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Alg II Unit 4-6 Completing the Square
This document provides instruction on solving quadratic equations by completing the square. It begins by explaining that completing the square allows one to factor a trinomial as the square of a binomial. It then provides examples of completing the square to solve quadratic equations in various forms, including perfect square trinomials and those requiring the addition of (b/2)2. The document demonstrates transforming equations into vertex form by completing the square. Students are assigned practice problems applying these techniques.
Alg II Unit 3-5-sytemsthreevariables
Three variable systems of equations can be solved using elimination or substitution similarly to two variable systems. For elimination, equations are paired to eliminate a variable leaving two equations with two unknowns that can then be solved. For substitution, one equation is solved for one variable in terms of others and substituted into remaining equations to create a system that can be solved. An example application involving budgets shirts is worked through to demonstrate solving a three variable system.
Alg II Unit 4-8 Quadratic Equations and Complex Numbers
The document discusses complex numbers, including:
- Complex numbers are based on the imaginary unit i, where i^2 = -1.
- Complex numbers can be expressed as a + bi and graphed in the complex plane.
- Operations like addition, subtraction, multiplication, and division can be performed on complex numbers by combining real and imaginary parts.
- Quadratic equations can have complex number solutions. Finding these solutions involves factoring or using the quadratic formula.
Shipley - Algebra II Ch3 Proficiency Charts
This document contains test score data from multiple Algebra II classes on their chapter 3 exam and retake exam. It shows the distribution of scores on scatter plots for the original and retake exams for 2nd hour, 3rd hour, 5th hour, and 8th hour classes. The number of students who retook each exam is also provided.
Alg II 3-2 Solving Systems Algebraically
This document provides an overview of solving systems of linear equations algebraically. There are two main methods: substitution and elimination. Substitution involves isolating one variable and substituting it into the other equation. Elimination involves adding or subtracting equations to eliminate one variable. Examples are provided to demonstrate both methods. The objectives are for students to be able to solve linear systems algebraically and relate it to representing relationships between quantities with graphs and equations.
Geo 7-1 Ratios and Proportions
The document discusses ratios, proportions, and how to write and solve them. It provides examples of writing ratios for measurements like width to height. It also demonstrates how to set up and solve proportions using variables, cross products, and equations to find missing values like angle measures when given a ratio relationship. Examples include finding side lengths of triangles when the extended ratio and perimeter are given.
Geo 7-2 Similar Polygons
This document discusses key concepts related to similar polygons including:
- Polygons are similar if corresponding angles are congruent and corresponding sides are proportional.
- The scale factor is the ratio of corresponding sides in similar figures.
- Scale drawings use proportions to relate lengths in a drawing to actual lengths, and are used in applications like poster design.
Geometry 1-7 Constructions
This document introduces geometric constructions using a straightedge and compass. It defines key terms like straightedge, compass, and construction. The objectives are for students to be able to make basic constructions to copy segments and angles, bisect segments and angles, and construct perpendicular lines. Links are provided for online instructions on various geometric constructions.
Recommended
Alg II Unit 4-6 Completing the Square
This document provides instruction on solving quadratic equations by completing the square. It begins by explaining that completing the square allows one to factor a trinomial as the square of a binomial. It then provides examples of completing the square to solve quadratic equations in various forms, including perfect square trinomials and those requiring the addition of (b/2)2. The document demonstrates transforming equations into vertex form by completing the square. Students are assigned practice problems applying these techniques.
Alg II Unit 3-5-sytemsthreevariables
Three variable systems of equations can be solved using elimination or substitution similarly to two variable systems. For elimination, equations are paired to eliminate a variable leaving two equations with two unknowns that can then be solved. For substitution, one equation is solved for one variable in terms of others and substituted into remaining equations to create a system that can be solved. An example application involving budgets shirts is worked through to demonstrate solving a three variable system.
Alg II Unit 4-8 Quadratic Equations and Complex Numbers
The document discusses complex numbers, including:
- Complex numbers are based on the imaginary unit i, where i^2 = -1.
- Complex numbers can be expressed as a + bi and graphed in the complex plane.
- Operations like addition, subtraction, multiplication, and division can be performed on complex numbers by combining real and imaginary parts.
- Quadratic equations can have complex number solutions. Finding these solutions involves factoring or using the quadratic formula.
