L1+Bates,+Tristan

=**UMF LESSON PLAN FORMAT**=

G**rade Level: 10 Topic: Deriving graphs from equations**

 * =**Objectives**:= ||
 * Student will understand that functions and graphs are related. ||
 * Student will know definitions for function, graph, equation ||
 * Student will be able to derive a graph from an equation. ||

Functions and Relations Grade 9-Diploma 4. **Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.** c. Use concepts such as domain, range, zeros, intercepts, and maximum and minimum values.
 * =**Maine Learning Results Alignment**= ||
 * //Maine Learning Results//: Mathematics- D. Algebra


 * Rational:** During this lesson students will be introduced to the idea of writing an equation and graphing it. Concepts such as domain and range will be used. ||

Students will start with brainstorming ideas of definitions of equations and graphs. They will also discuss what will happen to the velocity of a ball when it is rolled across the table. We will roll a steel ball across the table and time where it is at certain places. Using this data we will plot the points on a spreadsheet and use it to make a graph. The students will write an equation based on this information. During class the teacher will also run the same experiment and put the data into a spreadsheet that will be projected on a screen so the entire class can follow along. The work sheets the students work on will be collected at the end of the activity and graded and passed back the next class. || At the end of class the project dealing with the stock market will be introduced. By next class the students are to look up data for the past two weeks for 3-5 stocks. They should make a decision on which stocks they want to invest the $100,000 allowed to them. ||
 * =Assessment= ||
 * **Formative** (Assessment for Learning)
 * **Summative** (Assessment of Learning)

= = Technology- I will use an online [|music video] that will hook students and get them thinking about math. I am also using a spreadsheet processor to make graphs that will depict distance versus time and ultimately the velocity of an object. ||
 * =**Integration**= ||
 * Science- I am going to be making a graph and equation for the formula for velocity. The basic form of the formula for velocity is y=mx+b where y is the distance from the origin, x is the time, m is the speed, and b is the starting distance.


 * =**Groupings**= ||
 * The class is going to break into groups of four to find the equation for velocity. One member of the group will have to get all the supplies (steel balls, watch, etc). Another member of the group will roll the ball while a member keeps track of the time when the ball is at certain points. The last member will have to enter the data into a spread sheet and they will all answer the questions that go along with the activity as a group. The groups will be the teams that I have assigned earlier and will be the same groups that work on the stock market project. ||

I will review student's IEP, 504 or EL LIDEP and make appropriate modifications and accommodations. If you miss a class then you are to check the class folder located next to my desk for papers that you may have missed. You can talk to me, or your fellow peers, to get the assignments and I would be more than glad to share with you any notes for the class missed. Any assignment given on a day you are absent will have the due date pushed back for you and the amount of time you will be given will depend on the assignment. || A [|math rap video] will be shown at the beginning of class to engage the students. A spreadsheet to build graphs using data points will also be used. The graphs will be discussed with team mates and a line of best fit will be determined. The class wiki for the project dealing with the stock market will also be shown and the students will be told how to post documents to the wiki and how to use the discussion feature. ||
 * =Differentiated Instruction= ||
 * **Strategies**
 * Verbal:** We will be defining some words including equations, functions, graphs and slope.
 * Logical:** The in-class activity will require the students to solve for an equation using coodinate points.
 * Kinesthetic:** The students are breaking up into groups and will get a chance to move around and perform an activity involving rolling a ball.
 * Visual:** The math rap at the beginning will be visual as well as the teacher's spreadsheet which will be projected so everyone can see it.
 * Intrapersonal:** The students are going to work alone for a while during class thinking about what will happen to the velocity of a ball when it is rolled.
 * Interpersonal:** The group work involving the rolling ball activity will allow the students to work together in small groups.
 * Natural:** We will be discussing how linear functions are found in universal laws (such as velocity of a moving object)
 * Musical:** The math rap will help engage the musical students. ||
 * **Modifications/Accommodations**
 * **Extensions**

Wiki handout Step-by-step Velocity/spreadsheet Worksheet Laptops with excel Pencils/pens Stopwatch Steel balls Projector and Screen ||
 * =Materials, Resources and Technology= ||
 * Class wiki

Wikispace: batesmath.wikispaces.com
 * =Source for Lesson Plan and Research= ||

[|Video math rap] : __ http://www.youtube.com/watch?v=Ooa8nHKPZ5k&feature=related __ Velocity/spreadsheet worksheet: Tristan Bates Content Notes __ http://www.mathwords.com/ __ ||


