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Sutherland Applied Geometry Strand Title: Geometric/Measurement Content Standard # Characteristics: Students will analyze characteristics, properties, and relationships among geometric shapes and objects. MA 12.2.1 Unit Outcomes MA 12.2.1 (a) Identify and explain the necessity of and give examples of definitions and theorems. MA 12.2.1 (b) Analyze properties and relationships among classes of two and three-dimensional geometric objects using inductive reasoning and counterexamples. MA 12.2.1 (c) State and prove geometric theorems using deductive reasoning (e.g., parallel lines with transversals, congruent triangles, similar triangles) MA 12.2.1 (d) Apply geometric properties to solve problems (e.g., parallel lines, line transversals, similar triangles, congruent triangles, proportions) MA 12.2.1 (e) Identify and apply right triangle relationships (e.g., soh, cah, toa, (30,60, 90 and 45,45, 90 triangles), converse of the Pythagorean Theorem) MA 12.2.1 (g) Know the definitions and basic properties of a circle and to solve problems. Additional: The students will classify two-dimensional shapes by the number of sides and angle measurements The students will classify three-dimensional shapes by bases, lateral faces, and base angles The students will determine lengths and angles of geometric shapes using similarity and line transversal. The following special angle pairs will be applied: corresponding angles, alternate interior angles, alternate exterior angles, same side interior angles, and vertical angles. The students will incorporate the triangle sum theorem when two angles of any triangle are known The students will apply similarity properties to form proportions to find missing lengths of polygons District Assessment 5/4/17 Vocabulary Theorem Definition Inductive reasoning Deductive reasoning Transversal Triangle Congruent Parallel Similar Proportion Circle Base Face Corresponding angles Alternate exterior angles Alternate interior angles Same side interior angles Vertical angles Suggested Resources Inspiration software to classify 2-D shapes Sutherland Applied Geometry Strand Title: Geometric/Measurement Content Standard # Coordinate Geometry: Students will use coordinate geometry to analyze and describe relationships in the coordinate plane. MA 12.2.2 Unit Outcomes Vocabulary MA 12.2.2 (a) Use coordinate geometry to analyze geometric situations (e.g., parallel lines, perpendicular lines, and circle equations) MA 12.2.2 (b) Apply the midpoint formula when given two points. MA 12.2.2 (c) Apply the distance formula when given two points. MA 12.2.2 (d) Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square) Additional: Perpendicular Midpoint formula Distance formula Quadrilateral Isosceles Trapezoid Parallelogram Rectangle Square Slope Suggested Resources The students will determine the slope and midpoints of sides of polygons from a graph or when given vertices of the polygon The students will compare and contrast slopes of parallel and perpendicular lines of sides of a polygons District Assessment 5/4/17 Sutherland Applied Geometry Strand Title: Geometric/Measurement Content Standard # Transformations: Students will apply and analyze transformations. MA 12.2.3 Unit Outcomes MA 12.2.3 (a) Explain and justify the effects of simple transformations on the ordered pairs of two-dimensional shapes. Vocabulary Transformation MA 12.2.3 (b) Perform and describe multiple transformations Suggested Resources Geogebra software for transformation District Assessment 5/4/17 Sutherland Applied Geometry Strand Title: Geometric/Measurement Content Standard # Spatial Modeling: Students will use visualization, spatial reasoning, and geometric modeling to solve problems. MA 12.2.4 Unit Outcomes Vocabulary MA 12.2.4 (a) Sketch and draw appropriate representations of geometric objects using ruler, protractor or technology MA 12.2.4 (b) Use geometric models to visualize, describe, and solve problems (e.g., find the height of a tree; find the amount of paint needed for a room, the amount of shingles for a roof; scale model) Ruler Protractor Geometric model Accuracy Line segment Additional: The students will demonstrate the accuracy of several measuring devices for various angles and line segments. Suggested Resources An example of a hail claim on a roof District Assessment 5/4/17 Sutherland Applied Geometry Strand Title: Geometric/Measurement Content Standard # Measurement: Students will apply the units, systems, and formulas to solve problems. MA 12.2.5 Unit Outcomes MA 12.2.5 (a) Use strategies to find surface area and volume of complex objects MA 12.2.5 (b) Apply appropriate units and scales to solve problems involving measurement MA 12.2.5 (c) Convert between various units of area and volume, such as square feet to square yards MA 12.2.5 (d) Convert equivalent rates (e.g., feet/second to miles/second to miles/hour) MA 12.2.5 (e) Find arc length and area of sectors of a circle MA 12.2.5 (f) Determine surface area and volume of threedimensional objects (e.g., spheres, cones, pyramids, prisms, cylinders) MA 12.2.5 (g) Know that the effect of a scale factor K on length, area and volume is to multiply each k, K^2, and K^3 respectively) Additional: Students will calculate perimeter and area of 2-D shapes with given formulas. (e.g., triangles, quadrilaterals, pentagons through n-gons, and circles) Students will convert between metric and standard units of measurement Students will select the proper equation and conversion factor to model the conversion District Assessment 5/4/17 Vocabulary Surface area Volume Arc length Area of a sector Spheres Cone Pyramid Prisms Cylinder Scale factor Perimeter Suggested Resources Sutherland Applied Geometry 5/4/17