Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 1 Unit of Study: Basics of Geometry Pacing-Teaching: 6 lessons – approximately 12 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. How can you visualize geometric concepts? 2. How can you measure and construct a line segment? 3. How can you find the midpoint and length of a line segment in a coordinate plane? 4. How can you measure and classify an angle? 5. How can you describe angle pair relationships and use these descriptions to find angle measures? CCSS Math Standards G.CO.A.1, G.CO.D.12, G.GPE.B.7, G.MG.A.1 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Concepts (Need to Know) Skills Name points, lines, planes, segments, and rays Find segment lengths using the Ruler Postulate, the Segment Addition Postulate, midpoints, segment bisectors, and the Distance Formula Classify polygons and angles Find perimeters and areas of polygons in the coordinate plane Construct congruent segments and angles, and bisect segments and angles *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create Blooms Level *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 1, Quiz #1 Unit 1, Quiz #2 Unit 1, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 1 Unit of Study: Reasoning and Proof Pacing-Teaching: 6 lessons – approximately 12 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. When is a conditional statement true or false? 2. How can you use reasoning to solve problems? 3. In a diagram, what can be assumed and what needs to be labeled? 4. How can algebraic properties help you solve an equation? 5. How can you prove a mathematical statement? 6. How can you use a flowchart to prove a mathematical statement? CCSS Math Standards G.CO.C.9, G.CO.C.10, G.CO.C.11, G.SRT.B.4 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Concepts (Need to Know) Skills Write conditional and biconditional statements Use inductive and deductive reasoning Use properties of equality to justify the steps in solving equations and to find segment lengths and angle measures Write two-column proofs, flowchart proofs, and paragraph proofs *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create Blooms Level *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 2, Quiz #1 Unit 2, Quiz #2 Unit 2, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 1 Unit of Study: Parallel and Perpendicular Lines Pacing-Teaching: 5 lessons – approximately 12 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. What does it mean when two lines are parallel, intersecting, coincident, or skew? 2. When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? 3. For which of the theorems involving parallel lines and transversals is the converse true? 4. What conjectures can you make about perpendicular lines? 5. How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point? CCSS Math Standards G.CO.A.1, G.CO.C.9, G.CO.D.12, G.GPE.B.5, G.GPE.B.6 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Concepts (Need to Know) Identify planes, pairs of angles formed by transversals, parallel lines, and perpendicular lines Use properties and theorems of parallel lines Prove theorems about parallel lines and about perpendicular lines Write equations of parallel lines and perpendicular lines Find the distance from a point to a line Skills Blooms Level *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 3, Quiz #1 Unit 3, Quiz #2 Unit 3, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 1 Unit of Study: Transformations Pacing-Teaching: 6 lessons, approximately 12 days of lessons Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. How can you translate a figure in a coordinate plane? 2. How can you reflect a figure in a coordinate plane? 3. How can you rotate a figure in a coordinate plane? 4. What conjectures can you make about a figure reflected in two lines? 5. What does it mean to dilate a figure? 6. When a figure is translated, reflected, rotated or dilated in the plane, is the image similar to the original figure? CCSS Math Standards G.CO.A.2, G.CO.A.3, G.CO.A.4, G.CO.A.5, G.CO.B.6, G.MG.A.3, G.SRT.A.1a, G.SRT.A.1b, G.SRT.A.2 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task Concepts (Need to Know) Skills Perform translations, reflections, rotations, dilations, and compositions of transformations Solve real-life problems involving transformations Identify lines of symmetry and rotational symmetry Describe and perform congruence transformations and similarity transformations *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create Blooms Level *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 4, Quiz #1 Unit 4, Quiz #2 Unit 4, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 1 Unit of Study: Congruent Triangles Pacing-Teaching: 8 lessons, approximately 15 teaching days Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. How are the angle measures of a triangle related? 2. Given two congruent triangles, how can you use rigid motions to map one triangle to the other triangle? 3. What can you conclude about two triangles when you know that two pairs of corresponding sides and the corresponding included angles are congruent? 4. What conjectures can you make about the side lengths and angle measures of an isosceles triangle? 