* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry-Quarter-1-P..
Survey
Document related concepts
Riemannian connection on a surface wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Technical drawing wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Multilateration wikipedia , lookup
History of geometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Trigonometric functions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Line (geometry) wikipedia , lookup
Euler angles wikipedia , lookup
Transcript
Geometry Quarter 1 Curriculum Map 2013-2014 • Review Standards CCSS for Mathematical Practice: • (M)ajor Content, 1. Make sense of problems and persevere in solving them • (S)upporting Content 2. Reason abstractly and quantitatively • (A)dditional Content 3. Construct viable arguments and critique the reasoning of others • (+) Honors 4. Model with mathematics 5. Use appropriate tools strategically Textbook Resource: Pearson’s Geometry Common Core 6. Attend to precision Pearson’s online resource: www.pearsonsuccess.net 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unit Introduction to Geometry Parallel and Perpendicular Unit 1: Introduction to Geometry Timeline Standards 7 days G.CO.1 Know precise definitions of angle, for circle, perpendicular line, parallel line, and line instructio segment, based on the undefined notions of n and point, line, distance along a line, and distance review around a circular arc. 1st Quarter Learning Expectation Identify the building blocks of geometry 1 day for assessme nt Make a conjecture and prove that it is true G.CO.9Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Unit 2: Parallel and Perpendicular 6 days G.CO.9Prove theorems about lines and for angles. Theorems include: vertical angles are instructio congruent; when a transversal crosses parallel n and lines, alternate interior angles are congruent review and corresponding angles are congruent; Describe the attributes of a segment or angle 1st Quarter Prove that lines are parallel Find the sum of the measures of the angles of a triangle. Suggested Instructional Days: 8 Vocabulary Resources Page 2 1-2 Points, Lines, and Angle bisector Planes Congruent segments Constructions 1-3 Measuring Segments Linear pair 1-4 Measuring Angles Perpendicular bisector 1-5 Exploring Angle Postulate Pairs Segment bisector 2-2 & 2-3 Conditionals, Supplementary angles Bi-conditionals, and Vertical angles Definitions 2-6 Proving Angles Page 80 Congruent Biconditional Conclusion Conditional Conjecture Converse Deductive reasoning Hypothesis Inductive reasoning Theorem Suggested Instructional Days: 7 Page 138: 3-1 Lines and Angles Alternate exterior 3-2 Properties of angles Parallel Lines Alternate interior 3-3 Proving Lines angles Parallel Geometry Quarter 1 p. 1 Geometry Quarter 1 Curriculum Map 2013-2014 1 day for assessme nt points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Unit 3: Right Triangles and Trigonometry Right 6 (8) days G.CO.9Prove theorems about lines and Triangles and angles. Theorems include: vertical angles for Trigonometry instruction are congruent; when a transversal crosses and review parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular 1 day for assessment bisector of a line segment are exactly those equidistant from the segment’s endpoints. G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, 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 problems. (+)G.SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems. (+)G.SRT.11 Understand and apply the Law Corresponding angles Exterior angles of polygons Parallel lines Perpendicular lines Same-side interior angles Skew lines Transversal 1st Quarter Find the length of the side and measure the angles in a right triangle. Determine the usage of trigonometric ratios in right triangles. 3-4 Parallel and Perpendicular Lines *possibly combine with 3-5 3-5 Parallel Lines and Triangles Suggested Instructional Days: 7-9 days Page 282 5-4 Medians and Altitude Altitudes Equidistant 8-1 Pythagorean Median Theorem Page 488 Angle of depression Angle of elevation Cosine Law of cosines Law of sines Pythagorean triple Sine Tangent 8-2 Special Right Triangles 8-3 Right Triangle Trigonometry 8-4 Angles of Elevation and Depression 8-5 Law of Sines *Honors, Regular do if time 8-6 Law of Cosines *Honors, Regular do if time Geometry Quarter 1 p. 2 Geometry Quarter 1 Curriculum Map 2013-2014 of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces). Quarter 1 Assessment Additional Resources: Right Triangles (Hopewell Geometry): http://map.mathshell.org/materials/tasks.php?taskid=258&subpage=apprentice Proofs of Pythagorean Theorem: http://map.mathshell.org/materials/lessons.php?taskid=419&subpage=concept Trig Video Resources: http://app.discoveryeducation.com/player/?assetGuid=cc670dc6-‐122b-‐4320-‐921c-‐ cceda37dae7c&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid = Trig Video Resources: http://app.discoveryeducation.com/player/?assetGuid=f17142cf-‐a29a-‐4a96-‐a366-‐ 3cdafcedf832&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid = Special Right Triangle Video Resource: http://app.discoveryeducation.com/player/?assetGuid=107e0043-‐f490-‐4ef4-‐9ddf-‐ ff4e81cc4dda&fromMyDe=0&isPrinterFriendly=0&provider=&isLessonFromHealth=0&productcode=US&isAssigned=false&includeHeader=YES&homeworkGuid = NOTES/REFLECTIONS: Geometry Quarter 1 p. 3