Name: Paul Madden

Date: 10/24/2007

Subject/Grade: 11th / Algebra II Honors

Unit/Theme: Solving Systems of Linear Equations

__Standards Covered____ __

**Mathematics Curriculum Framework Standards:**

- 10.P.8 - Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems.

**ELPBO Standards:**

- R.6.7 - Evaluates relevant information gained from a variety of sources
- S.1.25 - Understands words and of grade-level academic content, including technical and abstract terms.
- S.1.28 - Communicates academic knowledge, using specific, technical, and abstract vocabulary of grade-level academic content.
- S.2.48 - Understands when engaged in sustained, interpersonal interaction.
- S.3.36 - Understands specific information given in an academic context.
- S.3.43 - Participates in limited classroom discussions and activities when clarification is given.
- W.1.6c - Organizes ideas in logical order for expository writing.

__Lesson Objectives__

**Content Objectives:**

-Students will be able to solve systems of linear equations by using the multiplication with addition rule, by drawing on their prior knowledge of the addition rule and the distributive property.

-Students will be able to make real life connections to the material presented

-Students will be able to think critically about their solutions to word problems and the context of the problem itself.

**Language Objectives:**

-Students will discuss their solutions and reasoning for their solutions during think peer share activities throughout the lesson using content specific vocabulary.

-Students will actively listen to their peers during group work.

-Students will decode a word problem in order to set up an equation, which they will solve in pairs.

-Students will demonstrate their understanding of the material by writing their solutions to examples done in pairs during class on the white board and by explaining their solutions with the assistance of the teacher and a partner.

-Students will respond logically in writing to the “what if” questions presented by the word problem.

**Key Vocabulary Words/Phrases:**

Systems of linear Equations (review)

Addition rule/method (review)

Distributive Property

Multiply through

Solve for a variable

**Materials:**

Scaffolded Notes w/ Worksheets (Appendix 1)

Red Sox World Series, real to life word problem (Appendix 2)

Overhead projector

Overhead transparency with grid on it

TI83, TI83 projector

**SIOP Lesson Features:**

Preparation Scaffolding Grouping Options

_X_Adaptation of Content _X_Modeling _X_Whole Class

_X_Links to Background _X_Guided Practice _ X_Small Groups

_X_Links to Past Learning _X_Independent Practice _X_Partners

_X_Strategies Incorporated _X_Comprehensible Input _X_Independent

Integration of Processes Application Assessment

__X_Reading _X_Hands-on _X_Individual

_X_Writing _X_Meaningful _X_Group

_X_Speaking _X_Linked to Objectives _X_Written

_X_Listening _X_Promotes Engagement _X_Oral

**Procedures**

**Opening**

-Before the lesson begins, I will have written the content and language objectives, the homework, and an agenda for the period on the top of the white board.

-When my students enter the classroom and sit down, I will tell them to take out their homework packet, previously assigned by my cooperative teacher, and tell them to write their names on it and to place it on the front desk, next to the projector. As they hand in their homework I will hand them a notes packet (See Appendix 1) that contains explanations of concepts and practice problems for my students to do during the course of the class, an agenda, and a word problem which I will be referencing during class.

-I will begin the class by telling my students what I hope they will learn and will be able to do by the end of the period, what we will be doing throughout the period and what is for homework while referencing the information I placed on the board before class and in their notes.

-Then, I will ask my students to summarize in their own words what they learned in yesterday’s class about solving systems of linear equations using the additive method.

-Next, I will review the material by going over one of the homework problems on the board, with the help of students input. In addition, I will ask my students questions about the equations, which are very simplistic: “Are these problems realistic or not? Do you think you would see problems or situations where adding linear equations immediately results in the canceling of a variable? Why?”

-I will use their responses, which I will write on the board, to state why using the multiplication with the additive rule is necessary in most realistic situations, as life and math are not always so neat.

