Social Studies Grade 8 s9

Mathematics – Geometry Unit: Prioritized TAKS Review Fourth Grading Period – Weeks 1-3 (12 days) CURRICULUM OVERVIEW Big Idea Unit Rationale TAKS has been developed to reflect good instructional practice and measure student learning. TAKS Success on TAKS for all of our students is our common goal. Passing TAKS should connect directly with what our students should know and be able to do to be academically at the Exit level is a requirement for high school graduation. The key to successful. success for each individual student is to address that individual student’s math strengths and weaknesses. TEKS TEKS Specificity - Intended Outcome s

t 8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional or non-

p proportional linear relationships in problem situations and solves problems. The student is ” I CAN” statements highlighted in yellow should be displayed for e

c expected to: students. n

o I can: 8.3B estimate and find solutions to application problems involving percents and other C  estimate and find solutions to real-life problems involving percents proportional relationships such as similarity and rates. and proportional relationships such as similarity and rates (8.3B) 8.6 Geometry and spatial reasoning. The student uses transformational geometry to develop  generate similar figures through dilations which either enlarge or spatial sense. The student is expected to: reduce the original shape (8.6A)  graph dilations, reflections, and translations on a coordinate plane 8.6A generate similar figures using dilations including enlargements and reductions: and (8.6B) 8.6B graph dilations, reflections, and translations on a coordinate plane.  relate the physical attributes of concrete models of prisms, cylinders, pyramids, spheres, and cones to the variables in the abstract 8.8 Measurement. The student uses procedures to determine measures of three-dimensional formulas (8.8B) figures. The student is expected to:  solve real-world problems involving lateral and total surface area by 8.8B connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume estimating measurements and using formulas (8.8C) of these objects: and  use proportionality to find the missing measurements in two- dimensional or three-dimensional figures. (8.9B) 8.8C estimate measurements and use formulas to solve application problems involving lateral  describe the changes on perimeter and area when the dimensions and total surface area and volume. of a shape are altered proportionally (8.10A) 8.9 Measurement. The student uses indirect measurement to solve problems. The student is  make decisions and predictions based on either theoretical or expected to: experimental probabilities (8.11B)  justify a choice of decision for a particular decision by selecting an 8.9B use proportional relationships in similar two-dimensional figures or similar three- appropriate measure of central tendency or range fr the related set of dimensional figures to find missing measurements. data (8.12A) 8.10 Measurement. The student describes how changes in dimensions affect linear, area, and  present and display relationships among collected data by selecting volume measures. The student is expected to: and appropriately using one of several listed representations (8.12C)  apply mathematical procedures and concepts to everyday 8.10A describe the resulting effects on perimeter and area when dimensions of a shape are experiences (8.14A) changed proportionally.  use a problem solving model that at a minimum includes the 8.11 Probability and statistics. The student applies concepts of theoretical and experimental following 4 steps – understanding the problem, making a plan to solve it, probability to make predictions. The student is expected to: executing the plan, and checking the solution for reasonability (8.14B)  select or develop an appropriate problem solving strategy from a 8.11B use theoretical probabilities and experimental results to make predictions and decisions. given list (8.14C) 8.12 Probability and statistics. The student uses statistical procedures to describe data. The  communicate mathematical ideas using language, efficient tools, student is expected to: appropriate units, and graphical, numerical, physical, or algebraic mathematical models (8.15A) 8.12A select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation: and SAISD © 2008-09 – Fourth Grading Period Mathematics- Geometry Page 1 of 20

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.  describe functional relationships for given problem situations and 8.12C select and use an appropriate representation for presenting and displaying relationships write equations or inequalities to answer questions arising from the among collected data, including line plots, stem and leaf plots, circle graphs, bar graphs, box and situations (A.1.C) whisker plots, histograms, and Venn diagrams, with and without the use of technology.  represent relationships among quantities using concrete models, 8.14 Underlying processes and mathematical tools. The student applies Grade 8 mathematics tables, graphs, diagrams, verbal descriptions, equations, and inequalities to solve problems connected to everyday experiences, investigations in other disciplines, and (A.1.D) interpret and make decisions, predictions, and critical judgments activities in and outside of school. The student is expected to: from functional relationships (A.1.E)  identify and sketch the general forms of linear ( y = x ) and 8.14A identify and apply mathematics to everyday experiences, to activities in and outside of quadratic ( y = x2 ) parent functions (A.2.A) school, with other disciplines, and with other mathematical topics:  symbols to represent unknowns and variables (A.3.A) 8.14B use a problem-solving model that incorporates understanding the problem, making a  look for patterns and represent generalizations algebraically (A.3.B) plan, carrying out the plan, and evaluating the solution for reasonableness; and  use the commutative, associative, and distributive properties to simplify algebraic expressions (A.4B) 8.14C select or develop an appropriate problem-solving strategy from a variety of different  relate direct variation to linear functions and solve problems types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it involving proportional change (A.6.G) out, making a table, working a simpler problem, or working backwards to solve a problem.  analyze situations involving linear functions and formulate linear equations or inequalities to solve problems (A.7.A) 8.15 Underlying processes and mathematical tools. The student communicates about Grade 8  investigate methods for solving linear equations and inequalities mathematics through informal and mathematical language, representations, and models. The using concrete models, graphs, and the properties of equality, select a student is expected to: method, and solve the equations and inequalities (A.7.B) 8.15A communicate mathematical ideas using language, efficient tools, appropriate units, and  analyze situations and formulate systems of linear equations in two graphical, numerical, physical, or algebraic mathematical models. unknowns to solve problems (A.8.A)  interpret and determine the reasonableness of solutions to systems A.1 Foundations for functions. The student understands that a function represents a of linear equations (A.8.C) dependence of one quantity on another and can be described in a variety of ways. The student is  solve quadratic equations using concrete models, tables, graphs, expected to: and algebraic methods (A.10.A)  use patterns to generate the laws of exponents and apply them to A.1C describe functional relationships for given problem situations and write equations or problem-solving situations (A.11.A) inequalities to answer questions arising from the situations A.1D represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and A.1E interpret and make decisions, predictions, and critical judgments from functional relationships. A.2 Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: A.2A identify and sketch the general forms of linear ( y = x ) and quadratic ( y = x 2 ) parent functions. A.3 Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to: A.3A use symbols to represent unknowns and variables; and A.3B look for patterns and represent generalizations algebraically.

