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Alamance-Burlington School System Math III Unit Plan Priority standards are highlighted in yellow. Unit 1: Geometry and Proofs Mathematical Practices Conceptual Overview Essential Understandings G.CO.9 Common Core Standards G.CO.10 G.CO.11 G-CO.12 G-SRT.2 G.SRT.3 The Mathematical Practices are K-12 standards and together with the content standards prescribe that students experience mathematics as a coherent, useful, and logical subject. Teachers of mathematics should intentionally provide daily opportunities for students to develop these mathematical habits of mind. Suggested Unit Pacing (# of days): 12 P4 P5 P6 P7 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. P8 Look for and express regularity in repeated reasoning. P1 P2 P3 Students will be able to understand basic geometric concepts and complete proofs. In this unit students will start by learning basic geometric definitions such as vertical angles, and complementary angles. Students will then explore the angles that are formed when two parallel lines are cut by a transversal. After mastering these concepts student will transition into investigating segments found in triangles. Finally student will learn how to complete basic proofs involving various shapes. Prove 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. 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. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. G.SRT.4 G.SRT.5 Learning Targets Essential Terminology Literacy Integration Technology Integration Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. These suggested learning targets were determined based on the intentions of the CCSS and/or NCES. Teachers will need to add the criteria for success in order to create outcome-based targets. The learner will… define angle, circles, perpendicular lines, parallel lines, and line segments. apply properties to prove lines parallel. make geometric Constructions (copying a segment, copying an angle, bisecting an angle, constructing a line parallel to a given line through a point not on line) with a variety of tools and methods. identify congruent figures, prove triangles congruent by ASA, AAS, SSS, SAS, HL identify and apply the properties of parallelograms. identify, prove theorems and apply midsegments, concurrent lines, altitudes, perpen dicular bisectors, and medians of triangles. solve ratios and proportions, identify similar polygons, prove triangles similar, ratio nalize denominators, apply properties of special right triangles and use congruence and similarity to prove relationships in geometric figures. Vertical angles Alternate interior angles Corresponding angles Same-side interior angles Perpendicular bisector Equidistant Isosceles triangle Base angles Vertex angle Legs of an isosceles triangle Midsegment of a triangle Median of a triangle Concurrent lines Parallelogram Opposite angles Consecutive angles Diagonals Rectangles Squares Literacy Standards Literature Connections Technology Standards Technology Resources Proof resources Additional Resources http://ahs.arabcityschools.org/ourpages/auto/2013/1/14/57509334/Triangle%20Proofs%20R eview%201_14_13.pdf http://www.letspracticegeometry.com/wp-content/uploads/2011/11/proofs-involvingcongruent-triangles.pdf http://basic-geometry.wikispaces.com/Chapter+3+Lessons Cross Curricular Integration Assessment Pre-/Postassessment On-going/ Formative Assessment Summative Teachers determine the learning plan while reflecting on the range of abilities, styles, interests and needs of students. How will the work be personalized and differentiated in order to achieve the desired learning targets? Considerations for the Learning Plan Re-teaching Enrichment