**During Lesson**

-After, building upon my student’s prior knowledge concerning the additive method, I will remind and provide direct instruction to my students about the distributive property on the board while referencing their notes and by thinking about this process out loud. Also, I will reinforce this concept by asking my students to multiply out the algebraic statements [2 * (X + 2), 5 * (4-X), 6*(X-X2+3), 3* (4X+5=3], that are in their packet using the distributive property in pairs or on their own. Then I will ask a few students to explain and write their answers up on the board. In doing this, my students will see how the distributive property works and thus what it actually is.

-Then after building up and recalling my student’s prior knowledge about solving linear equations by using the addition method and of the distributive property I will demonstrate to my students, while using their active input how to solve systems of linear equations by multiplication with the addition rule. During this process I will be revealing my thought process in solving these types of problems by doing a think-aloud. Then I will ask my students to do 4 of these problems, which are in their packets in pairs. I will hand four groups a different colored dry erase marker so that they can write their answers to these problems on the board.

-While my students are doing this activity in pairs, I will walk around and help my students as needed while reminding them to help and to rely on each other for help first, as this is the point of working in groups or pairs.

-During this time I will take a few minutes to check, record, and hand back their homework from the night before.

-I will stop this activity after 8 minutes and ask the four pairs that I handed the dry erase marker to, to explain and write their solutions to the problem assigned to them on the board. As the students are explaining their solutions I will be guiding, rewording, affirming, and checking their answers to enhance my students learning.

-After this problem, I will ask my students if they have any lingering questions. I will answer any of their questions before I move on.

-I will ask my student to turn to the page of the packet, where the real to life Red Sox Fanatic word problem question is, while I erase the board, turn on the project, and place a copy of the problem on the projector (See Appendix 3). Then I will explain to the students that we will be solving a real to life problem using what we learned today about solving linear equations by multiplication with the addition rule.

-First, I will ask my students to take turns reading the word problem out loud. After they finish reading the whole problem once, I will ask one of the students to summarize the problem as best as they can with my assistance. Then, my students and I will go through the word problem sentence by sentence together on the projector as they follow along in their packets. I will and ask them to help me underline and take note on what is important in the problem and to cross out and discard irrelevant information not needed to solve the problem. During this process I will practice thinking aloud to make explicit my thought process when solving a word problem.

-After we finish going through the problems, we will write all of the important information we underlined or circled and transfer all the notes we took onto the board. With this information, I will ask the students to get together in groups of 2 or 3 to create the appropriate two equations with the key information presented. During this time I will walk around and assist any of the groups if needed while reminding them to rely on each others skills and knowledge to solve the problem.

-After 5 minutes I will ask my students to state and discuss their thought processes used in creating the 2 equations that they derived from the information provided. I will help to clarify and elaborate on these students thought processes.

-Then the students should resume their group work in order to solve these linear equations by multiplication with the addition rule. Then, alone, the students should write short answers for their solution to the questions I posed and then discuss these solutions in groups. Once they finish writing out their own solutions they should discuss these solutions with a partner.

-Next, I will solicit my student’s answers to these problems, which I will ask follow up questions about, expand upon, and clarify.

-I will show and explain to my students my answer and solutions to the problem. In addition, I will specifically show them the structure of my written solutions, as to explicitly expose the register of mathematical writing and thinking.

**Closing**

-I will end the class by asking a student to explain, in their own words what they learned in class today. I will also ask my students what they felt was and was not helpful and what they believe may need further development. I will remind them of the homework on the board and inform them that tomorrow they will be learning about solving systems of linear equations using the substitution method.

**Homework**

-Finish solving the word problem and the “what if” questions asked.

**Assessment**

-Have students summarize what they have learned the day before when class begins and ask student to summarize what they learned today at the end of class.

-Have students respond orally to thought provoking “what if,” “why?,” and “how?” questions during class.

-Ask students to explain in their own words why they solve the problem the way they do.

-Check completion of individual written work that they complete for homework.

-Have students write their solutions on the board.

-Oversee group and paired interactions.