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
Regular polytope wikipedia , lookup
Noether's theorem wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
List of regular polytopes and compounds wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Line (geometry) wikipedia , lookup
Tessellation wikipedia , lookup
Trigonometric functions wikipedia , lookup
Integer triangle wikipedia , lookup
History of geometry wikipedia , lookup
Euclidean geometry wikipedia , lookup
The School District of Palm Beach County GEOMETRY REGULAR 3rd Quarter Scope 2010 - 2011 Benchmarks Topic & Suggested Pacing Next Generation Sunshine State Standards January 4 March 11 MA.912.G.2.4 MA.912.G.2.5 MA.912.G.2.7 MA.912.G.3.1 Core I can… Pearson Geometry • Classify polygons in the coordinate plane Polygons in the • Name coordinates of special figures by using their properties Coordinate Plane • Prove theorems using figures in the coordinate plane • Write ratios and solve proportions Use properties of congruent and similar polygons to solve Applying • Identify and apply similar polygons mathematical or real-world problems. Coordinate • Use the AA ~ Postulate and the SAS ~ and SSS ~ 7.1-7.3, 10.4 Geometry Theorems Proofs Using • Use similarity to find indirect measurements Apply transformations (translations, reflections, rotations, Coordinate • Find and use relationships in similar right triangles dilations, and scale factors) to polygons. to determine Geometry • Use the Side-Splitter Theorem and the Triangle-Anglecongruence, similarity, and symmetry. Know that images Bisector Theorem formed by translations, reflections, and rotations are Ratios and • Use the Pythagorean Theorem Proportions congruent to the original shape. Create and verify tessellations • Use the converse of the Pythagorean Theorem of the plane using polygons. Similar • To use the properties of 45 – 45 – 90 and 30 – 60 – 90 9.1-9.7 Polygons triangles • Use the sine, cosine, and tangent ratios to determine Proving Explain the derivation and apply formulas for perimeter and side lengths Triangles area of polygons (triangles, quadrilaterals, pentagons, etc.). Similar • Use the sine, cosine, and tangent ratios to find angle 10.1-10.4 measures in right triangles Similarity in • Use angles of elevation and depression to solve Right Triangles Determine how changes in dimensions affect the perimeter problems and area of common geometric figures. Proportions in • Identify isometries 10.1, 10.3-10.4 Triangles • Find translation images of figures • Find reflection images of figures Describe, classify, and compare relationships among The • Draw and identify rotation images of figures quadrilaterals including the square, rectangle, rhombus, Pythagorean • Identify the type of symmetry in a figure Theorem parallelogram, trapezoid, and kite. • Understand dilation images of figures 6.7 Special Right • Find compositions of reflections, including glide Find the lengths and midpoints of line segments in twoMA.912.G.1.1 dimensional coordinate systems. 6.7 MA.912.G.2.3 Student Target 6.7 6.8 6.9 7.1 7.2 7.3 7.4 7.5 8.1 8.2 8.3 8.4 9.1 9.2 9.3 9.4 9.5 9.6 9.7 10.1 10.2 10.3 10.4 Tutorial Support AYP Support MA.912.G.1.1 Coordinate Geometry MA.912.G.2.3 Proofs in Coordinate Geometry MA.912.G.2.4 Ratio and Proportion Video MA.912.G.2.5 Similar Shapes Video MA.912.G.3.3 Similar Triangles Video (Part 1) MA.912.G.4.6 Use coordinate geometry to prove properties of congruent, MA.912.G.3.3 regular, and similar quadrilaterals. 6.7-6.9 Classify, construct, and describe triangles that are right, acute, MA.912.G.4.1 obtuse, scalene, isosceles, equilateral, and equiangular. 6.7 Use properties of congruent and similar triangles to solve MA.912.G.4.4 problems involving lengths and areas. Special Right Triangles • Find compositions of reflections, including glide reflections Trigonometry • Classify isometries • Identify figures that tessellate Angles of • Identify transformations and symmetries in tessellations Elevation and • Find the area of parallelograms and triangles Depression • Find the area of a trapezoid • Find the area of a rhombus or kite Translations • Find the area of a regular polygon Reflections • Find the perimeters and areas of similar polygons Rotations 7.1, 7.3, 10.4 Similar Triangles Video (Part 2) MA.912.G.5.4 Pythagorean Theorem Video MA.912.T.2.1 Intro to 30-6090 Triangles Video Symmetry MA.912.G.4.5 Apply theorems involving segments divided proportionally. 7.5 Dilations Compositions of Reflections Prove that triangles are congruent or similar and use the MA.912.G.4.6 concept of corresponding parts of congruent triangles. 7.3 MA.912.G.5.1 Prove and apply the Pythagorean Theorem and its converse. 8.1 State and apply the relationships that exist when the altitude is MA.912.G.5.2 drawn to the hypotenuse of a right triangle. 7.4 Use special right triangles (30° - 60° - 90° and 45° - 45° - 90°) to Tessellations Areas of Parallelograms and Triangles Areas of Trapezoids, Rhombuses, and Kites Areas of Regular Polygons MA.912.G.5.3 solve problems. 8.2, 10.3 MA.912.G.5.4 Solve real-world problems involving right triangles. 7.3, 8.1-8.4 Perimeters and Areas of Similar Figures 30 - 60 - 90 Triangles Part II Video 45 - 45 - 90 Triangles Video Basic Trigonometry Video Basic Trigonometry Video II Angles of Elevation and Depression Translations Determine whether a solution is reasonable in the context of MA.912.G.8.3 the original situation. 7.4, 8.1 Reflections Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a MA.912.G.8.5 variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs. 6.8-6.9 Rotations Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right MA.912.T.2.1 triangles. 8.3-8.4 Symmetry Dilations and Similarity Area and Perimeter of Rectangles and Triangles Video Area of Trapezoids Video Area of Regular Polygons Video Perimeters and Areas of Similar Figures Video Secondary Data-Driven Benchmark Comprehension Check