5. What can you conclude about two triangles when you know the corresponding sides are congruent? 6. What information is sufficient to determine whether two triangles are congruent? 7. How can you use congruent triangles to make an indirect measurement? 8. How can you use a coordinate plane to write a proof? CCSS Math Standards G.CO.C.10, G.MG.A.1, G.CO.B.7, G.CO.B.8, G.CO.D.13, G.MG.A.3, G.SRT.B.5, G.GPE.B.4. Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Concepts (Need to Know) Skills Blooms Level Identify and use corresponding parts Use theorems about the angles of a triangle Use SAS, SSS, HL, ASA, and AAS to prove two triangles congruent Prove constructions Write coordinate proofs *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and 1to create. Assessments: Unit 5, Quiz #1 Unit 5, Quiz #2 Unit 5, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 1 Unit of Study: Relationships within Triangles Pacing-Teaching: 6 lessons, approximately 13 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. What conjectures can you make about a point on the perpendicular bisector of a segment and a point on the bisector of an angle? 2. What conjectures can you make about the perpendicular bisectors and the angle bisectors of a triangle? 3. What conjectures can you make about the medians and altitudes of a triangle? 4. How are midsegments of a triangle related to the sides of triangle? 5. How are the sides related to the angles of a triangle? How are any two sides of a triangle related to the third side? 6. If two sides of one triangle are congruent to two sides of another triangle, what can you say about the third sides of the triangles? CCSS Math Standards G.CO.C.9, G.MG.A.1, G.CO.D.12, G.C.A.3, G.MG.A.3, G.CO.C.10 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Concepts (Need to Know) Skills Blooms Level Understand and use angle bisectors and perpendicular bisectors to find measures Find and use the circumcenter, incenter, centroid, and orthocenter of a triangle Use the Triangle Midsegment Theorem and the Triangle Inequality Theorem Write indirect proofs *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 6, Quiz #1 Unit 6, Quiz #2 Unit 6, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 2 Unit of Study: Quadrilaterals and Other Polygons Pacing-Teaching: 5 lessons, approximately 12 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. What is the sum of the measures of the interior angles of a polygon? 2. What are the properties of parallelograms? 3. How can you prove that a quadrilateral is a parallelogram? 4. What are the properties of the diagonals of rectangles, rhombuses, and squares? 5. What are some properties of trapezoids and kites? CCSS Math Standards G.CO.C.11, G.SRT.B.5, G.MG.A.1, G.MG.A.3 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Concepts (Need to Know) Skills Find and use the interior and exterior angle measures of polygons Use properties of parallelograms and special parallelograms Prove that a quadrilateral is a parallelogram Identify and use properties of trapezoids and kites *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create Blooms Level *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 7, Quiz #1 Unit 7, Quiz #2 Unit 7, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 2 Unit of Study: Similarity Pacing-Teaching: 4 lessons, approximately 10 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. How are similar polygons related? 2. What can you conclude about two triangles when you know that two pairs of corresponding angles are congruent? 3. What are two ways to use corresponding sides of two triangles to determine that the triangles are similar? 4. What proportionality relationships exist in a triangle intersected by an angle bisector or by a line parallel to one of the sides? CCSS Math Standards G.SRT.A.2, G.MG.A.3, G.SRT.A.3, G.SRT.B.5, G.SRT.B.4, G.GPE.B.5, G.MG.A.1, G.GPE.B.6 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task Concepts (Need to Know) Skills Use the AA, SSS, and SAS similarity Theorems to prove triangles are similar Decide whether polygons are similar Use similarity criteria to solve problems about lengths, perimeters, and areas Prove the slope criteria using similar triangles Use the Triangle Proportionality Theorem and other proportionality theorems *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create Blooms Level *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 8, Quiz #1 Unit 8, Quiz #2 Unit 8, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 2 Unit of Study: Right Triangles and Trigonometry Pacing-Teaching: 7 lessons, approximately 15 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. How can you prove the Pythagorean Theorem? 2. What is the relationship among the side lengths of 45°-45°-90° triangles and 30°-60°90° triangles? 3. How are altitudes and geometric means of right triangles related? 4. How is a right triangle used to find the tangent of an acute angle? Is there a unique right triangle that must be used? 5. How is a right triangle used to find the sine and cosine of an acute angle? Is there a unique right triangle that must be used? 6. When you know the lengths of the sides of a right triangle, how can you find the measures of the two acute angles? 