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. A.4 Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to: A.4B use the commutative, associative, and distributive properties to simplify algebraic expressions. A.6 Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to: A.6G relate direct variation to linear functions and solve problems involving proportional change. A.7 Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: A.7A analyze situations involving linear functions and formulate linear equations or inequalities to solve problems; and A.7B investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities. A.8 Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: A.8A analyze situations and formulate systems of linear equations in two unknowns to solve problems; and A.8C interpret and determine the reasonableness of solutions to systems of linear equations. A.10 Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to: A.10A solve quadratic equations using concrete models, tables, graphs, and algebraic methods. A.11 Quadratic and other nonlinear functions: The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situation. The student is expected to: A.11A use patterns to generate the laws of exponents and apply them to problem-solving situations. Evidence of Learning At least 80% of the time, students will demonstrate on paper or use models to show they can  estimate and find solutions to real-life problems involving percents and proportional relationships such as similarity and rates  generate similar figures through dilations which either enlarge or reduce the original shape  graph dilations, reflections, and translations on a coordinate plane  relate the physical attributes of concrete models of prisms, cylinders, pyramids, spheres, and cones to the variables in the abstract formulas  solve real-world problems involving lateral and total surface area by estimating measurements and using formulas

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.  use proportionality to find the missing measurements in two-dimensional or three-dimensional figures  describe the changes on perimeter and area when the dimensions of a shape are altered proportionally  make decisions and predictions based on either theoretical or experimental probabilities  justify a choice of decision for a particular decision by selecting an appropriate measure of central tendency or range for the related set of data  present and display relationships among collected data by selecting and appropriately using one of several listed representations  apply mathematical procedures and concepts to everyday experiences  use a problem solving model that at a minimum includes the following 4 steps – understanding the problem, making a plan to solve it, executing the plan, and checking the solution for reasonability  select or develop an appropriate problem solving strategy from a given list  communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models  describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations  represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations  interpret and make decisions, predictions, and critical judgments from functional relationships  identify and sketch the general forms of linear ( y = x ) and quadratic ( y = x2 ) parent functions  use symbols to represent unknowns and variables  look for patterns and represent generalizations algebraically  use the commutative, associative, and distributive properties to simplify algebraic expressions  relate direct variation to linear functions and solve problems involving proportional change  analyze situations involving linear functions and formulate linear equations or inequalities to solve problems  investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities  analyze situations and formulate systems of linear equations in two unknowns to solve problems  interpret and determine the reasonableness of solutions to systems of linear equations  solve quadratic equations using concrete models, tables, graphs, and algebraic methods  use patterns to generate the laws of exponents and apply them to problem-solving situations

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. Mathematics – Geometry Unit : Prioritized TAKS Review Fourth Grading Period – Weeks 1-3 (12 days) CURRICULUM GUIDE The Teaching Plan Apr 6 – 24, 2009 These days are set aside for campuses to prepare their students for success on the April 28-30 High School Math TAKS. Individual student TAKS strengths and weaknesses should drive the focus and timeline for these 12 classroom days. All high schools should be using at a minimum the following data for determining these student strengths and weaknesses:  Individual student item analysis from previously taken TAKS exams  Individual student item analysis from district TAKS benchmark exams and FMAs  Individual student item analysis from campus/teacher prepared TAKS diagnostics or benchmarks.  School-wide, grade level TAKS data by student expectation (SE) (i.e., Kilgo data). Objectives for the student success focus are increased individual student awareness of:  his/her specific TAKS history and the steps to be taken leading to a higher level of achievement  his/her impact on the campus accountability evaluations, both federal and state  all the TAKS assistance available  the benefits of a strong performance on TAKS  how to incrementally improve SE by SE and how to document the improvement  his/her responsibility and accountability to do well on TAKS  how to use the tools available during the TAKS – TAKS Mathematics Chart and graphing calculators Individual lessons to focus on district-wide TAKS weaknesses by SE are provided. These lessons are provided as samples of the type of lessons provided in the following sources and are not intended to be prescriptive:  TEA TAKS Study Guides – both online interactive and printed – Grades 9-11(Exit)  TEA TAKS Information Booklets – Grades 9-11  Region 4 Closing the Distance – A Flexible Tutorial for TAKS Series for Grades 9 through 11 (Exit)  Region 4 TAKS Mathematics Preparation Guides for Grades 9-11  Region 4 Accelerated Curriculum for Mathematics Grade 11 Exit TAKS  McDougal Littell Math TAKS Objectives Review and Practice – Grades 9-11 (Exit)  McDougal Littell textbooks for Algebra 1, Geometry and Algebra 2 Click TAKS SE/Region IV Publications Matrix for a matrix which delineates where in each Region 4 publication the SEs are addressed with prepared lessons. This matrix is also found on the Math Department website under RTI Secondary. Instructional Model & Teacher Directions So students can… The teacher will… Region 4 Closing the Distance TAKS Grade 10 Math Region 4 Closing the Distance TAKS Grade 10 Math Lesson 3: Interpreting Graphs Lesson 3 Interpreting Graphs SEs A.1.D, A.1.E, A.2.B, A.2.D SEs A.1.D, A.1.E, A.2.B, A.2.D Engage (10 minutes) Engage (10 minutes)  The class should be arranged in groups of 3-4  Write down 6 statements about the displayed graph  Display the Transparency Soccer Ball  Discuss what you wrote with your group members  Ask the students to write down 6 statements about the graph  Share with the rest of the class what your group discussed  Ask the students to share with their group members what they wrote Explore (20 minutes)  Ask a student to act as a scribe on the chalkboard as the teacher chooses students and  Do 2 of the 4 Interpreting graphs problems (A.1.D, A.1.E, A.2.B, A.2.B) small groups to share what they wrote  Answer questions as needed (A.1.D, A.1.E, A.2.B, A.2.B)  Use the facilitation questions on page 44 to address observations about the parent function, Explain (20-25 minutes) domain, range, x-intercept, and y-intercept that the students may have missed  Display and present your work to the rest of the class (A.1.D, A.1.E,