Shipley - Algebra II Ch3 Proficiency Charts
This document contains test score data from multiple Algebra II classes on their chapter 3 exam and retake exam. It shows the distribution of scores on scatter plots for the original and retake exams for 2nd hour, 3rd hour, 5th hour, and 8th hour classes. The number of students who retook each exam is also provided.
Alg II 3-2 Solving Systems Algebraically
This document provides an overview of solving systems of linear equations algebraically. There are two main methods: substitution and elimination. Substitution involves isolating one variable and substituting it into the other equation. Elimination involves adding or subtracting equations to eliminate one variable. Examples are provided to demonstrate both methods. The objectives are for students to be able to solve linear systems algebraically and relate it to representing relationships between quantities with graphs and equations.
Geo 7-1 Ratios and Proportions
The document discusses ratios, proportions, and how to write and solve them. It provides examples of writing ratios for measurements like width to height. It also demonstrates how to set up and solve proportions using variables, cross products, and equations to find missing values like angle measures when given a ratio relationship. Examples include finding side lengths of triangles when the extended ratio and perimeter are given.
Geo 7-2 Similar Polygons
This document discusses key concepts related to similar polygons including:
- Polygons are similar if corresponding angles are congruent and corresponding sides are proportional.
- The scale factor is the ratio of corresponding sides in similar figures.
- Scale drawings use proportions to relate lengths in a drawing to actual lengths, and are used in applications like poster design.
Geometry 1-7 Constructions
This document introduces geometric constructions using a straightedge and compass. It defines key terms like straightedge, compass, and construction. The objectives are for students to be able to make basic constructions to copy segments and angles, bisect segments and angles, and construct perpendicular lines. Links are provided for online instructions on various geometric constructions.
Angle Sum Theorem
This document discusses polygons and quadrilaterals. It introduces the Angle Sum Theorem, which states that the sum of the interior angles of an n-gon is (n-2)180. It also presents the Polygon Exterior Angle Theorem, which says that the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. The document provides examples of applying these theorems and assigns homework problems related to polygons and quadrilaterals.
Bullying Prevention Certification
This certificate of completion recognizes that Jessica Tentinger from Urbandale attended a bullying prevention training on July 16, 2013. It provides her contact information, folder number, and notes that she does not have a nursing license. The certificate documents her participation in a bullying prevention activity.
Ethics
This certificate of completion recognizes that Jessica Tentinger from Urbandale attended an ethics training for Iowa educators on July 5th, 2013. It provides her folder number, notes that she does not have a nursing license, and specifies the training was on ethics for educators in Iowa.
Shipley - Algebra II Ch2 Proficiency Charts
The document contains test score data from multiple Algebra II classes on their chapter 2 exam and retake exam. Bar graphs show the distribution of scores on the initial test and retake for each class, along with the number of students who retook the test. This data allows comparison of student performance on the chapter 2 material across different class periods and on the retake exam.
Shipley - Semester 1 Summary Data
The document contains graphs showing the percentage of students achieving over 80% proficiency in various chapters, chapter reviews (Ch1R, Ch2R, etc.), and final exams for four different class periods (2nd hour, 3rd hour, 5th hour, 8th hour) during semester 1. For each chapter and assessment, the graphs indicate the percentage of students scoring over 80% proficiency. Performance varied across class periods and assessments, with proficiency generally higher on chapter reviews compared to initial chapter material and higher on semester 1 finals compared to individual chapter assessments.
Ch4 Matrices - How to use the Calculator
1) The document provides step-by-step instructions for entering matrices and performing matrix operations like determinant and inverse on a TI-84 graphing calculator.
2) It also shows how to set up and solve a system of equations using the calculator by writing the system as an augmented matrix, performing row reduced echelon form, and reading off the solutions.
3) Key steps include entering the matrix dimensions and elements, using menu options to calculate the determinant and inverse, and setting up and solving the system of equations as an augmented matrix.
Pre-observation Form Oct 2013
Jessica Tentinger will teach Algebra II to her 5th hour class at Urbandale High School. She will use direct instruction and small group work to teach students how to solve systems of equations in three variables by elimination and substitution. During the lesson, some students will receive direct instruction while others work independently or in small groups. The teacher will check for understanding informally by asking questions and reviewing homework, and formally through an upcoming test. The administrator is asked to observe student engagement during both whole-class instruction and independent work time.