7. What are the Law of Sines and the Law of Cosines? CCSS Math Standards G.SRT.B.4, G.SRT.C.8, G.MG.A.1, G.SRT.B.5, G.SRT.C.6, G.SRT.C.7, G.MG.A.3, G.SRT.D.9, G.SRT.D.10, G.SRT.D.11 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task Concepts (Need to Know) Skills Blooms Level Use the Pythagorean Theorem and the Converse of the Pythagorean Theorem Use geometric means Find side lengths and solve real-life problems involving special right triangles Find the tangent, sine, and cosine ratios and use them to solve real-life problems Use the Law of Sines and Law of Cosines to solve triangles *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 9, Quiz #1 Unit 9, Quiz #2 Unit 9, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 2 Unit of Study: Circles Pacing-Teaching: 7 lessons, approximately 16 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. What are the definitions of the lines and segments that intersect a circle? 2. How are circular arcs measured? 3. What are two ways to determine when a chord is a diameter of a circle? 4. How are inscribed angles related to their intercepted arcs? How are the angles of an inscribed quadrilateral related to each other? 5. When a chord intersects a tangent line or another chord, what relationships exist among angles and arcs formed? 6. What relationships exist among the segments formed by two intersecting chords or among segments of two secants that intersect outside a circle? 7. What is the equation of a circle with center (h, k) and radius r in the coordinate plane? CCSS Math Standards G.CO.A.1, G.C.A.2, G.C.A.4, G.C.A.1, G.MG.A.3, G.CO.D.13, G.MG.A.1, G.GPE.A.1, G.GPE.B.4 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task Concepts (Need to Know) Skills Blooms Level Identify chords, diameters, radii, secants, and tangents of circles Find angle and arc measures Use inscribed angles and polygons and circumscribed angles Use properties of chords, tangents, and secants to solve problems Write and graph equations of circles *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 10, Quiz #1 Unit 10, Quiz #2 Unit 10, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 2 Unit of Study: Circumference, Area, and Volume Pacing-Teaching: 8 lessons, approximately 17 teaching days Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. How can you find the length of a circular arc? 2. How can you find the area of a sector of a circle? 3. How can you find the area of a regular polygon? 4. What is the relationship between the numbers of vertices V, edges E, and faces F of a polyhedron? 5. How can you find the volume of a prism or cylinder that is not a right prism or right cylinder? 6. How can you find the volume of a pyramid? 7. How can you find the surface area and the volume of a cone? 8. How can you find the surface area and the volume of a sphere? CCSS Math Standards G.GMD.A.1, G.C.B.5, G.CO.A.1, G.MG.A.2, G.GMD.A.3, G.GMD.B.4, G.GMD.A.2, G.MG.A.1, G.MG.A.3, Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task Concepts (Need to Know) Skills Blooms Level Measure angles in radians Find arc lengths and areas of sectors of circles Find areas of rhombuses, kites, and regular polygons Find and use volumes of prisms, cylinders, pyramids, cones, and spheres Describe cross-sections and solids of revolutions *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 11, Quiz #1 Unit 11, Quiz #2 Unit 11, Comprehensive Test Madras High School Unit Plan Subject: Geometry Grades: 9-12 Semesters: 2 Unit of Study: Probability Pacing-Teaching: 6 lessons, approximately 14 days of teaching Assessment Pacing: Formative Assessments – 2 Quizzes (1 day each), 1 mid-way through the unit & 1 near the end of the unit Summative Assessment – 1 comprehensive test (1 day) at the end of the unit Essential Questions: 1. How can you list the possible outcomes in the sample space of an experiment? 2. How can you determine whether two events are independent or not? 3. How can you construct and interpret a two-way table? 4. How can you find probabilities of disjoint and overlapping events? 5. How can a tree diagram help you visualize the number of ways in which two or more events can occur? 6. How can you determine the frequency of each outcome of an event? CCSS Math Standards S.CP.A.1, S.CP.A.2, S.CP.A.3, S.CP.A.4, S.CP.A.5, S.CP.B.6, S.CP.B.7, S.CP.B.8, S.CP.B.9, A.APR.C.5 Common Core Writing Standards: ELA-Literacy.SL.9-10.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Concepts (Need to Know) Skills Find probabilities of independent and dependent events Use conditional relative frequencies to find conditional probabilities Use the formulas for the number of permutations and the number of combinations Construct and interpret probability distributions and binomial distributions *Blooms level: 1 -Remember, 2-Understand, 3-Apply, 4- Analyze, 5-Evaluate, 6-Create Blooms Level *Assessment levels: 1-Beginning to identify, 2- Developing simple knowledge & skills, 3 Proficient- demonstrates knowledge & skills along with applying details, 4- Masterydemonstrates knowledge & skills along with analyzing, evaluating, and being able to create. Assessments: Unit 12, Quiz #1 Unit 12, Quiz #2 Unit 12, Comprehensive Test