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. Explore (20 minutes) A.2.B, A.2.B)  Distribute the Interpreting Graphs activity  Answer questions related to scatterplots and functions (A.1.D, A.1.E,  Assign each pair of students 2 of the 4 problems to complete A.2.B, A.2.B)  Ask 2 student groups that finish early to complete the transparencies for the Interpreting  Record the solutions of the two problems that each student did not do graphs activity for questions 1-4. These transparencies will be used in the explain phase of the (A.1.D, A.1.E, A.2.B, A.2.B) lesson. Elaborate (20 minutes)  Use the facilitation questions on pp 45-46 to assist student groups as needed.  Complete the card match activity (A.1.D, A.1.E, A.2.B, A.2.B) Explain (20-25 minutes)  Answer questions related to scatterplots and functions (A.1.D, A.1.E,  Ask the student groups to display and present their work from the Interpreting graphs A.2.B, A.2.B) activity by using blank transparencies or the interpreting graphs transparencies Evaluate (15-20 minutes)  For the 2 problems that each students did not work, they should record the solutions as  Answer the evaluate questions presented  Discuss in your journal what you learned about functions and  Use the facilitation questions on pp 47-48 to check the students conceptual understanding scatterplots, be sure to include key vocabulary such as parent function, and connect procedures to their understanding as they present their work domain, range, x-intercept, y-intercept and inequality Elaborate (20 minutes)  The students should work in pairs for this activity  Distribute one cut and bagged set of cards from the activity card match to each pair of students  Ask the students to complete the activity by matching a graph to its domain, range and a sentence that interprets the graph. There are 4 sets of 4 matching cards  Use the facilitation questions on page 50 to assist students as needed. Evaluate (20 minutes)  Distribute a copy of Evaluate: Scatterplots and Functions to each student  Ask the students to answer the evaluate questions individually showing all work on the pages  Have the students trade papers for grading  Have the students write a summary of what they learned about scatterplots and functions in their journal.  Collect the assessments and analyze for the need to reteach  Use the error analysis on page 51 to analyze the results for effective reteaching Region 4 Closing the Distance TAKS Grade 10 Math Region 4 Closing the Distance TAKS Grade 10 Math Lesson 5: Equations and Inequalities Lesson 5: Equations and Inequalities SEs A.7.A, A.7.B , A.7.C, 8.3B SEs A.7.A, A.7.B , A.7.C, 8.3B Engage (10 minutes) Engage (10 minutes)  The students should be in groups of 2-4  Write the variables and numerals above the corresponding quantity on  Distribute the activity writing equations and writing equation cards to each student the first question on the writing Equations activity (A.7.A, A.7.B, A.7.C, 8.3B)  Display Transparency 1: Writing Equations which corresponds to the first problem in the  Work together in your group to organize the cards on their desks to Writing Equations activity represent the equation (A.7.A, A.7.B, A.7.C, 8.3B)  Ask the students to write the variables and numerals above the corresponding quantity on  After successfully organizing the cards, write the equation (A.7.A, the first question on the writing Equations activity A.7.B, A.7.C, 8.3B)  Ask the students to work together to organize the cards on their desks to represent the Explore (20 minutes) equation  Work problems 2 and 3 on the Writing Equations activity (A.7.A, A.7.B,  After students have successfully organized the cards, ask them to write the equation A.7.C, 8.3B)  Monitor the students to make sure they can correctly form the equation  Answer questions as needed (A.7.A, A.7.B, A.7.C, 8.3B)  Use the facilitation questions on page 82 to assist student groups as necessary Explain (15- 20 minutes) Explore (20 minutes)  Participate in a discussion about problems 2 and 3 (A.7.A, A.7.B, A.7.C,  Students work in small groups (2-4 students) 8.3B)  Make sure the students have a calculator  Answer questions related to equations and inequalities (A.7.A, A.7.B, SAISD © 2008-09 – Fourth Grading Period Mathematics- Geometry Page 6 of 20

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.  Ask students to work problems 2 and 3 on the Writing Equations activity A.7.C, 8.3B)  Actively monitor the students as they work  Use the facilitation questions on pp 83-84 to assist students as needed Elaborate (20 minutes) Explain (15- 20 minutes)  Complete the equations and inequalities activity (A.7.A, A.7.B, A.7.C,  Display Transparency 2: Writing Equations 8.3B)  Ask the questions on p 85 to lead a discussion  Answer questions related to equations and inequalities (A.7.A, A.7.B,  Display Transparency 3: Writing Equations A.7.C, 8.3B)  Ask the questions on p 86 to lead a discussion Evaluate (20 minutes) Elaborate (20 minutes)  Answer the evaluate questions (A.7.A, A.7.B, A.7.C, 8.3B)  Distribute the equations and inequalities activity to each student  Discuss in your journal what you learned about equations and  Ask each student to complete the activity page inequalities, be sure to include key vocabulary (A.7.A, A.7.B, A.7.C, 8.3B)  Use the facilitation questions on pp 87-88 to as needed to develop students’ conceptual understanding of writing and solving equations and inequalities Evaluate (20 minutes)  Distribute a copy of Evaluate: Exploring Equations and Inequalities to each student  Ask the students to answer the evaluate questions individually showing all work on the pages  Have the students write a summary of what they learned about equations and inequalities in their journal.  Collect the assessments and analyze for the need to reteach  Use the error analysis on page 89 to analyze the results for effective reteaching Region 4 Closing the Distance TAKS Grade 10 Math Region 4 Closing the Distance TAKS Grade 10 Math Lesson 6: Solving Equations Lesson 6: Solving Equations SEs A.4.A, A.4.B, A.7.B SEs A.4.A, A.4.B, A.7.B

