Lesson+plans,+Assessment,+Project+dates


 * Day 1 **
 * **Essential Questions**
 * Can all real world situations be described by an equation with only one variable?
 * How can more than one variable be used to model a real world situation?
 * What techniques can be used to solve real world models in more than one variable?
 * **Objectives**
 * Understand that algebraic equations can have more than one variable.
 * Understand that more than one equation is required to solve a problem with more than one variable.
 * Understand the graphing method for solving systems of equations.
 * **Tasks and Activities**
 * Review graphing of linear equations in standard and non-standard forms
 * Graph two linear equations on the same coordinate grid
 * Whole class discussion about what the point of intersection might mean
 * Whole class discussion of parallel and perpendicular lines and how they relate to systems of linear equations
 * Worksheet
 * **Assessments – Formal and Informal**
 * Participation in classroom discussions
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Level of effort while completing worksheet
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Other**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Describe a real world situation that can be modeled using a system of linear equations. Describe how the graphing technique can be used to solve the system of equations.


 * Day 2 **
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Essential Questions**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">How can systems of equations be solved by transforming them into an equation with one unknown?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">How does this transformation provide a method for solving a system of equations?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Objectives**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Understand the substitution method for solving systems of equations.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Tasks and Activities**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework review
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Have one student read the answers to last night’s homework
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Are there any “problem” problems that require further discussion or clarification?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Develop substitution method by leading an interactive whole class discussion
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Whether to substitute for x or for y
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> When is it appropriate to use this method
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Visually determining if the system of equations has a solution
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Students will work with their partners on several example problems.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">One student will solve the equations by graphing; the other by substitution. They will work together to decide which method is more appropriate in a given circumstance and why. They will alternate solution methods for each system of equations.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Assessments – Formal and Informal**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework completeness and accuracy
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Participation in whole class discussions
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Active work with partner
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Other**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Solve the systems of equations on the homework handout. Be sure to follow the directions for each system, since each problem may require a different method.

**Day 3**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Essential Questions**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">What are three methods for solving systems of linear equations in multiple unknowns?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Objectives**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Understand the linear combination method for solving systems of equations
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Understand when it is appropriate to use this method
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Tasks and Activities**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework review using same techniques as day 2. A different student will lead the discussion.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Whole class discussion about linear combination
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Why do we need another method to solve systems of equations?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will work in their small, heterogeneous learning groups. One student from each group will solve a problem at the board using the linear combination technique. The other students in the group will solve the same problem at his desk on a personal white board using any of the other techniques which have been studied. There will be a short discussion period at the end of each problem to review the answer and the appropriateness of each technique. This activity will be repeated four times, so that each member of the group has an opportunity to solve a problem at the board.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Assessments – Formal and Informal**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework completion and accuracy
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Work effort while working at board and at desk
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Effort will be assessed by quickly looking at each student's work to determine if the selected solution technique has been used properly and if the correct answer has been obtained. If a student is struggling, did he attempt a solution. Determine any areas requiring additional understanding.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Other**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> There are 15 systems of linear equations on this handout. For each system, describe the technique that you would use to solve it. Be sure to include why you selected this technique. You do not need to actually solve the systems.

**Day 4**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Essential Questions**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> What situation would be appropriate for using each of these techniques?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">What are two situations in which systems of linear equations cannot be uniquely solved?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Objectives**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Learn to describe real world situations by using systems of linear equations
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Review all 3 methods for solving systems of linear equations with 2 unknowns
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Tasks and Activities**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework review using same method described above
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Introduction of authentic assessment assignment
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will begin work on authentic assessment
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Assessments – Formal and Informa**l
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Homework completeness and accuracy
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Participation in class discussion
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Participation on authentic assessment
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Other**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Homework
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Complete authentic assessment

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 169%;">**Day 5** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 169%;">
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Essential Questions**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">All of the essential questions documented above
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Objectives**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will demonstrate their knowledge of solving systems of linear equations with two unknowns by continuing their work on the authentic assessment.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Tasks and Activities**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will work in their learning groups to develop a consensus solution to the authentic assessment
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Assessments – Formal and Informal**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Observe student participation in group work. Is the student working towards the understanding of the entire cooperative learning group?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Other**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Prepare for authentic assessment group presentations
 * Day 6**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Essential Questions**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">All of the essential questions documented above
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Objectives**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will continue to demonstrate their knowledge of solving systems of linear equations with two unknowns.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Tasks and Activities**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">The teacher will select a random student from each group to present the groups' consensus solution to the authentic assessment problem. There will be a short whole class discussion following each presentation.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> **Assessments – Formal and Informal**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Student participation in group presentation and whole class discussion
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> **Other**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Homework
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Begin to study for the unit test

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 169%;">**Day 7** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Assessments – Formal and Informal**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Essential Questions**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">All of the essential questions documented above
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Objectives**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will continue to demonstrate their knowledge of solving systems of linear equations with two unknowns.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Tasks and Activities**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Whole class discussion
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Any questions related to authentic assessment
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Any specific questions related to entire unit
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Unit review
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will complete a unit review worksheet with their partner
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Review of any issues on the unit review worksheet
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Student participation on unit review work sheet
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Student willingness and ability to help partner resolve any problem areas
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> **Other**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Homework
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Continue to study for the unit test

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 169%;">**Day 8**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Essential Questions**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">All of the essential questions documented above
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Objectives**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will continue to demonstrate their knowledge of solving systems of linear equations with two unknowns.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Tasks and Activities**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Unit test
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Assessments – Formal and Informal**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Completion and accuracy on unit test
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Did student show all steps required to solve system
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Did the student demonstrate understanding of when to use each method of solution?
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> **Other**
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">None