 * =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:** This lesson will show a demonstration of 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 because it will use many different intelligences. The class will be split into groups that will be in charge of assigning roles to each member that best fits the student. The activity will need people that are physical, logical, interpersonal, and natural. The students will be given freedom while doing the activity while they will also have a guideline to follow. Each group will come up with its own graph and equation while the students will be able to question the teacher or watch what the teacher is doing so that they know they are doing it correctly. Also included in the lesson will be a time for students to think about how the world around them functions.   ||
 * __Standard 4__ - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.
 * Rationale:** This lesson will show a planned instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. Students will have a chance to use a step-by-step assessment to figure out the general formula for velocity and how it relates to linear equations. Before the activity the students will be provided with definitions of slope, equation, graph, and function. The MI theory will be used to make sure that the lesson speaks to as many of the students as possible. Finally, s tudents’ IEPs, 504s or ELLIDEPs will be reviewed and the appropriate modifications and accommodations will be made.  ||
 * __Standard 5__ - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.
 * Rationale:** This lesson shows an understanding and it uses a variety of instructional strategies and appropriate technology to meet students’ needs. An on-line [|math rap video] will be used to help engage the students at the beginning of class. Next students will be introduced to spreadsheet and its uses when it comes to making graphs from a set of data points. Lastly the students will learn about the class wiki and how to post document to a wiki and use the discussion board on the wiki. Also during class the students will work in small groups and pool eachothers skills to determine the general formula for the velocity of an object. ||
 * __Standard 8__ - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.
 * Rationale:** This lesson shows an understanding and it uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. At the beginning of class the students will brain storm what will happen when a ball is rolled and be given a little bit of time to discuss as a class what they think will happen (the ball will speed up, slow down, or stay at a generally contant speed). Then they will also discuss the definitions of slope, functions, graphs, and equations. While they are conducting the experiment they will fill out an assignment and answer questions about the velocity of a ball rolled across a table. The students will also choose 3-5 stocks that they are interested in investing in and they will be expected to have past data for 2 weeks on the stocks for the next class. ||

The room is going to be arranged such that there are groups of four desks. At first the desks will all face forward so the students will pay attention to the music video and participate in the discussion at the beginning of class.
 * =Teaching and Learning Sequence:= ||

Agenda: Show video Discuss definitions Group work Discuss Stock Market Project Pass out Syllabus

 Students will understand that functions and graphs are related. They will have to do this because it is important to realize that there is more than one way to solve a problem. They will develop this understanding by finding a graph and equation that depicts the distance versus time of a rolled object across a low friction surface. **// Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques //.** After the class files in they will watch a [|video] __ http://www.youtube.com/watch?v=Ooa8nHKPZ5k&feature=related __ that has to do with math and how people know more in math than they think. This movie will get the class engaged and excited for the lesson. After the video the teacher will ask the students to give their opinions on what they know about math. (5 minutes) **What, Where, Why, Hook, Tailor: Visual, Musical, Intrapersonal.** || The class is going to break into groups of four to find the equation for velocity. One member of the group will have to get all the supplies (steel balls, watch, etc). This member is the "runner" and whenever something is needed they will go and get it. Another member of the group will roll the ball while the third member will keeps track of the time when the ball is at certain points. The member keeping track of the time of the ball at different points will also be in charge of time overall and making sure that the group will complete the activity in a timely manner. The last member will have to enter the data into a spread sheet. The last member will also be in charge of making sure the group stays on topic and will resolve any conflicts within the group. All the group member will be responsible for answering the questions that go along with the activity and completing the worksheet. The groups will be the teams that I have assigned earlier and will be the same groups that work on the stock market project. While they are doing this the teacher will also be doing the same activity and walking the class through it while the teacher's data will be projected on a screen for the whole class to see. After completing the worksheet students will discuss what they found about velocity and what type of formula it uses. The worksheet should be passed in at the end of the activity and will be graded according to completeness and accuracy. (45 minutes) **Explore, Experience, Rethink, Revise Tailor: Interpersonal, Visual, Logical, Natural, Kinesthetic** || While the students are working on their activity the teacher will be doing the same activity and walking the class through it. This will allow students to check their work and it will make sure that everyone is on the same page. After passing in the worksheet the students will stay with their groups. The teacher will describe the new activity which is outlined on the class wiki __ http://batesmath.wikispaces.com __. The students are to, in their groups of four, pick 3-5 stocks that they are interested in analyzing. They should do this in class and then determine who will research each stock. The teacher will show how to post data on the class wiki and how to navigate it. At this point the rubric should be passed out for the Stock Market Project (see attached). The teacher will go over the rubric and make sure everyone understands it and how to access the class wiki. For homework they should review the past data for their stocks for 2 weeks and at the beginning of the next class they will decide which stocks to invest in and how much to invest. At the end of class the teacher will pass out the class syllabus and instruct the students to read it for next class and bring it back signed by both the student and a parent (see attached). (20 minutes) **Evaluate Tailor: Interpersonal, Logical** ||
 *  After the video is over the class will discuss the definitions of slope, function, graph, and equation (see content notes). This will allow the teacher to get some understanding of what the students already know about these concepts. Students will need to know the definition of function, graph and equations and to do this the teacher will provide definitions after the class has discussed the different words. They will then move on to an activity that will help them understand how they all relate. While moving into the activity the students will get into groups that have been determine before hand and they will make groups of four desks to work together. The students will get a step-by-step activity worksheet that will lead them to finding the velocity of a rolling ball (see attachment). (10 minutes) **Equip Tailor: Intrapersonal, Interpersonal, Logical, Verbal** ||

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