Engage (10 minutes) Engage (10 minutes)  The students should be in groups of 2-4  Work in your groups to match the problem on one side of a card with the  Distribute one set of cards from the Activity Master: Simplifying Expressions to each student solution on the side of another card (A.4.A, A.4.B, A.7.B) group  Answer questions related to solving equations (A.4.A, A.4.B, A.7.B)  Have students work in their groups to match the problem on one side of a card with the Explore (20 minutes) solution on the side of another card  Complete the activity Solving Equations (A.4.A, A.4.B, A.7.B)  When the cards are put together they form a 3 x 3 grid  Answer questions related to solving equations (A.4.A, A.4.B, A.7.B)  Use the facilitation questions on p 100 to assist struggling students Explain (20 minutes) Explore (20 minutes)  Present the group findings to the class using the Activity transparencies  Distribute Activity: Solving Equations and a graphing calculator to each student (A.4.A, A.4.B, A.7.B)  Ask the students to complete the activity in their groups  Discuss the facilitation questions related to solving equations (A.4.A,  As the students finish assign 1 group to prepare to present problem 1 and another to A.4.B, A.7.B) prepare to problem 2 in the explain phase Elaborate (20 minutes)  Actively monitor the students as they work  Complete the Activity: Solving Equations (A.4.A, A.4.B, A.7.B)  Use the facilitation questions on pp 101-102 to assist students as needed Evaluate (20 minutes) Explain (20 minutes)  Answer the evaluate questions (A.4.A, A.4.B, A.7.B)  Ask the student groups that were assigned problems 1 and 2 to show and explain their work  Discuss in your journal what you learned about solving equations, be on transparencies of the Activity: Solving Equations sure to include key vocabulary (A.4.A, A.4.B, A.7.B)  Make sure and clarify key vocabulary as the students discuss their work  After the students present their work use the facilitation questions on pp103-104 to help solidify the students’ understanding Elaborate (20 minutes)  This part of the lesson is designed for individuals or small groups SAISD © 2008-09 – Fourth Grading Period Mathematics- Geometry Page 7 of 20

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.  Distribute Activity: Solutions to Equations to each student  Students should be able to work with minimal assistance  Use the facilitation questions on pp 105-106 to assist students as needed Evaluate (20 minutes)  Distribute a copy of Evaluate: Solving Equations to each student  Ask the students to answer the evaluate questions individually showing all work on the pages  Have the students write a summary of what they learned about equations and inequalities in their journal.  Collect the assessments and analyze for the need to reteach  Use the error analysis on page 107 to analyze the results for effective reteaching Region 4 Closing the Distance TAKS Grade 10 Math Region 4 Closing the Distance TAKS Grade 10 Math Lesson 7: Systems of Equations Lesson 7: Systems of Equations SEs A.8.A, A.8.B, A.8.C SEs A.8.A, A.8.B, A.8.C Engage (10 minutes) Engage (10 minutes)  Whole group discussion  Discuss the Transparency: Cell Phone Plans  Display the Transparency: Cell Phone Plans Explore (20 minutes)  Lead a class discussion on the transparency using the facilitation questions on p 118  Match the problems to the proper equation, and the proper calculator Explore (20 minutes) screens (A.8.A, A.8.B, A.8.C)\  Students should work individually Explain (10-15 minutes)  Distribute a set of Systems Card Sort cards to each student  Participate in a discussion concerning solving systems of equations  Distribute a graphing calculator to each student (A.8.A, A.8.B, A.8.C)  Have the students match the problems to the proper equation, and the proper calculator  Be able to explain how to solve for Y and how to use the calculator screens properly (A.8.A, A.8.B, A.8.C)  Use the facilitation questions on p 119 to assist students as needed Elaborate (20 minutes) Explain (10-15 minutes)  Solve at least 2 problems from the Activity: Systems of equations  Use the facilitation questions on p 120 to lead a class discussion (A.8.A, A.8.B, A.8.C)  Remind students of Calculator techniques (teacher note p 120)  Be able to explain to the class how the problem is solved (A.8.A, A.8.B, Elaborate (20 minutes) A.8.C)  The students should work in small groups for this part of the lesson Evaluate (20 minutes)  Distribute a copy of Activity: Systems of Equations to each student  Answer the evaluate questions (A.8.A, A.8.B, A.8.C)  Ask the student groups to solve 2 of the problems  Discuss in your journal what you learned about solving equations, be  After listening to the student groups select the problem that needs clarification the most for sure to include key vocabulary and key procedures such as solving for Y and debriefing proper calculator technique (A.8.A, A.8.B, A.8.C)  Use the facilitation questions on p 121-124 to reinforce proper concepts and procedures  Repeat the process with the other 2 problems as time allows Evaluate (20 minutes)  Distribute a copy of Evaluate: Systems of Linear Equations to each student  Ask the students to answer the evaluate questions individually showing all work on the pages  Have the students write a summary of what they learned about equations and inequalities in their journal.  Collect the assessments and analyze for the need to reteach  Use the error analysis on page 125 to analyze the results for effective reteaching Region 4 Closing the Distance TAKS Grade 10 Math Region 4 Closing the Distance TAKS Grade 10 Math Lesson 8: Quadratic Functions Lesson 8: Quadratic Functions SEs A.1.B, A.9.B, A.9.C, A.9.D, A.10.A, A.10.B SEs A.1.B, A.9.B, A.9.C, A.9.D, A.10.A, A.10.B Engage (10 minutes) Engage (10 minutes) SAISD © 2008-09 – Fourth Grading Period Mathematics- Geometry Page 8 of 20

