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1 EGG HARBOR TOWNSHIP PUBLIC SCHOOLS CURRICULUM Geometry Length of Course: Full Year Schools: High School Student Eligibility: Grades 9-12 Credit Value: 5 Credits Date Approved: ____________ 2 TABLE OF CONTENTS Mission Statement ………………………………………….. Philosophy …………………………………………………… Statement of Purpose ………………………………………. Introduction ………………………………………………….. District Curriculum Template ………………………………. Guiding Principles …………………………………………… Intent of the Guide …………………………………………… Unit 1 – Basics of Geometry ……..…………..……………. Unit 2 – Reasoning and Proofs…………………………...… Unit 3 – Parallel and Perpendicular Lines ……….……….. Unit 4 – Transformations …………………………………… Unit 5 – Congruent Triangles ……………………………… Unit 6 – Relationships within Triangles …...……………… Unit 7 – Polygons and Quadrilaterals …………………….. Unit 8 – Similarity ……………………………………………. Unit 9 – Right Triangles and Trigonometry………….. …... Unit 10 - Circles ………………………………..................... Unit 11 – Circumference, Area and Volume ……………… This curriculum guide was prepared by: Thomas Marshall, High School Christian Wiech, High School Christine Stafford, High School Jen DiMaio, High School Harry Kiedaisch, High School Stephanie Haupin, High School Danielle Lynch, High School Coordinated by: Greg Ryan, Supervisor of Mathematics 3 3 3 3 4 4 5 6 8 10 12 14 16 18 20 22 24 26 3 DISTRICT MISSION STATEMENT Our mission in the Egg Harbor Township School District is to partner with the student, family, school, and community to provide a safe learning environment that addresses rigorous and relevant 21st Century standards and best practices which will develop academic scholarship, integrity, leadership, citizenship, and the unique learning style of students, while encouraging them to develop a strong work ethic and to act responsibly in their school community and every day society. MATHEMATICS - PHILOSOPHY We believe that ALL students regardless of race, ethnicity, socio-economic status, religious background, and/or any other classification are deserving of a holistic mathematics education. This holistic approach would include an education that will allow them to fully discover themselves, their strengths and weaknesses, and benefit from necessary real world/real life mathematical instruction. Mathematics curricula are designed to reinforce 21st Century Learning, to maximize rigor, relevance, and relationships, and to engage students individually through differentiated instruction. MATHEMATICS - STATEMENT OF PURPOSE Education exists for the purpose of enabling each individual to realize and maintain her/his full potential. Mathematics education specifically involves the development of each individual's understanding and appreciation and serves as an essential element to the developmental process and toward the future success of students in the world at large. The Mathematics programs provide the opportunity for each individual to develop a comprehensive foundation of basic knowledge, skills, and techniques and serve not only as pathways to future success but also provide students with opportunities to excel and challenge themselves in preparation for lifelong learning. This curriculum guide has been designed to expose all students to the mathematics educational experience outlined within. Each student will be offered thorough and analogous mathematics instruction and will be fully prepared for the continuing education offered at the secondary level. Additionally, through active participation, students will develop positive individual and group behavioral patterns while exploring the vast cultural and ethnic diversity reflective of our community. Our school district provides an extensive mathematics program, which will enable students to succeed and compete in the global marketplace using the Common Core State Standards (CCSS). INTRODUCTION The most precious resource teachers have is time. Regardless of how much time a course is scheduled for, it is never enough to accomplish all that one would like. Therefore, it is imperative that teachers utilize the time they have wisely in order to maximize the potential for all students to achieve the desired learning. 4 High quality educational programs are characterized by clearly stated goals for student learning, teachers who are well-informed and skilled in enabling students to reach those goals, program designs that allow for continuous growth over the span of years of instruction, and ways of measuring whether students are achieving program goals. THE EGG HARBOR TOWNSHIP SCHOOL DISTRICT CURRICULUM TEMPLATE The Egg Harbor Township School District has embraced the backward-design model as the foundation for all curriculum development for the educational program. When reviewing curriculum documents and the Egg Harbor Township curriculum template, aspects of the backward-design model will be found in the stated enduring understandings/essential questions, unit assessments, and instructional activities. Familiarization with backward-design is critical to working effectively with Egg Harbor Township’s curriculum guides. GUIDING PRINCIPLES: WHAT IS BACKWARD DESIGN? WHAT IS UNDERSTANDING BY DESIGN? “Backward design” is an increasingly common approach to planning curriculum and instruction. As its name implies, “backward design” is based on defining clear goals, providing acceptable evidence of having achieved those goals, and then working ‘backward’ to identify what actions need to be taken that will ensure that the gap between the current status and the desired status is closed. Building on the concept of backward design, Grant Wiggins and Jay McTighe (2005) have developed a structured approach to planning programs, curriculum, and instructional units. Their model asks educators to state goals; identify deep understandings, pose essential questions, and specify clear evidence that goals, understandings, and core learning have been achieved. Programs based on backward design use desired results to drive decisions. With this design, there are questions to consider, such as: What should students understand, know, and be able to do? What does it look like to meet those goals? What kind of program will result in the outcomes stated? How will we know students have achieved that result? What other kinds of evidence will tell us that we have a quality program? These questions apply regardless of whether they are goals in program planning or classroom instruction. The backward design process involves three interrelated stages for developing an entire curriculum or a single unit of instruction. The relationship from planning to curriculum design, development, and implementation hinges upon the integration of the following three stages. Stage I: Identifying Desired Results: Enduring understandings, essential questions, knowledge and skills need to be woven into curriculum publications, documents, standards, and scope and sequence materials. Enduring understandings identify the “big ideas” that students will grapple with during the course of the unit. Essential questions provide a unifying focus for the unit and students should be able to answer 5 more deeply and fully these questions as they proceed through the unit. Knowledge and skills are the “stuff” upon which the understandings are built. Stage II: Determining Acceptable Evidence: Varied types of evidence are