Algebra II Classroom and Homework Expectations
The Algebra II class uses a student-centered, self-paced model where students work at their own pace to learn material. Lessons are short but provide necessary content, then students work independently or in small groups on practice problems while receiving one-on-one help from the teacher. Homework consists of worksheets for students to complete problems until they understand concepts. Assignments are graded for completion, and students are responsible for their own learning by asking questions when stuck.
Sina workshop, day 1, january 25, 2013
The document outlines an agenda for a workshop on January 25th about the Iowa Support System for Schools and Districts in Need of Assistance. The workshop will help participants understand the support system and engage in a school improvement process. On this first day, participants will learn about the Audit Phase and use tools to analyze their school's "current reality". They will review documents and answer questions to complete an Audit Profile in preparation for on-site work on the next workshop date.
Iowa Assessment Math Growth Rates Grades 7-11th
- 42 students in Geometry were tested and enrolled for the full 2011-2012 academic year. 60% of students met or exceeded expected growth targets, while 19% made growth but did not meet expected targets and 21% showed negative growth.
- 1 student was tested in Algebra 2 and enrolled for the full year. This student made growth but did not meet the expected growth target.
- Data provided achievement results for students in Geometry and Algebra 2 classes from the 2011-2012 school year. The majority of Geometry students met growth targets, while the single Algebra 2 student grew but did not reach the expected level.
Geometry Chapter 3 Test Scores and Retake Test
This blank score sheet is for a geometry class taught by Ms. J. Tentingger during the first quarter. It lists the date and leaves spaces for a student's name and scores on various assignments and tests. No other information is provided on the document.
Alg II 3-6 Solving Systems - Matrices
This document discusses representing and solving systems of linear equations using matrices. It defines what a matrix is and how to identify matrix elements. A system of equations can be represented by a matrix with each row representing an equation and each column representing a variable, except the last column which holds the constants. To solve the system, the matrix is row reduced into reduced row echelon form through operations like row switching, scalar multiplication, and row addition. The solutions can then be read from the reduced matrix. Graphing calculators can also use the rref function to row reduce a matrix representing a system of equations and directly give the solutions.
Alg II 3-5 Sytems Three Variables
Three variable systems of equations can be solved using elimination or substitution similarly to two variable systems. For elimination, equations are paired to eliminate one variable, resulting in two equations with two unknowns that can then be solved. For substitution, one equation is solved for one variable in terms of others and substituted into the remaining equations to yield a system that can be solved. An example application involving budgets shirts is worked through to demonstrate solving a three variable system.
Alg II 3-4 Linear Programming
The document discusses the process of linear programming which involves defining variables, writing constraints as inequalities, graphing the feasible region, finding the vertices, writing an objective function, substituting the vertices into the function, and determining the maximum or minimum value. It provides two examples of using linear programming to maximize profits by determining the optimal number of acres to plant different crops or units of steel to produce.
Alg II 3-3 Systems of Inequalities
This document provides an overview of solving systems of linear inequalities through graphing and tables. It defines a system of inequalities as a set of inequalities where the solution satisfies all inequalities. Two main methods are discussed: using a table to systematically substitute values to find solutions, and graphing the inequalities as half-planes to find the overlap region as the solution. Several examples are provided and solved to illustrate these concepts. Key objectives are to be able to solve systems of linear inequalities and represent the solutions graphically.
Alg II3-1 Solving Systems Using Tables & Graphs
The document discusses solving systems of linear equations using tables and graphs. It provides the essential understanding that solving a system involves finding values for the variables that make each equation true. Methods covered include graphing the lines defined by the equations and finding their point of intersection, as well as using a table to find the solution values. Examples are provided to illustrate both graphing and table approaches.
Alg II 3.1-3.3 Quiz Review
This document summarizes key concepts and examples from an algebra 2 unit on linear systems. It outlines different methods for solving linear systems, including graphing, substitution, and elimination. It provides an example of a real-world linear system involving the costs of refrigerators over multiple years and finds the break-even point of 4 years where total costs are equal. Students are assigned homework problems applying these concepts.
