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1 Master Map Geometry District Course# Grade Level Notes Blair Community Schools (withheld) Blair Community Schools Show Icon August 2012 A. Introducing Geometry -Basic -Building Blocks of Geometry -Midpoint -Angles, Rays -Polygons -Triangles -Special Quadrilaterals -Cirlces -Application Problems -Space Geometry A. Learn the terminology and notation of points, segments, lines, rays, planes, angles, and collinear and coplanar points A. Learn the idea of congruence of line segments A. Begin keeping a notebook of conditions A. Learn how to show the measurement of angles and segments on figures A. Practice using the tools of measurement (protractor and ruler) A. Become familiar with the symbols for marking figures A. Learn the idea of congruence of angles A. Practice writing definitions A. Define special angle relationships A. Define and classify polygons and related terms A. Define and classify and quadrilaterals, along with their related parts A. Define a circle and related figures A. Identify the parts of a circle A. Translate descriptions into diagrams, and vice versa A. Visualize objects and relationships in two to three dimensions A. Practice drawing skills A. Introduce some of the geometric solids September 2012 A. Reasoning in Geometry -Inductive Reasoning -Deductive Reasoning -Function Rules -Mathematical Modeling -Angle Relationships -Special Angles on Parallel Lines -Slope A. Use inductive reasoning to find the next term in a number or picture pattern A. Learn the relationship between inductive and deductive reasoning A. Generalize basic number patterns to a method for finding the nth term in a linear number sequence A. Apply mathematical models to problem solving A. Discover relationships between special pairs of angles A. Practice performing investigations and writing conjectures A. Practice measurement skills A. Explore relationships of angles formed by a transversal cutting parallel lines A. Find the slope of lines A. Review basic algebra solving skills 1 of 5 7/4/12 8:37 AM
2 October 2012 A. Using Tools of Geometry -Duplicating Segments and Angles -Perpendicular Bisectors -Midsegments/Medians/Altitudes -Distance from a point to a line -Angle Bisectors -Parallel Lines (slopes) -Points of Concurrency (orthocenter, circumcenter, and centroid) -Euler Segment A. Discover construction methods to duplicate a segment, an angle, and a polygon A. Discover a method of constructing perpendicular bisectors and midpoints A. Make conjectures about perpendicular biseoctors A. Determine a method of finding the shortest path from a point to a line A. Discover methods of constructing an angle bisector A. Make a conjecture about angle bisectors A. Investigate the relationship between the slopes of parallel lines A. Investigate the relationship between the slopes of perpendicular lines A. Discover points if concurrency of the angle bisectors, perpendicular bisectors, and altitudes of a triangle A. Explore the relationship between points of concurrency and inscribed and circumscribed circles A. Discover the concurrence of the medians of a triangle (the centroid) and its applications A. Explore length relationships among the segments into which the centroid divides each median A. Look for a relationship among the centroid, incenter, circumcenter, and orthocenter November 2012 A. Discovering and Proving Triangle Properties -Triangle Sum Conjecture -Properties of Isosceles Triangles -Writing Linear Equations -Triangle Inequalities -Exterior Angles of Triangles -Triangle Congruency Shortcuts -Corresponding Parts of Congruent Triangles A. Discover and explain the sum of the measures of the angles of a triangle A. Develop inductive and deductive reasoning A. Discover a relationship between the base angles of an isosceles triangle A. Review the relationship between the constant term in a linear equation of the form y = a + bx (or y = mx + b) and the y-intercept of the equation's graph A. Review the relationship between the coefficient of x and the slope of the graph of a linear equation in intercept (or slope-intercept) form A. Write a linear equation from the graph of a line A. Investigate inequalities among sides and angles in A. Discover the Exterior Angle Conjecture A. Explore shortcut methods for determining whether are congruent A. Dicover that SSS and SAS are valid congruence shortcuts but SSA is not A. Discover that ASA and SAA are valid congruence shortcuts but AAA isnot A. Show that pairs of angles or pairs of sides are congruent by identifying related and proving them congruent, than appyling CPCTC A. Create flowchart proofs A. Develop problem-solving skills A. Practice writing flowchart proofs A. Investigate vertex angle bisectors of isosceles 2 of 5 7/4/12 8:37 AM