specified to ensure that students demonstrate attainment of desired results. While discrete knowledge assessments (e.g.: multiple choice, fill-in-the-blank, short answer, etc…) will be utilized during an instructional unit, the overall unit assessment is performance-based and asks students to demonstrate that they have mastered the desired understandings. These culminating (summative) assessments are authentic tasks that students would likely encounter in the real world after they leave school. They allow students to demonstrate all that they have learned and can do. To demonstrate their understandings students can explain, interpret, apply, provide critical and insightful points of view, show empathy and/or evidence self-knowledge. Models of student performance and clearly defined criteria (i.e.: rubrics) are provided to all students in advance of starting work on the unit task. Stage III: Designing Learning Activities: Instructional tasks, activities, and experiences are aligned with stages one and two so that the desired results are obtained based on the identified evidence or assessment tasks. Instructional activities and strategies are considered only once stages one and two have been clearly explicated. Therefore, congruence among all three stages can be ensured and teachers can make wise instructional choices. At the curricular level, these three stages are best realized as a fusion of research, best practices, shared and sustained inquiry, consensus building, and initiative that involves all stakeholders. In this design, administrators are instructional leaders who enable the alignment between the curriculum and other key initiatives in their district or schools. These leaders demonstrate a clear purpose and direction for the curriculum within their school or district by providing support for implementation, opportunities for revision through sustained and consistent professional development, initiating action research activities, and collecting and evaluating materials to ensure alignment with the desired results. Intrinsic to the success of curriculum is to show how it aligns with the overarching goals of the district, how the document relates to district, state, or national standards, what a high quality educational program looks like, and what excellent teaching and learning looks like. Within education, success of the educational program is realized through this blend of commitment and organizational direction. INTENT OF THE GUIDE This guide is intended to provide teachers with course objectives and possible activities, as well as assist the teacher in planning and delivering instruction in accordance with the Common Core State Standards (CCSS). The guide is not intended to restrict or limit the teacher’s resources or individual instruction techniques. It is expected that the teacher will reflectively adjust and modify instruction and units during the course of normal lessons depending on the varying needs of the class, provided such modified instruction attends to the objectives and essential questions outlined below. 6 Unit Name: Basics of Geometry Time Frame: 12 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:Students will apply basic facts about points, planes, segments, and angles. They will also measure and construct segments and angles, and use formulas to find distance and midpoint on the coordinate plane. An understanding of points, lines, planes, and segments is fundamental to the entire geometry course. UNIT RESOURCES:Textbook, Calculator, Straightedge, Protractor, Compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Construction tutorials: http://www.mathsisfun.com/geometry/constructions.html -Study Island: http://www.studyisland.com/ STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Congruence G-CO Experiment with transformations in the plane G.CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.12. Make formal geometric constructions with a variety of tools and methods (compass and straight edge, string, reflective devices, paper folding, dynamic geometric software, etc.) CCSS: Mathematics, CCSS: HS: Geometry, Similarity, Right Triangles, & Trigonometry G-SRT Define trigonometric ratios and solve problems involving right triangles G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied probl ems. CCSS: Mathematics, CCSS: HS: Geometry, Expressing Geometric Properties with Equations G-GPE Use coordinates to prove simple geometric theorems algebraically G-GPE.7. Use coordinates to compute perimeters of polygons and areas for triangles and rectangles, e.g. u sing the distance formula. CCSS: Mathematics, CCSS: HS: Geometry, Modeling with Geometry G-MG Apply geometric concepts in modeling situations G-MG.1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tre e trunk or a human torso as a cylinder). 7 ENDURING UNDERSTANDINGS -There is a distinct and definite bridge between the worlds of algebra and algebraic thinking and the field of geometry. -Simple figures and shapes are a part of the larger understanding of complex geometric ideas. ESSENTIAL QUESTIONS -What algebra tools and concepts will I use in Geometry? -How are diagrams marked? How are angles measured? -How can constructions reinforce the meaning of geometric definitions? -How can spatial relationships, including shape and dimension, be used to represent real life scenarios? KNOWLEDGE AND SKILLS *Review algebra skills from previous course 1.1- Identify, sketch and name points, lines, planes, segments, and rays 1.2- Use length and midpoint of segments. Construct midpoints and congruent segments 1.3- Develop and apply the formula for midpoint. Use Distance Formula and Pythagorean Theorem to find the distance between two points. 1.4- Apply formulas for perimeter, area, and circumference. 1.5- Name and classify angles. Measure and construct angles and angle bisectors Apply formulas for perimeter, area, and circumference. 1.6- Identify adjacent, vertical, complementary, and supplementary angles. Find measures of pairs of angles STAGE TWO PERFORMANCE TASKS 1.2- Use a compass to construct congruent segments. Paper folding to construct a segment bisector 1.5 –Students learn how to use a protractor to measure angles. Construct congruent angles and construct angle bisectors using a compass 1.3- Students use both Distance Formula and Pythagorean Theorem to find the distance between two points to show either one will yield the same result. OTHER EVIDENCE : Algebra Review quiz, Quiz 1.1-1.4, Ch. 1 Test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points Algebra Review and Quiz 1.1-1.5 -Review factoring quadratics, one and two- step equations, rules of exponents, multiplying binomials and monomials -Remind students to read correct side on protractor/ Be careful when placing protractor on vertex of angle -When using distance formula, remember to take square root at the end of problem. -For Pythagorean theorem, count spaces, not lines, when finding leg lengths 1.3 8 Unit Name: Reasoning and Proofs Time Frame: 9 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:Students will use logical thinking to determine the truth value of a statement and verify geometric and algebraic theorems and properties. UNIT RESOURCES:Textbook, Calculator Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Study Island: http://www.studyisland.com/ -Truth Value practice: http://www.regentsprep.org/regents/math/geometry/GP1/PracAnd.htm STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Congruence G-CO Prove geometric theorems G.CO.9. Prove theorems about lines and angles. CCSS: Mathematics, CCSS: HS: Geometry, Expressing Geometric Properties with Equations G-GPE Use coordinates to prove simple geometric theorems algebraically. G.GPE.4.Use coordinates to prove simple geometric theorems algebraically. CCSS: Mathematics, CCSS: HS: Algebra, Reasoning with Equations and Inequalities A-REI Understand solving equations as a process of reasoning and explain the reasoning. A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted a t the previous step, starting from the assumption that the original equation has a solution. Construct a viab le argument to justify a solution method. ENDURING UNDERSTANDINGS - Inductive reasoning can be used to discover patterns and properties of geometric figures. -Deductive reasoning can be used to verify or refute geometric conjectures. ESSENTIAL QUESTIONS -How can I use inductive and deductive reasoning to think logically? -How can geometric properties be used to prove relationships? -Is visualization alone a sufficient tool to form an accurate conclusion. 9 KNOWLEDGE AND SKILLS 2.1 Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contrapositive and biconditional of a conditional statement. 2.2 Use inductive reasoning to identify patterns and make conjectures. Find counterexamples to disprove conjectures. 2.3 Identify postulates using diagrams. Sketch and interpret diagrams 2.4 Review properties of equality and use them to write algebraic proofs. Identify properties of equality and congruence. 2.5 Write basic two-column proofs (This includes algebraic proofs and fill in the blank proofs.) 2.6 Use common segments theorem and vertical angles theorems in fill-in proofs. (Do not write flowchart or paragraph proofs). STAGE TWO PERFORMANCE TASKS 2.1 –Draw Venn Diagrams based on conditional statements 2.2- Solve Logic puzzles 2.5-Introduction to proof as giving directions-this develops understanding of necessity of detailed thinking 2.6- Cooperative learning project-Students receive a proof that has been cut up- they must reconstruct it with proper order. OTHER EVIDENCE : Quiz on 2.1-2.4, Ch. 2 Test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 2.1 -Supplement with PARCC pattern problems 2.1 -Be sure students understand the difference between conditional and biconditional -When writing a proof, some students may incorrectly assume things from the figure. If students make this mistake. -Supplement proof problems with fill-in worksheet 2.5-2.6 10 Unit Name: Parallel and Perpendicular Lines Time Frame: 8-9 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:Students will gain a deeper understanding of angles and parallel lines through construction and proof. UNIT RESOURCES:Textbook, Calculator, Straightedge, Protractor, Compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Construction tutorials: http://www.mathsisfun.com/geometry/constructions.html -Study Island: http://www.studyisland.com/ STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Congruence G-CO Make Geometric Constructions G.CO.12. Make formal geometric constructions with a variety of tools and methods (compass and straight edge, string, reflective devices, paper folding, dynamic geometric software, etc.) CCSS: Mathematics, CCSS: HS: Geometry, Expressing Geometric Properties with Equations G-GPE Use coordinates to prove simple geometric theorems algebraically G-GPE.7. Use coordinates to compute perimeters of polygons and areas for triangles and rectangles, e.g. u sing the distance formula. CCSS: Mathematics, CCSS: HS: Geometry, Congruence G-CO Prove geometric theorems G.CO.9. Prove theorems about lines and angles. CCSS: Mathematics, CCSS: HS: Geometry, Expressing Geometric Properties with Equations G-GPE Use coordinates to prove simple geometric theorems algebraically G-GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric p roblems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a g iven point). 11 ENDURING UNDERSTANDINGS -Parallel and perpendicular lines have characteristics that make them special. -Geometric relationships provide a mean to make sense of a variety of phenomena. ESSENTIAL QUESTIONS -How do I prove and use properties of parallel lines? -How can we prove two lines are parallel using a transversal? -What is the relationship between slope and lines? KNOWLEDGE AND SKILLS 3.1- Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal. 3.2-Prove and use theorems about the angles formed by parallel lines and a transversal. 3.3-Use the angles formed by a transversal to prove two lines are parallel. 3.4-Prove and apply theorems about perpendicular lines. 3.5- Find the slope of a line. Use slopes identify parallel and perpendicular lines. Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding. STAGE TWO PERFORMANCE TASKS 3.1- Algebra connection using systems of equations 3.2- Have students sketch and label two parallel lines cut by a transversal. Use a protractor to measure the angles and use the sketch to explain the relationship among all the angles. 3.3- Construct parallel lines 3.4- Construct the perpendicular bisector of a segment OTHER EVIDENCE : Quiz on 3.1-3.4, Ch. 3 Test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 3.3 -Remind students that they should not assume that lines in the diagram are parallel only by appearance. They need to justify each answer with a postulate or theorem learned in this lesson. -Review equations for vertical and horizontal lines 3.5 12 Unit Name: Transformations Time Frame: 11 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:In this chapter, we will investigate and use transformations, specifically translations, rotations, and reflections. UNIT RESOURCES:Textbook, Calculator, Straightedge, protractor, compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Construction tutorials: http://www.mathsisfun.com/geometry/constructions.html -Study Island: http://www.studyisland.com/ STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Congruence G-CO Understand congruence in terms of rigid motions G.CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions CCSS: Mathematics, CCSS: HS: Geometry, Similarity, Right Triangles, & Trigonometry . G-SRT Understand similarity in terms of similarity transformations G-SRT.1. Verify experimentally the properties of dilations: G-SRT.1a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. G-SRT1b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide i f they are similar;explain using similarity transformations the meaning 13 CCSS: Mathematics, CCSS: HS: Geometry, Modeling with Geometry G-MG Apply geometric concepts in modeling situations G-MG.1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tre e trunk or a human torso as a cylinder). G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy constraints or minimize cost; working with typographic grid systems based on ratios). ENDURING UNDERSTANDINGS -Translations, rotations, and reflections are all rigid motions. -Dilations are nonrigid motions ESSENTIAL QUESTIONS -How can you translate, rotate, and reflect a figure in the coordinate plane? -What does it mean to dilate a figure? KNOWLEDGE AND SKILLS 4.1- perform translations. 4.2- perform reflections. 4.3- perform rotations. 4.4- describe congruence transformations. 