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.  The students should be in groups of 2-4  Discuss in your group, then with the class what you observe in the  Ask students if they have ever launched a model rocket Transparency: Rocket launch (A.1.B, A.9.B, A.9.C, A.9.D, A.10.A, A.10.B)  Display the Transparency: Rocket launch  Discuss in your group, then with the class what you observe in the  Ask the students to discuss in their groups what they observe in the graphs. Transparency: Finding Zeros and Roots (A.1.B, A.9.B, A.9.C, A.9.D, A.10.A,  After students are finished sharing in their groups ask them to share their observations with A.10.B) the class  Use the facilitation questions on p 134 to guide a short whole group discussion  Display the Transparency: Finding Zeros and Roots Explore (20 minutes)  Ask the students to discuss in their groups what they observe in the graphs  Investigate the effects of changing a and c in functions of the form  After students are finished sharing in their groups ask them to share their observations y=ax²+c (A.1.B, A.9.B, A.9.C, A.9.D, A.10.A, A.10.B)  Use the facilitation questions on p 135 to guide a short whole group discussion  Record their results on your individual activity sheets (A.1.B, A.9.B, Explore(20 minutes) A.9.C, A.9.D, A.10.A, A.10.B) Explain (20 minutes)  Distribute a copy of Activity: Changing a and c in y=ax²+c to each student  As a group present 1 match from the Activity: Changing a and c in  Distribute a graphing calculator to each student y=ax²+c by making a poster or a transparency or by displaying your work  Ask students to work in groups to investigate the effects of changing a and c in functions of using the viewscreen (A.1.B, A.9.B, A.9.C, A.9.D, A.10.A, A.10.B) the form y=ax²+c  Answer the facilitation question in a class discussion (A.1.B, A.9.B,  They should record their results on their individual activity sheets A.9.C, A.9.D, A.10.A, A.10.B)  Use the facilitation questions on p 136 to assist students as needed Elaborate (20 minutes) Explain (20 minutes)  Work in groups to match each function with its graphical and tabular  Ask student groups to display and present 1 match from the Activity: Changing a and c in representation, determine the zeros and roots then record the results (A.1.B, y=ax²+c by making a poster or a transparency or by displaying their work using the viewscreen A.9.B, A.9.C, A.9.D, A.10.A, A.10.B)  Use the facilitation questions on p 138 to help solidify the students’ conceptual Evaluate (20 minutes) understanding and procedural knowledge  Answer the evaluate questions (A.1.B, A.9.B, A.9.C, A.9.D, A.10.A, Elaborate (20 minutes) A.10.B)  Distribute 1 set of Tables, Graphs, Roots and Zeros to each student group  Discuss in your journal what you learned about solving equations, be  Distribute 1 copy of the Recording Sheet for Tables, Graphs, Roots and Zeros and a sure to include key vocabulary and key procedures such as proper calculator graphing calculator to each student on their individual recording sheets. technique (A.1.B, A.9.B, A.9.C, A.9.D, A.10.A, A.10.B)  Ask students to work in groups to match each function with its graphical and tabular representation, determine the zeros and roots then record the results  Use the facilitation questions on p 139-140 to assist students as neede Evaluate (20 minutes)  Distribute a copy of Evaluate: Investigating Quadratic Functions to each student  Ask the students to answer the evaluate questions individually showing all work on the pages  Have the students write a summary of what they learned about equations and inequalities in their journal.  Collect the assessments and analyze for the need to reteach  Use the error analysis on page 141 to analyze the results for effective reteaching Region 4 Closing the Distance TAKS Grade 10 Math Region 4 Closing the Distance TAKS Grade 10 Math Lesson 11: Area Models Lesson 11: Area Models SEs A.3.A, A.4A, A.11A SEs A.3.A, A.4A, A.11A Engage (10 minutes) Engage (10 minutes)  The students should be in groups of 3-4  Determine the area of the largest rectangle, the shaded and unshaded  Display Transparency: Rectangles and Area regions and answer the relationship question (A.3.A, A.4A, A.11A)  Ask the students to determine the area of the largest rectangle, the shaded and unshaded Explore (20 minutes) regions and answer the relationship question  Complete the Activity: Area of Shaded regions in terms of x (A.3.A,  After the students have discussed the answers in their groups, use the facilitation questions A.4A, A.11A) on p 190 to guide a short discussion SAISD © 2008-09 – Fourth Grading Period Mathematics- Geometry Page 9 of 20