Alg II 2-8 Inequalities
This document provides an overview of graphing two-variable linear inequalities. It defines a linear inequality as one whose graph is bounded by a line and separates the plane into two regions, one representing the solution set. To graph, a test point not on the boundary line is selected and the region shaded based on whether the point satisfies the inequality. Examples of inequalities to graph are provided, along with objectives and standards addressed. Practice problems are assigned from pages 118-119.
Alg II 2-6 Transformations
This chapter covers functions, equations, and graphs. Students will learn to analyze transformations of functions by graphing square root, cube root, piecewise-defined, step functions and absolute value functions. The essential understanding is that functions can be organized into families where each function is a transformation of a parent function.
Alg II 2-5 Linear Models
This document provides an overview of chapter 2 in an Algebra II textbook about functions, equations, and graphs. It discusses using linear equations to model real-world data and make predictions. Various types of correlations in scatter plots are defined, including trend lines and lines of best fit. Examples are provided of using scatter plots and linear regressions to analyze relationships between variables, like test scores and hours online or home prices over time. Students are assigned related practice problems to work.
Temple of Asclepius in Thrace. Excavation results
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
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Angle Sum Theorem
This document discusses polygons and quadrilaterals. It introduces the Angle Sum Theorem, which states that the sum of the interior angles of an n-gon is (n-2)180. It also presents the Polygon Exterior Angle Theorem, which says that the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. The document provides examples of applying these theorems and assigns homework problems related to polygons and quadrilaterals.
Bullying Prevention Certification
This certificate of completion recognizes that Jessica Tentinger from Urbandale attended a bullying prevention training on July 16, 2013. It provides her contact information, folder number, and notes that she does not have a nursing license. The certificate documents her participation in a bullying prevention activity.
Ethics
This certificate of completion recognizes that Jessica Tentinger from Urbandale attended an ethics training for Iowa educators on July 5th, 2013. It provides her folder number, notes that she does not have a nursing license, and specifies the training was on ethics for educators in Iowa.
Shipley - Algebra II Ch2 Proficiency Charts
The document contains test score data from multiple Algebra II classes on their chapter 2 exam and retake exam. Bar graphs show the distribution of scores on the initial test and retake for each class, along with the number of students who retook the test. This data allows comparison of student performance on the chapter 2 material across different class periods and on the retake exam.
Shipley - Semester 1 Summary Data
The document contains graphs showing the percentage of students achieving over 80% proficiency in various chapters, chapter reviews (Ch1R, Ch2R, etc.), and final exams for four different class periods (2nd hour, 3rd hour, 5th hour, 8th hour) during semester 1. For each chapter and assessment, the graphs indicate the percentage of students scoring over 80% proficiency. Performance varied across class periods and assessments, with proficiency generally higher on chapter reviews compared to initial chapter material and higher on semester 1 finals compared to individual chapter assessments.
Ch4 Matrices - How to use the Calculator
1) The document provides step-by-step instructions for entering matrices and performing matrix operations like determinant and inverse on a TI-84 graphing calculator.
2) It also shows how to set up and solve a system of equations using the calculator by writing the system as an augmented matrix, performing row reduced echelon form, and reading off the solutions.
3) Key steps include entering the matrix dimensions and elements, using menu options to calculate the determinant and inverse, and setting up and solving the system of equations as an augmented matrix.
Pre-observation Form Oct 2013
Jessica Tentinger will teach Algebra II to her 5th hour class at Urbandale High School. She will use direct instruction and small group work to teach students how to solve systems of equations in three variables by elimination and substitution. During the lesson, some students will receive direct instruction while others work independently or in small groups. The teacher will check for understanding informally by asking questions and reviewing homework, and formally through an upcoming test. The administrator is asked to observe student engagement during both whole-class instruction and independent work time.
Algebra II Classroom and Homework Expectations
The Algebra II class uses a student-centered, self-paced model where students work at their own pace to learn material. Lessons are short but provide necessary content, then students work independently or in small groups on practice problems while receiving one-on-one help from the teacher. Homework consists of worksheets for students to complete problems until they understand concepts. Assignments are graded for completion, and students are responsible for their own learning by asking questions when stuck.
Sina workshop, day 1, january 25, 2013
The document outlines an agenda for a workshop on January 25th about the Iowa Support System for Schools and Districts in Need of Assistance. The workshop will help participants understand the support system and engage in a school improvement process. On this first day, participants will learn about the Audit Phase and use tools to analyze their school's "current reality". They will review documents and answer questions to complete an Audit Profile in preparation for on-site work on the next workshop date.