4.5- identify and perform dilations. 4.6-perform and describe similarity transformations. PERFORMANCE TASKS 4.6 Use dynamic geometry software to create a triangle, then rotate, reflect and translate it. Take measurements of angles and side lengths before and after to show rigid motion is achieved. OTHER EVIDENCE : 4.1-4.3 quiz, 4.4-4.6 quiz, Ch. 4 test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 12.1-12.3 - Have students construct a graphic organizer for all of the different types of transformations. They can use this organizer with their homework and as a study guide for the test. 14 Unit Name: Congruent Triangles Time Frame: 8-9 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:Students will explore all types of triangles and their properties. They will prove shapes congruent using triangle congruence theorems. UNIT RESOURCES:Textbook, Calculator, Straightedge, Protractor Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Construction tutorials: http://www.mathsisfun.com/geometry/constructions.html -Study Island: http://www.studyisland.com/ -Triangle Congruence Practice Proofs: http://www.regentsprep.org/regents/math/geometry/GP4/PracCongTri.htm STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Congruence G-CO Understand congruence in terms of rigid motions G.CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G-CO Prove geometric theorems G.CO.10. Prove theorems about triangles. CCSS: Mathematics, CCSS: HS: Geometry, Similarity, Right Triangles, & Trigonometry G-SRT Prove theorems involving similarity G-SRT.5. Use triangle congruence and similarity criteria to solve problems and to prove relationships in ge ometric figures. 15 ENDURING UNDERSTANDINGS -Congruent figures have special characteristics that can help us solve problems. -Triangles have limitations that give them special properties. ESSENTIAL QUESTIONS -Why is it necessary to prove two shapes are congruent? -What are the minimal conditions needed to prove two triangles are congruent? -When can a triangle exist? KNOWLEDGE AND SKILLS 5.1- Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths. Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior of triangles. 5.2- Use properties of congruent triangles. Prove triangles congruent by using the definition of congruence. 5.3- Apply SAS to prove triangles congruent. 5.4- Prove theorems about isosceles and equilateral triangles. Apply properties of isosceles and equilateral triangles. 5.5- Prove triangles congruent by using SSS. 5.6- Prove triangles congruent by ASA and AAS. 5.7- To use congruent triangles to solve problems. 5.8- TO place figures in the coordinate plane. To write coordinate proofs. STAGE TWO PERFORMANCE TASKS 5.1- Proving the triangle sum theorem activity 5.3- Optional activity to explore SSS and SAS 5.6- Construction activity to construct congruent triangles by using ASA OTHER EVIDENCE : Quiz 5.1-5.3, Quiz 5.4-4.8, Ch. 8 Test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 5.4-5.6 -Supplement with fill-in proof worksheets to prove two triangles congruent (using AAS, ASA, SSS, SAS, and HL) -Many students make the mistake of not paying attention to order. Be sure they know the difference between ASA and AAS. The order of the angles and sides in the triangles matter. -Use a graphic organizer to outline all 5 triangle congruence theorems. This helps the students remember which is which. 16 Unit Name: Relationships within Triangles Time Frame: 8-9 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:Students will study all types of segments and points of concurrency in triangles. They will also use inequalities in one and two triangles and Pythagorean inequalities to make valid conclusions about side and angle measures in triangles. UNIT RESOURCES:Textbook, Calculator, Straightedge, Protractor, Compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Construction tutorials: http://www.mathsisfun.com/geometry/constructions.html -Study Island: http://www.studyisland.com/ STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Congruence G-CO Prove geometric theorems G-CO.9. Prove theorems about lines and angles. G-CO.10. Prove theorems about triangles. G-CO Make geometric constructions G-CO.12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). CCSS: Mathematics, CCSS: HS: Geometry, Similarity, Right Triangles, & Trigonometry G-SRT Define trigonometric ratios and solve problems involving right triangles G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied probl ems. ENDURING UNDERSTANDINGS -Triangles have limitations that give them special properties. 17 ESSENTIAL QUESTIONS - How can I use properties and theorems about triangles to find side lengths and angles? -When can a triangle exist? KNOWLEDGE AND SKILLS 6.1- Prove and apply theorems about perpendicular bisectors and angle bisectors. 6.2- To find the circumcenter and incenter of a triangle 6.3- Apply properties of medians and altitudes of a triangle. 6.4- Prove and use properties of triangle midsegments. 6.5-Apply inequalities in one triangle. 6.6-Apply inequalities in two triangles. STAGE TWO PERFORMANCE TASKS 6.2- Paper folding activity to find circumcenter and incenter. After finding incenter, use a compass to construct inscribed circle (You could use Geometer’s Sketchpad to do this instead, if resources available). 6.3- Use straightedge to construct centroid of a triangle, Paper folding to construct orthocenter. 6.4- Construct midsegment, using a straightedge. Students then prove midsegment theorem by measuring with a ruler and protractor. OTHER EVIDENCE : Quiz 6.1-6.3, Quiz 6.4-6.6, Ch. 6 TEST STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 6.1-6.4 -Use graphic organizer to outline all types of segments and points of concurrency to prevent students from mixing up theorems and vocabulary 18 Unit Name: Quadrilaterals and Other Polygons Time Frame: 9-10 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:Parallelograms and other quadrilaterals have special properties that can be used to solve problems on and off the coordinate plane. In this unit, students will classify specific types of polygons and quadrilaterals, and use their classification to solve problems. UNIT RESOURCES:Textbook, Calculator, Straightedge, Protractor, Compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Construction tutorials: http://www.mathsisfun.com/geometry/constructions.html -Study Island: http://www.studyisland.com/ STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Congruence G-CO Prove geometric theorems G.CO.11. Prove theorems about parallelograms. CCSS: Mathematics, CCSS: HS: Geometry, Expressing Geometric Properties with Equations G-GPE Use coordinates to prove simple geometric theorems algebraically G-GPE.4. Use coordinates to prove simple geometric theorems algebraically. CCSS: Mathematics, CCSS: HS: Geometry, Modeling with Geometry G-MG Apply geometric concepts in modeling situations G-MG.1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tre e trunk or a human torso as a cylinder). G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy constraints or minimize cost; working with typographic grid systems based on ratios). ENDURING UNDERSTANDINGS - Parallel lines in quadrilaterals lend a plethora of information about the properties of the quadrilateral. -Interior angles of all convex polygon polygons have a universal formula and the exterior angles are a constant. -Using coordinate geometry and the properties of diagonals of parallelograms lets you identify what any given coordinates represent. 