L3+Bates,+Tristan

=**UMF LESSON PLAN FORMAT**=

**Grade Level: 10 Topic: Interpreting Functions**

 * =**Objectives**:= ||
 * Student will understand that there is more than one way to solve an equation. ||
 * Student will know terminology- domain, range, intercept, xy-axis, zeros, maximum, minimum, slope ||
 * Student will be able to interpret the characteristics of functions using graphs, tables, and algebraic techniques. ||

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: Students are going to work with describing graphs and equations in terms of domain, range, zeros, intercepts, and maximum and minimum values. ||

The students will work on their T-charts more as we discuss the new vocabulary. They will fill in any new terms and as before, this chart will not be officially graded; however, I will keep records of participation. The students will have a chance to ask questions over the homework that was assigned the night before and these will be passed in for a grade. During the class period the students will use an observation chart to help them determine what changing certain variable will do to a graph. This chart will not be passed in and I will grade it as participation. They will make graphs on excel that are to fit certain parameters and the graphs will be passed in and graded. || At the end of class the students will be assigned homework that deals with the topic covered in class. This homework will be collected next class. They will also be expected to continue to analyze their stocks and continue to get data. At this point they should be able to go on-line and read the questions posted by other members of the class and answer them. ||
 * =Assessment= ||
 * **Formative** (Assessment for Learning)
 * **Summative** (Assessment of Learning)

= = English- This lesson incorporates English because vocabulary is going to be discussed during class. The vocabulary that will be covered has to do with graphs and includes intercepts, domain, range, zeros, and maximum and minimum values. ||
 * =**Integration**= ||
 * Technology- During class the students will be using a spredsheet program to analyze the effects of changing different constants in a function. The students will load an excel spreadsheet and then they will write a formula for a linear function and a quadratic. They will then experiment with adding contants and changing values in the functions and fill out a worksheet based off the graphs.


 * =**Groupings**= ||
 * In this class the students are going to work with a partner to decide what changing m or b in a linear equation will do to the graph. They will write equations for graphs and fill out a worksheet to solve for m and b. Both the students will work together and determine how to make a graph fit certain perimeters. To pick the groups I am going to have them work with one member from their 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. || Students will use excel to write functions and to create graphs that fit certain perimeters. They will develop a deep knowledge of both how to use spreadsheet and graphs and equations. Spreadsheet will allow the students to change only a certain part of a formula and see how that change will affect a graph instantaneously. ||
 * =Differentiated Instruction= ||
 * **Strategies**
 * Verbal:** The students are going to have to define some words and use the definitions to problem solve.
 * Logical:** This lesson will incorporate the idea of how to change a graph by changing the constants in the formula.
 * Visual:** In the lesson the students will create graphs using excel.
 * Intrapersonal:** The students will get a chance to work alone at the beginning of class on their own opinions and thoughts on what changing constants will do to a graph.
 * Interpersonal:** The students are going to have a chance to work in small groups exploring the changes in a graph when certain constants are changed.
 * Natural:** When the students are discussing slope the idea of the slope of a hill will be brought up and discussed. In this discussion we will talk about a steep slope versus a gradual slope.
 * Physical:** There will be time to move around between activities and when forming groups. ||
 * **Modifications/Accommodations**
 * **Extensions**

Computers with spreadsheet and WPtools Spreadsheet activity sheet work=power/time "worksheet" pencils ||
 * =Materials, Resources and Technology= ||
 * Observation charts

batesmath.wikispaces.com work=power/time "worksheet": __ http://www.chaosmatrix.org/library/humor/equation.html
 * =Source for Lesson Plan and Research= ||
 * Wikispace:

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 demonstrates a knowledge of the diverse ways in which students learn by using verbal skills of defining words, logical knowledge by solving for equations and describing graphs, and visual intelligence by having visual images of graphs. Both intrapersonal and interpersonal intelligences will be used by having the students work alone and then later in small groups. I will build off the students previous knowledge of graphs and help link the new ideas to future uses of graphs.__ ||
 * Standard 4 __- Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory.
 * Rationale:** This lesson will show planned instructions based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. I have based the lesson around the Maine Learning Results for Mathematics. I am using many of the different multiples intelligences from the MI theory to help teach the lesson.__ ||
 * Standard 5 __- Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs.
 * Rationale:** In this class I will use spreadsheet to show the students how to look at graphs and to describe them in terms of mathematics. Also included in my lesson will be almost all the different intelligences from the theory of MI. I will group the students at the end of class with people who will be able to help each other and I am going to use a variety of teaching strategies.__ ||
 * Standard 8__ - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner.
 * Rationale:** I will start the class by going over the homework that was assigned last class. I will allow the students to ask any question they want on the homework so that everyone will be able to comprehend the information. I will use an observation chart to keep track of what making different changes in the equation will do to the graph of the function. This chart will not be formally graded however I will take a look at them to make sure the information is correct and they will be able to use the chart to study for their tests. I will also give some homework for the students to work on for that night. ||


 * =Teaching and Learning Sequence:= ||
 * When the students walk into the room the desks will be set up in groups of four for their stock market projects. The students will sit with their group members and before class starts they can discuss their projects. Also set up around the room will be some computers with the spreadsheet program running.

Power= work/time explanation Cover Homework Class Discussion on Constants Observation Chart Worksheet/Partner Work Assign Homework

Students will learn that there is more than one way to solve an equation. They will do this through the use of studying constants and determining what changing one does to a graph. This is an important lesson because it will teach the students that there is more than one right way of solving a problem. **// Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques. //** They will show mastery of this topic by the use of an observation chart and a group activity. Before class starts the students can work on their group projects. When class starts I will show them a problem where power=work/time. By making a few substitutions I will end up proving that the less you do the more you make. This will help loosen the class up and get them interested in math. At this point I will ask if there are any questions about the homework I had assigned the day before. We will go over any problem that the class wants to see done and after we have gone over al the questions the class has they will pass their homework in to me. (25 minutes) **What, Where, Why, Hook Tailor: Interpersonal, Logical, Intrapersonal** ||
 * After we have corrected homework we will discuss the new material (see content notes). In class we will discuss how it is possible to change a graph in two fundamental ways without changing the shape: you can either add a constant to the entire function or you can add a constant to the x-value of the function. Also involved in the discussion will be the definition of slope of a linear function (already covered in earlier classes). The connection will be made that a high m value is a steeper slope and I will use the analogy of a steep hill. I will pass out observation charts that will have a before and after picture (see attached). There will be two equations or two graphs in each example and the student is to fill in the remaining information. For example if there are two functions the student will have to fill in the corresponding graphs. The students are to work on this alone for a while and then we will work on it as a class. (25 minutes) **Equip,** **Explore,** **Tailor: Intrapersonal, Interpersonal, Logical, Verbal, Visual, Natural** ||
 * After we discuss the graphs and equations that the students made using the observation charts I will have the class break into groups of 2 or 3. One group member is going to be in charge of using the computer and entering data. The second group member is going to be the think tank for that example. If there is a third member they will assist the think tank. Both (or all three) members should pay attention to the time. The worksheet that will be passed out will have 6 examples on it and after every example the group members should switch roles (attached worksheet). The worksheet will describe different parameters for a graph to follow and it will have questions about moving a graph to different places. I will have example that use concepts from last class as well as new material that builds off the old material. As they work on the graphs and equation I will move around the room to answer questions. At the end of the activity the students are to print off their graphs and pass in the worksheet. (25 minutes) **Explore, Experience, Rethink, Revise Tailor: Interpersonal, Visual, Logical, Kinesthetic** ||
 * At the beginning of the class the teacher will go over the homework assigned from the last class. This will allow the student to get feedback on the material covered last class. Then the students will be lead by the teacher while filling out observation charts. The teacher will walk around the room and make sure that the information the students record is correct. These charts will be graded on whether the student does it or not. Finally the assignment that they do in class will be collected and graded. The students will get them back by the next class. For homework the students will be assigned homework that covers the material of moving graphs and making graphs that have certain properties. They will also be expected to continue to work on their stock market project. **Evaluate Tailor: Interpersonal, Logical** ||

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