3 December 2012 A. Discovering and Proving Polygon Properties -Polygon Sum Conjecture -Exterior Angles of Polygons -Kite Properties -Trapezoid Properties -Properties of Midsegments -Parallelogram Properties -Solving Systems of Linear Equations -Rectangle Properties -Rhombus Properties -Square Properties A. Discover the sum of the angle measures in a polygon A. Discover the sum of the measures of the exterior angles of a polygon A. Discover properties of kites and trapezoids A. Define and discover properties of midsegments in and trapezoids A. Discover properties of parallelograms A. Review finding the solutionto a system of linear equations in two variables A. Discover properties of rectangles, rhombuses, and squares January 2013 A. Discovery and Proving Circle Properties -Chord Properties -Tangent Properties -Arcs and Angles -Proving Circle Conjectures -Finding Circumcenter -Circumference and Diameter -Arc Length A. Review basic properties of a circle A. Discover properties of chords of circles A. Discover properties of tangents to a circle A. Explore common tangents and tangent circles A. Learn applications of tangents A. Discover relationships between an inscribed angle of a circle and its intercepted arc A. Review properties of inscribed angles and polygons A. Practice flowchart proofs A. Use algebra to find the circumcenter of a triangle A. Calculate pi, the ratio of the circumference of a circle to its diameter A. Discover a formula for finding the length of an arc of a circle February 2013 A. Area -Area of Rectangles -Area of Parallelograms -Area of Triangles -Area of Trapezoids -Area of Kites -Area Application Problems -Area of Regular Polygons -Area of Circles -Area of parts of Circles -Surface Area A. Develop the concept of area A. Derive formulas for the areas of a rectangle and a parallelogram A. Apply area formulas to solve problems A. Derive formulas for the areas of, trapezoids, and kites A. Practice measuring A. Practice estimation A. Solve area application problems using various problem-solving strategies A. Derive the formula for the area of a regular polygon A. Derive the formula for the area of a circle A. Discover formulas and methods for calculating the area of annuluses, sectors, and segments of circles A. Review terminology for solids A. Discover methods for finding the surface areas of solids 3 of 5 7/4/12 8:37 AM
4 March 2013 A. The Pythagorean Theorem -The Pythagorean Theorem -The Converse of the Pythagorean Theorem -Special Triangles -Distance Formula in Coordinate Geometry -Circles and the Pythagorean Theorem B. Volume -Geometry of Solids -Volume of Prisms -Volume of Cylinders -Volume of Pyramids -Volume of Cones -Volume Application Problems -Volume of a Sphere -Surface Area of a Sphere A. Understand the Pythagorean Theorem more deeply A. Practice simplifying square roots A. Discover relationships among the lengths of the sides of a triangle and a triangle A. Discover the Pythagorean relationship on a coordinate plane (the distance formula) A. Derive the equation of a circle from the distance formula A. Apply the Pythagorean relationship to problems involving circles B. Learn the vocabulary of polyhedrons-prisms and pyramids in particular B. Learn the vocabulary of spheres, cylinders, and cones B. Discover formulas for finding the volumes of prisms and cylinders B. Practice three-dimensional visual thinking skills B. Discover formulas for the volumes of pyramids and cones B. Solve applied problems involving polyhedrons, cones, cylinders, spheres, or hemishperes B. Derive the formula for the volume of a sphere B. Apply volume formulas to problems involving spheres or hemispheres B. Derive the formula for the surface area of a sphere B. Apply the surface area formula to solve problems April 2013 A. Similarity -Properties -Similar Polygons -Similar Triangles -Indirect Measurement with Similar Triangles -Corresponding Parts of Similar Triangles -Proportions with Area and Volume -Proportional Segments between Parallel Lines A. Learn or review the meanings of ratio and proportion A. Use ratios and proportions to solve word problems A. Develop an intuitive concept of similarity A. Define similar polygons A. Use the definition of similar polygons to solve problems A. Discover shortcut methods for determining similar A. Practice using proportions to find measures in similar figures A. Use similar to solve applied problems A. Discover a relationship between corresponding parts of similar A. Explore the ratio of the parts into which an angle bisector of a triangle divides the angle's opposite side A. Discover the relationship between the areas of similar figures A. Discover the relationship between the volumes of similar solids A. Apply the similarity conjectures to problems involving area and volume A. Discover the relationship between the ratios of the parts into which parallel lines cut the sides of a triangle 4 of 5 7/4/12 8:37 AM
5 A. Extend the Parallel/Proportionality Conjecture to include multiple parallel lines May 2013 A. Trigonometry -Trigonometric Ratios -Problem Solving with Right Triangles A. Encounter trigonometry and discover the sine, cosine, and tangent ratios A. Understand the usefulness of trigonometry A. Use trigonometry to solve applied problems 5 of 5 7/4/12 8:37 AM
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