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. Explore (20 minutes) Explain (20 minutes)  Distribute Activity: Area of Shaded regions in terms of x  Present their work from the Activity: Area of Shaded regions in terms of  Ask the students to follow the directions and complete the activity in their groups x as a student group by making a poster or using a blank transparency  Use the facilitation questions on p 192 to assist students as needed (A.3.A, A.4A, A.11A) Explain (20 minutes)  Answer the facilitation question as the presentation is made (A.3.A,  Ask student groups to display and present their work from the Activity: Area of Shaded A.4A, A.11A) regions in terms of x by either making a poster on chart paper or using a blank transparency Elaborate (20 minutes)  Use the facilitation questions on p 194-195 to help solidify the students’ conceptual  Complete the Activity: Area of Regions (A.3.A, A.4A, A.11A) understanding and procedural knowledge as they present their work Elaborate (20 minutes) Evaluate (20 minutes)  Distribute Activity: Area of Regions to each student  Answer the evaluate questions (A.3.A, A.4A, A.11A)  Have the students solve the problems in the activity  Discuss in your journal what you learned about solving equations, be  Use the facilitation questions on p 196 to aid struggling students. sure to include key vocabulary and key procedures such as proper calculator Evaluate (20 minutes) technique (A.3.A, A.4A, A.11A)  Distribute a copy of Evaluate: Area Models to each student  Ask the students to answer the evaluate questions individually showing all work on the pages  Have the students write a summary of what they learned about equations and inequalities in their journal.  Collect the assessments and analyze for the need to reteach  Use the error analysis on page 198 to analyze the results for effective reteaching Vocabulary: (TEKS verbs) Vocabulary: (TEKS verbs) Resources:  Identify  Present  TEA TAKS Study Guides – both online interactive and  Solve  Display printed – Grades 9-11(Exit)  Estimate  Evaluate  TEA TAKS Information Booklets – Grades 9-11  Develop  Represent  Region 4 Closing the Distance – A Flexible Tutorial for  Generate  Formulate TAKS Series for Grades 9 through 11 (Exit)  Graph  Sketch  Region 4 TAKS Mathematics Preparation Guides for  Determine  Manipulate Grades 9-11  Connect  Simplify  Region 4 Accelerated Curriculum for Mathematics  Describe  Relate Grade 11 Exit TAKS  Apply  Analyze  McDougal Littell Math TAKS Objectives Review and  Select  Investigate Practice – Grades 9-11 (Exit)  Present  McDougal Littell textbooks for Algebra 1, Geometry and Algebra 2 Problem Solving Checklist TAKS SE/Region IV Publications Matrix Evidence of Learning Differentiation Interims/TAKS/Benchmarks College-Readiness i.e., Anticipated Skills for SAT/ACT/AP/Career/Life

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. See the campus RTI plan. 2004 TAKS 10th Grade Problem 27 (SE 8.8B) SAT Prep

Each campus has multiple resources to address the wide If a cone is intersected by a plane parallel to its base, what spectrum of students’ levels of potential and performance does the boundary of the intersection most resemble? on TAKS. Refer to the Resource list above. A. square B. circle C. ellipse D. parabola E. hyperbola

2003 TAKS 10th Grade Problem 41 (SE A.11A)

2003 TAKS 10th Grade Problem 10 (SE A.4B)

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. SAISD © 2008-09 – Fourth Grading Period Mathematics- Geometry Page 12 of 20

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. Mathematics – Geometry Unit: Similarity Applications Fourth Grading Period – Weeks 5-6 (10 days) CURRICULUM OVERVIEW Big Idea Unit Rationale Using special relationships in right triangles Trigonometric ratios are initially introduced to solve right triangles, setting the stage to Using trigonometric ratios to solve right triangles use trigonometric ratios to solve oblique triangles in later math courses. TEKS TEKS Specificity - Intended Outcome G.5 Geometric Patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to: ” I CAN” statements highlighted in yellow should be displayed for students. G.5B use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and I can: angle relationships in polygons and circles; and  use geometric patterns to make generalizations about angle relationships G.5D identify and apply patterns from right triangles to solve meaningful problems, in triangles (G.5B) including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are  identify and apply patterns from right triangles to solve meaningful Pythagorean triples. problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples (G.5D) G.8 Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter,  derive, extend, and use the Pythagorean Theorem (G.8C) area, and volume in problem situations. The student is expected to:  develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of G.8C derive, extend, and use the Pythagorean Theorem. methods (G.11C) G.11 Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. The student is expected to: G.11C develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods. Evidence of Learning At least 80% of the time students will demonstrate on paper or use models to show they can  use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles  identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples  derive, extend, and use the Pythagorean Theorem  develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. Mathematics – Geometry Unit: Similarity Applications Fourth Grading Period – Weeks 5-6 (10 days) CURRICULUM GUIDE

