz with the students and answer any questions regarding it that the students may have. **Organize, Experience, Refine, Revise, Tailors: Intrapersonal, Verbal, Logical, Kinesthetic, Interpersonal**

Students will self assess their work by correcting their own homework problems and continuing to attempt more example problems. During their collaborative learning, I will go around the room to help the students with any questions they may have. The quiz that they took in day 2 of the lesson will be graded, handed back, and reviewed by the following class period. At the beginning of each class period, I will allow students to ask any questions they have regarding the homework, quiz, or material covered from the last class. In the next lesson, students will look at more applications of math that can be used in real world situations. **Evaluate, Tailors: Verbal, Logical, Intrapersonal, Interpersonal**


 * Content Notes**

Derivative: The rate of change an object undergoes from point A to point B. Velocity is the derivative of position, and acceleration is the derivative of velocity. If a function is given in the form of ax^2 + bx + c, then a derivative can be easily calculated.

How to calculate a derivative (Power Rule): f(x) = x^n, dy/dx (derivative of y (f(x)) with respect to x...also can be written as f '(x) and d/dx) is the derivative of f where dy/dx = nx^(n-1)

This basically says that for whatever power you have for x, drop it down in front of it and make it a constant (multiplying x and any other constants by it), then reduce the power of x by 1.

If f(x) = c any constant, then f '(x) = 0

Example problems:

Find the derivative of the following:


 * f(x) = 3x^2 - 6x + 5 || f(x) = -2x^2 + 5 ||
 * f '(x) = 6x - 6 || f '(x) = -4x ||
 * f(x) = (1/2)x^2 - (1/2)x - 4 || f(x) = 4x^4 + 6x^3 - 8x^2 +9x - 10 ||
 * f '(x) = x - 1/2 || f '(x) = 16x^3 + 18x^2 - 16x + 9 ||


 * Handouts**


 * Describing Wheel
 * Geogebra Checklist