19 -The similarities in quadrilaterals are essential for problem solving and the differences allow for identification for more specific analysis. ESSENTIAL QUESTIONS -What represents the best solution when tasks must be completed along the edges of a connected graph? -What are the relationships between the interior and exterior angles of a polygon? -What are the similarities and differences in diagonals of the various parallelograms? KNOWLEDGE AND SKILLS 7.1- Classify polygons based on their sides and angles. Find and use the measures of interior and exterior angles of polygons. 7.2- Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems. 7.3- Prove that a given quadrilateral is a parallelogram. 7.4- Prove and apply properties of rectangles, rhombuses, and squares. Use properties of rectangles, rhombuses, and squares to solve problems. 7.5- Use properties of kites and trapezoids to solve problems. STAGE TWO PERFORMANCE TASKS 7.1- Use geometer’s sketchpad or have students construct and complete table (without the sums and number of triangles filled in) to develop the formula for the polygon angle sum theorem. 7.2-Parallelogram activity: Students measure sides and angles of various parallelograms to discover relationships between opposite and consecutive angles, opposite sides, and diagonals. 7.3- Students complete fill-in proofs for proving a quadrilateral to be a parallelogram 7.4- Have students develop flow chart OR Venn diagram of quadrilaterals as a guide. OTHER EVIDENCE : Quiz on 7.1-7.3, (optional quiz on properties of special quadrilaterals 7.4-7.5), Ch. 7 test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 7.2-7.3 -Develop some kind of graphic organizer to outline all properties of parallelograms and use as a guide 7.4-7.5 -Be sure to use graphic organizers/charts so students can remember properties of different quadrilaterals. Oftentimes students mix up some of the properties of different quadrilaterals in this chapter because there is so much to remember. -SAT practice is a good way for students to see how questions from this Chapter would show up on the SAT. After test 20 Unit Name: Similarity Time Frame: 9 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:We use the definition of dilation to create similar figures. Also, we can prove how two figures a re similar and use properties of similar figures to solve problems. UNIT RESOURCES:Textbook, Calculator, Straightedge, Protractor, Compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Study Island: http://www.studyisland.com/ STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Similarity, Right Triangles, & Trigonometry . G-SRT Understand similarity in terms of similarity transformations G-SRT.1. Verify experimentally the properties of dilations: G-SRT.1a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. G-SRT1b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide i f they are similar;explain using similarity transformations the meaning of similarity for triangles as the equ ality of all pairs of angles and the proportionality of all pairs of sides. G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for similarity of trian gles. G-SRT Prove theorems involving similarity G-SRT.4. Prove theorems about triangles using similarity transformations. G-SRT.5. Use triangle congruence and similarity criteria to solve problems and to prove relationships in ge ometric figures. CCSS: Mathematics, CCSS: HS: Geometry, Modeling with Geometry G-MG Apply geometric concepts in modeling situations G-MG.1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tre e trunk or a human torso as a cylinder). G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy constraints or minimize cost; working with typographic grid systems based on ratios). 21 ENDURING UNDERSTANDINGS - Similar figures have properties that can help us solve problems. -When we graph figures and transform them, different algorithms require different manipulations to the pre-image ’s coordinates -Different polygons have properties that are exclusive to their own category. ESSENTIAL QUESTIONS -What makes similar figures special? -How can we use similarity to solve problems in real life? KNOWLEDGE AND SKILLS 8.1- To use similarity statements. Find corresponding lengths, perimeter and area in similar polygons. 8.2-Prove certain triangles are similar by using AA. Use triangle similarity to solve problems. 8.3 Prove certain triangles are similar by using SSS and SAS. Use triangle similarity to solve problems. 8.4- Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems. STAGE TWO PERFORMANCE TASKS 8.3- Test prep problems as exit questions 8.5- develop perimeter and area relationships for similar figures. Shadow project: Find unknown heights by measuring shadows of unknown object, using yard stick (Optional) Maps activity: Print out various maps (make sure they have a scale) and have students find actual distances using scale and proportions. OTHER EVIDENCE : Quiz on 8.1-8.3, Ch. 8 test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 8.2 - Read the “teacher to teacher” letter. Students need to be careful on letter order when writing similarity statements 22 Unit Name: Right Triangles and Trigonometry Time Frame: 8-9 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:Special properties of right triangles allow us to indirectly measure angles and lengths. In this c hapter, we will solve right triangles using a combination of trigonometry and Pythagorean Theorem and solve wor d problems involving right triangles. UNIT RESOURCES:Textbook, Calculator, Straightedge, Protractor, Compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Construction tutorials: http://www.mathsisfun.com/geometry/constructions.html -Study Island: http://www.studyisland.com/ STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Similarity, Right Triangles, & Trigonometry G-SRT Prove theorems involving similarity G-SRT.4. Prove theorems about triangles using similarity transformations. G-SRT Define trigonometric ratios and solve problems involving right triangles G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the trian gle, leading to definitions of trigonometric ratios for acute angles. G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles. G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problem s. CCSS: Mathematics, CCSS: HS: Geometry, Modeling with Geometry G-MG Apply geometric concepts in modeling situations G-MG.1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tre e trunk or a human torso as a cylinder). G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy constraints or minimize cost; working with typographic grid systems based on ratios). 23 ENDURING UNDERSTANDINGS -The concepts learned in this unit are used often in everyday life (e.g. building houses/sheds/rec areas and calculat ing square footage of a house) and regularly applied in fields such as surveying, architecture and physics. -Right triangle trigonometry allows for indirect measurement of triangles with less given and variable information than previous geometric studies. ESSENTIAL QUESTIONS -Why have societies developed techniques to measure indirectly? -How do you define and apply the sine, cosine, and tangent ratios to right triangles and to real life problems with ri ght triangles? KNOWLEDGE AND SKILLS 9.1- Use the Pythagorean Theorem and its converse. 