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. Essential Questions Essential Pre-requisite Skills 8 th Grade How can we use similar triangles to solve real world problems?  Select and use appropriate forms of rational numbers to solve real life How does the concept of similarity lead to the concept of the trigonometric functions? problems including those involving proportional relationships (8.1.B) How specifically do the effects of the Pythagorean theorem lead to only the tangent and  Approximate the value of irrational numbers as they arise from problem not the sine and cosine having no limit? situations (8.1.C) What tools are available to determine all the sides and angles of an oblique triangle?  Estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates (8.3.B)  Use pictures or models to demonstrate the Pythagorean theorem (8.7.C)  Use the Pythagorean theorem to solve real life problems (8.9.A)  Use proportional relationships in similar two-dimensional or similar three- dimensional figures to find missing measurements (8.9.B) The Teaching Plan So students can demonstrate competency, Instructional Model & Teacher Directions the student will… The teacher will… Days 1 & 2 Days 1 & 2 MDL Section 7.5 Apply the Tangent Ratio MDL Section 7.5 Apply the Tangent Ratio Engage Engage  Pose the following problem: A wire supports a tree. The wire is staked into the  Determine how high up the tree the wire is attached using tangent ratio. ground 10 feet from the tree and it forms an angle of 70 degrees with the tree. Explore Explore  Provide metric ruler, protractor, and calculator and assign students to draw a  Provide metric ruler, protractor, and calculator and assign students to draw a 30 30 degree angle and mark a point every 5cm as illustrated on page 466. degree angle and mark a point every 5cm as illustrated on page 466. Explain Explain  Discuss the findings from the exploring activity.  Discuss the findings from the exploring activity.  Explain complementary angles, and explain adjacent sides and opposite sides.  Explain complementary angles, and explain adjacent sides and opposite sides. Refer to page 467. Refer to page 467.  Introduce the tangent ratio.  Introduce the tangent ratio. Elaborate Elaborate  Relate the tangent ratio to the 30-60-90 special right triangle.  Relate the tangent ratio to the 30-60-90 special right triangle.  Refer to Best Practices Toolkit, page 353, Example 1  Refer to Best Practices Toolkit, page 353, Example 1 Evaluate Evaluate  Assign Skill Practice on page 469 #1-20 as class work and homework  Assign Skill Practice on page 469 #1-20 as class work and homework assignment. (G.5D, G.11C) assignment. Have students support their conclusions to the class.  Have students support their conclusions to the class.  ****Make sure students have their calculators in degree mode****  ****Make sure students have their calculators in degree mode**** Day 3 Day 3 MDL Section 7.6 Apply the Sine Ratio MDL Section 7.6 Apply the Sine Ratio Engage Engage  Pose the following problem (Extra Example 4 pg. 475, TE), A pilot is looking at  Draw a diagram illustrating the problem and label the lengths and angles. an airport from her plane. The angle of depression is 29 degrees. If the plane is at (G.11C) altitude of 10,000 feet, approximately how far is it from the airport?  Discuss in a class-wide format the solution to the problem. Explore Explore  Measure the opposite side and the hypotenuse.  Distribute rulers and pre-made similar right triangles to all students. Have  Compare their findings with other students and record them in their journals. students measure the opposite side and the hypotenuse. Have students compare (G.5B) their ratio findings with each other in class. Explain Explain  Complete the sine ratio sections of the notetaking guide.  Present warm-up transparency page 473 to review legs and hypotenuse of right  Discuss to class and explain the sine ratio concepts in their journals. triangle. SAISD © 2008-09 – Fourth Grading Period Mathematics- Geometry Page 15 of 20  Introduce the sine ratio. Evaluate Power AssignStandards note represent taking guidethe essential sections knowledge that are and sine skills ratio students only (pages need for 189-193) success in high school and beyond.Complete Power Skill Standards Practice must page be 477 mastered -478 # to 1-6, successfully 10-16, 22-27( pass the sine required only) (G.11C) Evaluateassessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.  Assign Skill Practice page 477 -478 # 1-6, 10-16, 22-27( sine only) Day 4 Day 4 MDL Section 7.6 Apply the Cosine Ratio MDL Section 7.6 Apply the Cosine Ratio Engage Engage Mathematics – Geometry Unit: Geometric Structure Fourth Grading Period – Weeks 7-9 (14 days) CURRICULUM OVERVIEW Big Idea Unit Rationale Develop an awareness of axiomatic systems Understanding inductive reasoning, deductive reasoning and axiomatic systems Use inductive reasoning to make and test conjectures is crucial for future mathematical development Use deductive reasoning to develop simple logical arguments Prove basic geometric theorems Writing proofs of geometric relationships TEKS TEKS Specificity - Intended Outcome G.1 Geometric structure. The student understands the structure of, and relationships within, an axiomatic system. The student is expected to: ” I CAN” statements highlighted in yellow should be displayed for students. G.1A develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems; I can: G.1B recognize the historical development of geometric systems and know mathematics  develop an awareness of the structure of a mathematical system, is developed for a variety of purposes; and connecting definitions, postulates, logical reasoning, and theorems (G.1.A)  recognize the historical development of geometric systems and know G.1C compare and contrast the structures and implications of Euclidean and non- mathematics is developed for a variety of purposes (G.1.B) Euclidean geometries.  compare and contrast the structures and implications of Euclidean and non-Euclidean geometries (G.1.C) G.2 Geometric structure. The student analyzes geometric relationships in order to make  use constructions to explore attributes of geometric figures and to make and verify conjectures. The student is expected to: conjectures about geometric relationship (G.2.A) G.2A use constructions to explore attributes of geometric figures and to make  make conjectures about angles, lines, polygons, circles, and three- conjectures about geometric relationships; and dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or G.2B make conjectures about angles, lines, polygons, circles, and three-dimensional axiomatic (G.2.B) figures and determine the validity of the conjectures, choosing from a variety of approaches  determine the validity of a conditional statement, its converse, inverse, such as coordinate, transformational, or axiomatic. and contrapositive (G.3.A) G.3 Geometric structure. The student applies logical reasoning to justify and prove  construct and justify statements about geometric figures and their mathematical statements. The student is expected to: properties (G.3.B)  use logical reasoning to prove statements are true and find counter G.3A determine the validity of a conditional statement, its converse, inverse, and examples to disprove statements that are false (G.3.C) contrapositive;  use inductive reasoning to formulate a conjecture (G.3.D) G.3B construct and justify statements about geometric figures and their properties;  use deductive reasoning to prove a statement (G.3.E)  select an appropriate representation (concrete, pictorial, graphical, G.3C use logical reasoning to prove statements are true and find counter examples to verbal, or symbolic) in order to solve problems (G.4) disprove statements that are false;  use numeric and geometric patterns to develop algebraic expressions G.3D use inductive reasoning to formulate a conjecture; and representing geometric properties (G.5.A) G.3E use deductive reasoning to prove a statement. G.4 Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. G.5 Geometric patterns. The student uses a variety of representations to describe  use numeric and geometric patterns to make generalizations about geometric relationships and solve problems. The student is expected to: geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles G.5A use numeric and geometric patterns to develop algebraic expressions representing (G.5.B) geometric properties;  use properties of transformations and their compositions to make G.5B use numeric and geometric patterns to make generalizations about geometric connections between mathematics and the real world, such as properties, including properties of polygons, ratios in similar figures and solids, and angle tessellations (G.5C) relationships in polygons and circles;  use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures (G.7.A) G.5C use properties of transformations and their compositions to make connections  derive and use formulas involving length, slope, and midpoint (G.7.C) between mathematics and the real world, such as tessellations  formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models (G.9.A) G.7 Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly. The student is expected to: G.7A use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures G.7C derive and use formulas involving length, slope, and midpoint. G.9 Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures. The student is expected to: G.9A formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models. Evidence of Learning At least 80% of the time students will demonstrate on paper or use models to show they can  develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems  recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes  compare and contrast the structures and implications of Euclidean and non-Euclidean geometries  use constructions to explore attributes of geometric figures and to make conjectures about geometric relationship  make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic  determine the validity of a conditional statement, its converse, inverse, and contrapositive  construct and justify statements about geometric figures and their properties  use logical reasoning to prove statements are true and find counter examples to disprove statements that are false  use inductive reasoning to formulate a conjecture  use deductive reasoning to prove a statement  select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems  use numeric and geometric patterns to develop algebraic expressions representing geometric properties  develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems  recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes  compare and contrast the structures and implications of Euclidean and non-Euclidean geometries  use constructions to explore attributes of geometric figures and to make conjectures about geometric relationship  make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic  determine the validity of a conditional statement, its converse, inverse, and contrapositive  construct and justify statements about geometric figures and their properties SAISD © 2008-09 – Fourth Grading Period Mathematics- Geometry Page 17 of 20

