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Taylor, Melani

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Algebra II

by Melani Taylor

Algebra II

1st 6 weeks

 

Introduction to Functions (5 days)
Students will collect data by experimentation, analyze collected and given data, interpret the scatterplots to make predictions, and fit the graph to the most reasonable parent function. Students will make predictions using representations of the data.

 

Relations and Functions (4 days)
Students will collect data by experimentation and analyze the data to determine if it represents a function. Students will determine characteristics of the relationship and model the data using various representations. Students will interpret the representations to make predictions and fit the graph to the most reasonable parent function.

 

Changing Parents (11 days)
Students apply geometric transformations to relations. Students determine rules to predict effects on changing parameters on parent functions. Students determine graphs and equations from the predictions.

 

 Investigating Inverses (4 days)
Students explore inverses of relations by comparing graphs, tables, and algebraic generalizations. This is an introductory investigation that will be extended when comparing inverse relations, such as quadratic and square root function and exponential and logarithmic functions.

2nd 6 weeks

 Linear Functions and Inequalities (6 days)
Students will identify characteristics of linear functions, describe effects of parameter changes on the parent function, and determine the equation of a line from given information. Students will analyze problem situations and collected data by representing the situation with tables, graphs, verbal descriptions, and algebraic generalizations, interpret the results, and predict values. Students will represent linear inequalities and apply them to solve problem situations.
   
Linear Equations and  Inequalities(4 days)
Students will identify characteristics of linear functions, describe effects of parameter changes on the parent function, and determine the equation of a line from given information. Students will analyze problem situations and collected data, represent the situation with tables, graphs, verbal descriptions, and algebraic generalizations, interpret the results, and predict values. Students will represent linear inequalities and apply them to solve problem situations.
  
 Systems Algebraically (5 days)
This lesson serves as the introduction to a unit on systems of equations and inequalities. The lesson begins with a puzzle that leads to a “trial and error” method for solving a system of equations. Then, various other methods for solving systems are investigated, including graphing, substitution, and combination/elimination. Next, students are asked to reflect on which method best suits certain types of systems. Finally, students must apply these skills in setting up and solving systems to model real-world situations.
   
 Systems with Technology (5 days)
This lesson continues the discussion of systems of equations by adding the use of technology. Specifically, matrices are introduced then used as tools for solving systems (particularly 3?3 systems). The lesson begins with some intuitive data problems that lead naturally to matrix operations. From this, students explore a variety of problem situations in which systems will be developed and solved with matrix methods.
 
Systems of Inequalities (5 days)
This lesson continues the discussion of systems. However, instead of systems of equations, students are led through an analysis of systems of inequalities. The lesson begins by shading values on a grid. Next, students graph systems of two, three, and four inequalities on graph paper and on a calculator. The lesson concludes with linear programming problems in which students must maximize or minimize values under certain constraints.
 

 

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