9.2- To find side lengths in special right triangles. 9.3- Use geometric mean to find segment lengths in right triangles. Apply similarity relationships in right triangles to solve problems. 9.4- Use the tangent ratio to solve real-life problems. 9.5- Find the sine and cosine of an acute angle. Use trigonometric ratios to find side lengths in right triangles and to solve real-world problems. 9.6- Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems. STAGE TWO PERFORMANCE TASKS 9.5- In pairs, give students coordinates of a right triangle. They need to graph, and solve right triangle for all angles and sides. 9.4-9.6- Think-pair-share with word problems. Students need to draw picture for problem, label it, and solve for indicated measure. 9.4-9.6- FlagpoleProject: Students go outside in cooperative groups and use the clinometer and walking stick to find the height of various objects OTHER EVIDENCE : Quiz on 9.1-9.3, Quiz 9.4-9.6, Ch. 9 Test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 9.4-9.6 - Supplement word problems with additional worksheets (Kuta software) Flagpole project -Make sure students remember to factor in their height when calculating the height of the flag pole. It makes it easier to all measure their heights in classroom before going outside. 24 Unit Name: Circles Time Frame: 11 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:In this chapter, we will investigate and use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles. UNIT RESOURCES:Textbook, Calculator, Straightedge, protractor, compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Construction tutorials: http://www.mathsisfun.com/geometry/constructions.html -Study Island: http://www.studyisland.com/ STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Circles G-C Understand and apply theorems about circles G-C.1. Prove that all circles are similar. G-C.2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationshi p between central, inscribed and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G-C.3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a q uadrilateral inscribed in a circle. G-C.4. (+) Construct a tangent line from a point outside a given circle to the circle. G-C Find arc lengths and areas of sectors of circles G-C.5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to th e radius, and define the radian measure of the angle as the constant of proportionality; derive the formula f or the area of a sector. CCSS: Mathematics, CCSS: HS: Geometry, Expressing Geometric Properties with Equations G-GPE Translate between the geometric description and the equation for a conic section G-GPE.1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; comple te the square to find the center and radius of a circle given by an equation. G-GPE Use coordinates to prove simple geometric theorems algebraically 25 G-GPE.4. Use coordinates to prove simple geometric theorems algebraically. CCSS: Mathematics, CCSS: HS: Geometry, Modeling with Geometry G-MG Apply geometric concepts in modeling situations G-MG.1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tre e trunk or a human torso as a cylinder). ENDURING UNDERSTANDINGS -Angles with their vertex at the center of the circle are equal to the intercepted minor arc; all other angles can also be described as having a mathematical relationship to the minor arc. -The standard form equation of a circle allows you to easily graph the circle on the coordinate plane because you k now the center and the radius. -Many real world applications use the circumference of a circle on a two dimensional plane. ESSENTIAL QUESTIONS -How are angles and arcs in a circle related? -What information can you extract from the algebraic standard equation of a circle? -How do areas of sectors and lengths of arcs relate to real world Geometry? KNOWLEDGE AND SKILLS 10.1- lines and segments that intersect circles. 10.2- finding arc measures. 10.3- using chords. 10.4- inscribed angle relationships in circles. 10.5- angle relationships in circles. 10.6- segment relationships in circles. 10.7- circles in the coordinate plane. PERFORMANCE TASKS 10.1- Make a circle out of construction paper and label all types of segments and lines to outline vocabulary. 10.7- Construct circles on graph paper, using a straightedge and compass, from equation of a circle. OTHER EVIDENCE : 10.1-10.3 quiz, 10.4-10.7 quiz, Ch. 10 test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 10.2-10.5 - Have students construct a graphic organizer for all of the different types of angles with circles. This chapter has a lot of slightly different pictures, and it is easy for students to mix up angle types. They can use this organizer with their homework and as a study guide for the test. 26 Unit Name: Extending Perimeter, Circumference, and Area Time Frame:10-11 days Author: Egg Harbor Township High School Math Department UNIT Subject:Geometry Country: USA Course/Grade: College Prep State/Group: NJ School: Egg Harbor Township High School UNIT SUMMARY:In this chapter, students will find the area and perimeter of two-dimensional figures on and off the coordinate plane. We will explore how surface area and volume of three dimensional figures are rela ted and find the surface area and volume of various 3-D figures. UNIT RESOURCES:Textbook, Calculator, Straightedge, Protractor, Compass Internet Resource Links: -On-line textbook -Geometer’s Sketchpad -Study Island: http://www.studyisland.com/ -Composite Figures Extra Problems: http://www.glencoe.com/sites/washington/support_student/additional_lessons/Course_1/519_523_WA_SE_Gr6_ AdlLsn_Onln.pdf STAGE ONE GOALS AND STANDARDS CCSS: Mathematics, CCSS: HS: Geometry, Geometric Measurement & Dimension G-GMD Explain volume formulas and use them to solve problems G-GMD.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volu me of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. G-GMD.3. Use volume formulas for cylinders, pyramids, cones and spheres to solve problems. G-GMD Visualize the relation between two-dimensional and three-dimensional objects G-GMD.4. Identify cross-sectional shapes of slices of three-dimensional objects, and identify three-dimensi onal objects generated by rotations of two-dimensional objects. CCSS: Mathematics, CCSS: HS: Geometry, Modeling with Geometry G-MG Apply geometric concepts in modeling situations G-MG.1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tre e trunk or a human torso as a cylinder). G-MG.2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per squa re mile, BTUs per cubic foot). 27 G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy constraints or minimize cost; working with typographic grid systems based on ratios). CCSS: Mathematics, CCSS: HS: Geometry, Expressing Geometric Properties with Equations G-GPE Use coordinates to prove simple geometric theorems algebraically G-GPE.4. Use coordinates to prove simple geometric theorems algebraically. CCSS: Mathematics, CCSS: HS: Geometry, Modeling with Geometry ENDURING UNDERSTANDINGS -Area and perimeter/circumference are used in a variety of real-world applications. -Before finding area of a figure, one must be sure of the exact type of figure, so as to find the area correctly. ESSENTIAL QUESTIONS -How can I find area and perimeter or circumference of a figure? -How can I use area and perimeter/circumference in real-world problems? KNOWLEDGE AND SKILLS 11.1- Use formula for circumference. Use arc lengths to find measures. 