Iowa Assessment Math Growth Rates Grades 7-11th
- 42 students in Geometry were tested and enrolled for the full 2011-2012 academic year. 60% of students met or exceeded expected growth targets, while 19% made growth but did not meet expected targets and 21% showed negative growth.
- 1 student was tested in Algebra 2 and enrolled for the full year. This student made growth but did not meet the expected growth target.
- Data provided achievement results for students in Geometry and Algebra 2 classes from the 2011-2012 school year. The majority of Geometry students met growth targets, while the single Algebra 2 student grew but did not reach the expected level.
Geometry Chapter 3 Test Scores and Retake Test
This blank score sheet is for a geometry class taught by Ms. J. Tentingger during the first quarter. It lists the date and leaves spaces for a student's name and scores on various assignments and tests. No other information is provided on the document.
Alg II 3-6 Solving Systems - Matrices
This document discusses representing and solving systems of linear equations using matrices. It defines what a matrix is and how to identify matrix elements. A system of equations can be represented by a matrix with each row representing an equation and each column representing a variable, except the last column which holds the constants. To solve the system, the matrix is row reduced into reduced row echelon form through operations like row switching, scalar multiplication, and row addition. The solutions can then be read from the reduced matrix. Graphing calculators can also use the rref function to row reduce a matrix representing a system of equations and directly give the solutions.
Alg II 3-5 Sytems Three Variables
Three variable systems of equations can be solved using elimination or substitution similarly to two variable systems. For elimination, equations are paired to eliminate one variable, resulting in two equations with two unknowns that can then be solved. For substitution, one equation is solved for one variable in terms of others and substituted into the remaining equations to yield a system that can be solved. An example application involving budgets shirts is worked through to demonstrate solving a three variable system.
Alg II 3-4 Linear Programming
The document discusses the process of linear programming which involves defining variables, writing constraints as inequalities, graphing the feasible region, finding the vertices, writing an objective function, substituting the vertices into the function, and determining the maximum or minimum value. It provides two examples of using linear programming to maximize profits by determining the optimal number of acres to plant different crops or units of steel to produce.
Alg II 3-3 Systems of Inequalities
This document provides an overview of solving systems of linear inequalities through graphing and tables. It defines a system of inequalities as a set of inequalities where the solution satisfies all inequalities. Two main methods are discussed: using a table to systematically substitute values to find solutions, and graphing the inequalities as half-planes to find the overlap region as the solution. Several examples are provided and solved to illustrate these concepts. Key objectives are to be able to solve systems of linear inequalities and represent the solutions graphically.
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The document discusses solving systems of linear equations using tables and graphs. It provides the essential understanding that solving a system involves finding values for the variables that make each equation true. Methods covered include graphing the lines defined by the equations and finding their point of intersection, as well as using a table to find the solution values. Examples are provided to illustrate both graphing and table approaches.
Alg II 3.1-3.3 Quiz Review
This document summarizes key concepts and examples from an algebra 2 unit on linear systems. It outlines different methods for solving linear systems, including graphing, substitution, and elimination. It provides an example of a real-world linear system involving the costs of refrigerators over multiple years and finds the break-even point of 4 years where total costs are equal. Students are assigned homework problems applying these concepts.
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This document provides an overview of graphing two-variable linear inequalities. It defines a linear inequality as one whose graph is bounded by a line and separates the plane into two regions, one representing the solution set. To graph, a test point not on the boundary line is selected and the region shaded based on whether the point satisfies the inequality. Examples of inequalities to graph are provided, along with objectives and standards addressed. Practice problems are assigned from pages 118-119.
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This chapter covers functions, equations, and graphs. Students will learn to analyze transformations of functions by graphing square root, cube root, piecewise-defined, step functions and absolute value functions. The essential understanding is that functions can be organized into families where each function is a transformation of a parent function.
Alg II 2-5 Linear Models
This document provides an overview of chapter 2 in an Algebra II textbook about functions, equations, and graphs. It discusses using linear equations to model real-world data and make predictions. Various types of correlations in scatter plots are defined, including trend lines and lines of best fit. Examples are provided of using scatter plots and linear regressions to analyze relationships between variables, like test scores and hours online or home prices over time. Students are assigned related practice problems to work.
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𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
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