Linear Models and Systems Unit 2 Advance Algebra

Objectives Sep Identify and algebraically transform systems of linear equations. Define what it means to solve a system of equations. Make connections between linear equations and arithmetic sequences.

Group work – 2 person, present on white board. The senior class hosted a spaghetti dinner to raise money for the local animal shelter. They sold CHILD tickets for $8 each and ADULT tickets for $12 each. Altogether they sold 137 tickets and they made a total of $1472 for the animal shelter. How many tickets of each type were sold?

September 19 Objectives Write explicit formulas for arithmetic sequences. Write linear equations in intercept form.

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Notes: Recursive formula Write the Explicit formula.

Consider the recursively defined arithmetic sequence. a.Find an explicit formula for the sequence. b.Use the explicit formula to find. c.Find the value of n so that.

September 22, 2014 Objectives: 1.Given two points on a graph determine the slope. 2.Convert a linear equation to Intercept form. 3.Use academic language to describe a linear equation Dependent variable, Independent variable, Domain, Range.

Convert the following linear equation to intercept form:

September Objectives: 1.Determine how to estimate a Line of Fit given a set of data. 2.Given the slope and one point of a line use the Point-Slope form to write a linear equation. Line of Fit Interpolation Extrapolation Point-Slope form

Point-Slope form.

September 29, 2014 Objectives: 1.Explain what is meant by a System of equations. 2.Given a set of data that represents a system of equation; find the solution. System of equations, Solution to a system of equations.

September 30, 2014 Objectives: 1.Given a system of linear equations use substitution to find the solution. Reminder: Unit 1 Portfolios are due Oct. 2 HW 3D ; page and page due Oct. 3

Warm-Up

October 1, 2014 Objectives: 1.Solve a system of linear equations using substitution and elimination. 2.Classify system of equations as a think pair share activity. Inconsistent Consistent Dependent Independent

Warm-Up Factor:

Substitution

Elimination Solve the system by elimination.

Elimination Solve the system by elimination.

Advance Algebra Oct. 3 Objectives:

Warm-up Graph the following 3 equations:

October 6, 2014 Objectives. 1.Students will analyze the work of other students and critique / grade the work for solving a system of linear equations. 2.Students will graph the appropriate region of a linear inequality.

Warm-Up Graph the 3 linear inequalities and shade in the area that overlap.

Describe what is happening with each step.

October 7, 2014 Objectives: 1.Students will graph linear inequalities and use a test point to check for correctness. 2.Students will be able to identify the feasible region of linear inequalities and describe this region in terms of constraints. Constraints Vertex Feasible Region

Warm-Up Factor the following.

Rachel has 3 hours to work on her homework tonight. She wants to spend more time working on math than on chemistry, and she must spend at least a half hour working on chemistry. Let x = time in hours spent on math. Let y = time in hours spent on chemistry. Write inequalities to represent the three constraints of the system.

Graph the Inequality.

October 9, 2014 Objectives: 1.Students will describe the procedure on creating a system of inequalities. 2.Use technology to graph inequalities. 3.Students will use an algebraic method to determine the solution of a 3 variable system.

Warm-Up: To use the graphing calculator a linear equation has to be in “y=“ form. Graph the following on your calculator:

To use the graphing calculator a linear equation has to be in “y=“ form. Graph the following on your calculator:

Now Graph the following Linear Inequalities: Prob. 5, page 357

Now Graph the following Linear Inequalities:

October 10, 2014 Objectives: 1.Given a situation with multiple constraints the student will develop a system of inequalities. 2.Identify the vertex points of a feasible region and determine if they are a maximum or minimum point.

Example A: Solving systems with 3 variables.

Example B: Solving systems with 3 variables.

Oct. 13, 2014 Objectives: 1.Organize information in a table and construct inequalities of the constraints. 2.Analyze the maximum or minimum of a system of inequalities.

Page 363, prob. 3 Graph this system of inequalities, label the vertices of the feasible region. And name the integer coordinates the maximize the function

October 14, 2014 Objectives: 1.Students will optimize a system of inequalities by finding the maximum profit. 2.Students will restate the solution of a system linear programing in the context of the problem.

Warm-Up Use technology and the inverse matrix method to solve this system

October 15, 2014 Objectives: 1.Students will demonstrate understanding of Linear Systems by use of: (Unit Test) a.Mathematical models b.Equations and Inequalities c.Tables d.Written explination

October 17, 2014