11.2- Use formula for area of a circle, population density. To find areas of sectors. 11.3- To find areas of rhombuses and kites. To find areas of regular polygons. 11.4- Classify three dimensional figures according to their properties. Use nets and cross sections to analyze them. Draw representations of three dimensional figures. 11.5- Learn and apply the formula for the volume of prisms and cylinders. 11.6- Learn and apply the formula for the volume of pyramids. 11.7- Learn and apply the formula for volume and surface area for cones. 11.8- Learn and apply the formula for volume and surface area for spheres. STAGE TWO PERFORMANCE TASKS 11.3- Students discover area formulas by using construction paper, scissors, and two-dimensional shapes 11.1- Students develop the value of 𝜋 11.4- Students will create nets of 3-dimensional objects/Use manipulativesof 3-D figures with removable nets OTHER EVIDENCE :Quiz on 11.1-11.3, Quiz on 11.4-11.8, Ch. 11 Test STAGE THREE LEARNING PLAN Sections Common Errors/ Key points 28 11.5-11.8 11.511.8 -Supplement with composite figures/real world application WS. - Extra figures can be found on website link above under resources. - Have students make a formula sheet that they can use on the test ***The order of these chapters is subject to change. EHT Special Education Interventions ABA strategies and Interventions for both behavior and Instruction (for autistic programs only) Picture Exchange Communication System (for non-verbal students) Ipad with Proloquo2Go (for non-verbal students) Go Talk device (for non-verbal students) Mike and Molly Program for language skills and reading (mostly for very low functioning students) Edmark Reading Program (mostly for very low functioning students) Reading Milestones (for deaf students) Menu Math (mostly for very low functioning students) Phonics First Wilson Reading (Miller and Alder only) Read 180 (High School only) Edmentum Math Labs (High School only) IXL Reading & Labs (High School only) Use of paraprofessionals and 1:1 nurses to assist students Weighted Vests (for calming agitated students) Specialized sensory equipment (for student who need sensory stimulation or students who have tactile or other sensory aversions) Learning Ally (audio version for textbooks and other published materials) – Also available for 504 students Think Through Math Apex Online Learning – Bridge students only Accommodations and Modifications Use of specialized equipment such as beeping balls, text to speech and speech to text software, special seats or desks Use of hands-on materials for problem solving Shopping trips on a regular basis with specific goals and objectives Cooking to teach math, measurement and functional reading and life skills Visual supports Extended time to complete tests and assignments Graphic Organizers Mnemonic tricks to improve memory Reducing work load Adjusting accountability for standards by focusing only on essential standards Practice materials unique to particular students in all subjects (ie workbooks for spelling at grades where it no longer is taught or for basic foundational math skills, telling time, etc.) Use of IPads or laptops for students with motor issues that make writing difficult Study guides Special paper for writing tasks Use of sand, sand paper and shaving cream for learning letters Individual behavior plans Use of special grips or other fine motor accommodation equipment Use agenda book for assignments Provide a posted daily schedule Provide breaks during the day Use of classroom behavior management system Use of rewards for students Use of “quiet room” for students struggling to maintain self-control Use of tangible rewards (certificates, small toys, etc. per behavior plan) Use prompts and model directions Use task analysis to break down activities and lessons into each individual step needed to complete the task Use concrete examples to teach concepts Have student repeat/rephrase written directions Provide multi-sensory, hands-on materials for instruction Break all instruction and verbal directions into small segments Focus on student’s goals and objectives from IEP instead of pacing guides Tests read to student Modify all fine motor tasks for example: (fat crayons, pencil grip, adaptive scissors) Functional or practical emphasis Differentiated Instruction Resources for Gifted & Struggling Students “Differentiating the Lesson” is located in Big Ideas on-line resources and is available for most sections. “Additional Topics” can be selected from Big Ideas on-line resources to find a wide variety of challenging problems for students. See Big Ideas MATH Pyramid of Tiered Interventions for additional resoruces. hmhco.com • 800.225.5425 Through print and digital resources, the Big Ideas Math program completely supports the 3-tier model. Using research-based instructional strategies, teachers can reach, challenge, and motivate students with relevant, high-quality instruction targeted to their individual needs. Tier 3: Customized Learning Intervention • Activities • Intensive Intervention Lessons Tier 2: Strategic Intervention • • • • • Lesson Tutorials Basic Skills Handbook Skills Review Handbook Differentiated Instruction Game Closet Tier 1: Daily Intervention • • • • Record and Practice Journal Fair Game Review Graphic Organizers Vocabulary Support Learn more at hmhco.com/bigideasmath BigIdeasMath HMHCo • • • • Mini Assessments Game Closet Lesson Tutorials On Your Own Distributed exclusively by Houghton Mifflin Harcourt BigIdeasLearning Big Ideas Math® and Big Ideas Learning® are registered trademarks of Larson Texts, Inc. Houghton Mifflin Harcourt™ is a trademark of Houghton Mifflin Harcourt. © Houghton Mifflin Harcourt. All rights reserved. Printed in the U.S.A. 02/15 MS132368 ELL Resources for Students within Big Ideas Math Program Big Ideas Math Student Editions are available online in Spanish Letters to Parents are available in the Resources by Chapter book to assist in guiding parents through each chapter and offer helpful suggestions they can use to demonstrate mathematical concepts for their child in daily activities. These letters are editable so teachers can customize them. Vocabulary Flash Cards Student Dynamic eBook Audio has the option to be read in English or Spanish Multi-Language Glossary for new Math vocabulary is available in 14 different languages. o Audio version is available in English or Spanish. Game Closet can be accessed in English or Spanish, while also allowing for all students to play and understand these educational games. ELL Notes included in Teacher Edition to help teachers overcome obstacles. Record & Practice Journal available in Spanish. Student Journal available in Spanish. Chapter Reviews available in English and Spanish. Mathematics ELL Resources TODOS: Mathematics for ALL – Excellence and Equity in Mathematics o http://www.todos-math.org/ o TODOS: Mathematics for ALL is an international professional organization that advocates for equity and excellence in mathematics education for ALL students - in particular, Latina/o students. As articulated in the mission and goals, TODOS advances educators' knowledge, develops and supports