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.  use logical reasoning to prove statements are true and find counter examples to disprove statements that are false  use inductive reasoning to formulate a conjecture  use deductive reasoning to prove a statement  select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems  use numeric and geometric patterns to develop algebraic expressions representing geometric properties  use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles  use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations  use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures  derive and use formulas involving length, slope, and midpoint  formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. Mathematics – Geometry Unit: Geometric Structure Fourth Grading Period – Weeks 7-9 (14 days) CURRICULUM GUIDE

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards. Essential Questions Essential Pre-requisite Skills 8 th Grade What is an axiomatic system?  Use appropriate operations to solve problems involving rational numbers in Are there different types of geometries? problem situations (8.2.B) How do you use inductive reasoning in mathematics?  Use geometric concepts and properties to solve problems (8.7.B) How do you rewrite a conditional statement?  Locate and name points on a coordinate plane using ordered pairs of rational How do you construct a logical argument? numbers (8.7.D) How can you represent a logical statement symbolically? Algebra 1 How can you identify postulates illustrated by a diagram?  Represent relationships among quantities using concrete models, tables, How do you write a geometric proof? graphs, diagrams, verbal descriptions, equations and inequalities (A.1.D) The Teaching Plan Instructional Model & Teacher Directions So students can… The teacher will… Day 1 Day 1 MDL Section 3.6 Extension: Taxicab Geometry MDL Section 3.6 Extension: Taxicab Geometry Euclidean and Non Euclidean Geometry Euclidean and Non Euclidean Geometry Engage Engage  Discuss with students the similarities and differences of Euclidean and Non-  Read about Euclidean and Non-Euclidean Geometry on the internet site Euclidean Geometry using internet resource: http://www.cs.unm.edu/~joel/NonEuclid/noneuclidean.html http://www.cs.unm.edu/~joel/NonEuclid/noneuclidean.html  Give examples of Euclidean and Non-Euclidean Geometry. (G.1C) Explore Explore  Provide students with Compare and Contrast Graphic Organizer handout.  Record their observations in order to compare and contrast the structures and Explain implications of Euclidean and non-Euclidean geometries.  Group students to compare their charts Explain  Give groups poster paper to create graphic organizer to present  Come to a consensus and create one large compare and contrast chart on Elaborate poster paper to display  Discuss and demonstrate the difference in a Euclidean Circle and a Taxicab Elaborate Circle (see example 2 pg 199)  Draw examples on their posters of the differences between a Euclidean Circle Evaluate and a Taxicab Circle and summarize findings in journals (G.7A, G.7C)  Use authentic assessment using group oral questioning techniques during each Evaluate presentation  Present to class and discuss findings of similarities and differences of the structures and implications of Euclidean and non-Euclidean geometries (G.1C) Day 2 Day 2 MDL Section 3.6 Extension: Taxicab Geometry MDL Section 3.6 Extension: Taxicab Geometry Euclidean and Non Euclidean Geometry Euclidean and Non Euclidean Geometry Engage Engage  Introduce the concept of Taxicab Geometry by asking question “How do you  Discuss and answer the question “How do you find the distance between two find the distance between two points on a coordinate plane when you can only move points on a coordinate plane when you can only move horizontally or vertically?” horizontally or vertically?” (G.7C) Explore Explore  Give Warm Up Questions ML TE p.198  Answer and discuss warm up questions  Ask for real world examples  Using warm up as an example, create their own real world problem representing Taxicab Geometry(G.7C) Explain  The key concept of Taxicab Distance Explain  The historical note on Euclidean and non-Euclidean Geometries  Discuss and make comparisons and Contrasts on Euclidean Geometry and Elaborate Taxicab Geometry  Demonstrate using Geo-Board or Geo-Board Paper example 1 page 198 ML Elaborate Evaluate  Take notes in their journal verbalizing and drawing examples of Taxicab  Facilitate group activity Practice questions 1-14 page 199 of ML distance on Geo-Board paper SAISD © 2008-09Assess –student Fourth Gradingwork for Period accuracy on Practice questions 1-14 page 199Mathematics- of ML GeometryEvaluate Page 20 of 20  Use Geo-Board or Geo-Board Paper to work on activity questions 1-14 page Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.199 of ML and present findings to entire class (G.1C, G.7A, G.7C) Day 3 Day 3 MDL Section 11.4 Extension: Geometry on a Sphere MDL Section 11.4 Extension: Geometry on a Sphere Spherical Geometry Spherical Geometry Engage