education leaders, generates and disseminates knowledge, informs the public, influences educational policies, and informs families about education policies and learning strategies. All of these goals ultimately result in providing access to high quality and rigorous mathematics for ALL students. FABRIC – A Learning Paradigm for ELLs (NJDOE resource) o http://www.state.nj.us/education/bilingual/pd/fabric/ o NJDOE ELL Resource: This paradigm allows teachers and administrators to provide diverse groups of ELLs with access to classroom content while they acclimate to an English learning environment. The six learning threads of the FABRIC paradigm provide a structure that teachers can use to address the needs of ELLs. Each section contains research-based recommendations, a classroom example, and application questions. FABRIC can be utilized during sheltered instruction training, professional learning community meetings, pre-service teacher education, etc. 4) 4GUQWTEG)WKFG (KIWTG/%#0&1&GUETKRVQTUHQTVJG.GXGNUQH'PINKUJ.CPIWCIG2TQſEKGPE[2TG- t Locate, select, order information from oral descriptions t Follow multi-step oral directions t Categorize or sequence oral information using pictures, objects t Compare/contrast functions, relationships from oral information t Analyze and apply oral information t Identify cause and effect from oral discourse t Draw conclusions from oral information t Construct models based on oral discourse t Make connections from oral discourse 52'#-+0) t Name objects, people, pictures t Answer WH- (who, what, when, where, which) questions t Ask WH- questions t Describe pictures, events, objects, people t Restate facts t Formulate hypotheses, make predictions t Describe processes, procedures t Retell stories or events t Discuss stories, issues, concepts t Give speeches, oral reports t Offer creative solutions to issues, problems t Engage in debates t Explain phenomena, give examples and justify responses t Express and defend points of view t Match icons and symbols to words, phrases or environmental print t Identify concepts about print and text features t Locate and classify information t Identify facts and explicit messages t Select language patterns associated with facts t Sequence pictures, events, processes t Identify main ideas t Use context clues to determine meaning of words t Interpret information or data t Find details that support main ideas t Identify word families, figures of speech t Conduct research to glean information from multiple sources t Draw conclusions from explicit and implicit text t Label objects, pictures, diagrams t Draw in response to a prompt t Produce icons, symbols, words, phrases to convey messages t Make lists t Produce drawings, phrases, short sentences, notes t Give information requested from oral or written directions t Produce bare-bones expository or narrative texts t Compare/contrast information t Describe events, people, processes, procedures t Summarize information from graphics or notes t Edit and revise writing t Create original ideas or detailed responses t Apply information to new contexts t React to multiple genres and discourses t Author multiple forms/ genres of writing .+56'0+0) .GXGN $TKFIKPI 94+6+0) .GXGN 'PVGTKPI .GXGN Beginning t Point to stated pictures, words, phrases t Follow one-step oral directions t Match oral statements to objects, figures or illustrations t Sort pictures, objects according to oral instructions t Follow two-step oral directions t Match information from oral descriptions to objects, illustrations .GXGN &GXGNQRKPI .GXGN4GCEJKPI .GXGN 'ZRCPFKPI 4'#&+0) For the given level of English language proficiency, with support, English language learners can: 9DULDELOLW\RIVWXGHQWV¶FRJQLWLYHGHYHORSPHQWGXHWRDJHJUDGHOHYHOVSDQVWKHLUGLYHUVLW\RIHGXFDWLRQDOH[SHULHQFHVDQGGLDJQRVHGOHDUQLQJGLVDELOLWLHVLIDSSOLFDEOHDUHWREH considered in using this information. (KIWTG0&GUETKREKÎPFGNCU*CDKNKFCFGUGPNQU0KXGNGUFGN.GPIWCLG#ECFÃOKEQFGN+PINÃU2TG- .''4 '5%4+$+4 0KXGN 'PVTCPFQ 0KXGN 'ORG\CPFQ 0KXGN &GUCTTQNNCPFQ 0KXGN 'ZVGPFKGPFQ 0KXGN %QPGEVCPFQ t Señalar dibujos, palabras o frases indicados t Seguir instrucciones orales de un paso t Emparejar declaraciones orales con objetos, figuras o ilustraciones t Clasificar dibujos u objetos siguiendo las instrucciones verbales t Seguir instrucciones verbales de dos pasos t Emparejar declaraciones verbales con objetos, figuras o ilustraciones t Localizar, seleccionar y ordenar información que proviene de descripciones orales t Seguir instrucciones verbales de paso múltiples t Clasificar o secuenciar información oral usando dibujos u objetos t Comparar y contrastar funciones y relaciones de acuerdo a información oral t Analizar y aplicar información oral t Identificar causa y efecto en discurso oral t Sacar una conclusión de información oral t Construir modelos basados en discurso oral t Hacer conexiones en información oral t Nombrar objetos, personas y dibujos t Contestar preguntas (quién, qué, cuándo, dónde, cuál) t Preguntar t Describir dibujos, eventos, objetos y personas t Reformular y decir hechos t Formular hipótesis y hacer predicciones t Describir procesos t Recontar cuentos o eventos t Discutir cuentos, cuestiones, y conceptos t Hacer presentaciones orales t Ofrecer soluciones creativas a cuestiones o problemas t Participar en debates t Explicar fenómenos, dar ejemplos y justificar respuestas t Expresar y defender puntos de vista t Emparejar símbolos y dibujos con palabras, frases o letras en la escritura en el medioambiente t Identificar conceptos de la organización de letras y elementos de textos t Localizar y clasificar información t Identificar hechos y mensajes directos t Seleccionar patrones de lenguaje asociados con hechos t Secuenciar dibujos, eventos y procesos t Identificar ideas principales t Usar pistas del contexto para determinar el significado de palabras t Interpretar información o datos t Encontrar detalles que apoyan las ideas principales t Identificar figuras retóricas y relaciones entre palabras t Realizar investigaciones para reunir información de fuentes múltiples t Sacar una conclusión de texto explícito e implícito t Etiquetar objetos, dibujos, diagramas t Dibujar respuestas a instrucciones t Producir íconos, símbolos, palabras y frases para comunicar un mensaje t Hacer listas t Producir dibujos, frases, oraciones cortas y apuntes t Dar información pedida por instrucciones orales o escritas t Producir textos básicos de estilo narrativo o informativo t Comparar y contrastar información t Describir eventos, personas, procesos t Resumir información de representaciones gráficas o apuntes t Corregir y revisar escritura t Crear ideas originales o respuestas detalladas t Aplicar información a contextos nuevos t Reaccionar a múltiples géneros y discursos t Redactar varias formas/géneros de composiciones 0KXGN#NECP\CPFQ *#$.#4 '5%7%*#4 En cada nivel de capacidad en el lenguaje inglés, con apoyo, un estudiante de inglés puede hacer lo siguiente: Translated by (Traducido por) Elizabeth J. Hartung, Monona Grove, WI; revised by (revisado por) Andrea Cammilleri, Mariana Castro and Stephanie Herrera, WIDA, Wisconsin Center for Education Research 4) (OGHVDUUROORFRJQRVFLWLYRGHORVHVWXGLDQWHVSXHGHYDULDUVHJ~QHGDGJUDGRGLYHUVLGDGGHODVH[SHULHQFLDVHGXFDFLRQDOHV\GLVFDSDFLGDGHVGHDSUHQGL]DMHVLH[LVWHQ Esto se debe considerar al usar ésta información. 4GUQWTEG)WKFG
