UNIT PLAN. Big Idea/Theme: Understanding transformations of coordinate geometry and vectors allows students to study movement in the outside world.

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1 UNIT PLAN Subject: Geometry Grade Level: Unit #: 10 Unit Name: Expansions of Coordinate Geometry Big Idea/Theme: Understanding transformations of coordinate geometry and vectors allows students to study movement in the outside world. Culminating Assessment: Geometry and spatial sense: transformations Unit Understanding(s) Students will understand Transformations can be applied to figures in the coordinate plane. Transformations can be applied in the coordinate plane using matrices. It is possible to represent the sum of 2 vectors geometrically. The magnitude and direction of 2 vectors can be determined with the application of a unique formula. Unit Essential Question(s): How do you apply transformations (translations, reflections, rotations, dilations) to figures in the coordinate plane? How do you apply transformations (translations and dilations) to figures in the coordinate plane using matrices? How do you represent the sum of 2 vectors geometrically (scale drawings, direct measurement, and Pythagorean Theorem)? How do you determine the magnitude and direction of 2 vectors? Students will know / Students will be able to Apply transformations to figures in the coordinate plane by using sketches and coordinates Apply transformations to figures in the coordinate plane by using matrices Represent the sum of 2 vectors geometrically by using the parallelogram method, a scale drawing and direct measurement, or by using the Pythagorean Theorem Determine the direction of the resultant of 2 perpendicular vectors by using a scale drawing and direct measurement 1

2 South Carolina Academic Standards: G-1.1 Formulate and demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries. G-1.2 Communicate knowledge of geometric relationships by using terminology appropriately. G-1.4 Conjecture by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software. G-1.7 Understand the historical development of geometry. G-1.8 Connect geometry with other branches of mathematics. G-1.9 Demonstrate an understanding of how geometry applies to real world contexts (including architecture, construction, farming, and astronomy). G-1.10 Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices) G-6.3 Apply transformations translation, reflection, rotation, and dilation to figures in the coordinate plane by using sketches and coordinates. G-6.4 Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices. G-6.5 Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method. G-6.6 Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement. G-6.7 Carry out a procedure to compute the magnitude of the resultant of two perpendicular vectors by using the Pythagorean theorem. G-6.8 Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement. Interim Assessment (formative) Quizzes/Tests Observations Question and answer Journals Class discussion Board work Group activities Key Criteria (to meet the standard/rubric) Rubric below (with the exception of Working with Others unless revised as a group project) to assess as students transform the objects below. 2

3 Culminating Assessment Unit 9 GEOMETRY AND SPATIAL SENSE: TRANSFORMATIONS (2) Don t forget to play the Transformation Golf game first! Go to mathfrog.ca for the link. 1. Draw the new cats obtained by performing the following transformations on AMBER. a) Translate, or slide AMBER seven units downwards and name it SMOKEY. b) Translate AMBER nine units to the left and name it WHISKERS. c) Reflect, or flip, AMBER in the x-axis and name it MISTY. d) Reflect AMBER in the y-axis and name it BANDIT. e) Rotate, or turn, AMBER clockwise 180 around point O and name it TIGER. f) Rotate AMBER anti-clockwise, or counter-clockwise, 90 around point O and name it SHADOW. 3

4 AMBER 4

5 2. Complete the following pairs of transformations on the F. a) Translate F five units left and then nine units down. b) Rotate F 90 clockwise around the point O and then reflect in the y- axis. c) Reflect F in the x-axis and then rotate 180 clockwise around the point O. d) Translate F up six units and then reflect in the y-axis. e) Translate F eleven units left and then reflect in the x-axis. 5

6 TRY THIS! On a piece of graph paper, draw a simple design of your choice. a) Apply a rotation, translation, and reflection of your choice. b) Apply these same three transformations again, but in a different order. c) Did you obtain the same result in parts (a) and (b)? d) Why or why not? 6

7 CATEGORY Mathematical Reasoning Uses complex and refined reasoning. Uses effective reasoning Some evidence of reasoning. Little evidence of reasoning. Mathematical Errors % of the steps and solutions have no Almost all (85-89%) of the steps and solutions have no Most (75-84%) of solutions have no More than 75% of solutions have Diagrams and Sketches sketches are clear and greatly add to the reader's understanding of the procedure(s). sketches are clear and easy to understand. sketches are somewhat difficult to understand. sketches are difficult to understand or are not used. Completion All problems are All but 1 of the problems is All but 2 of the problems are Several of the problems are not Explanation Explanation is detailed and clear. Explanation is clear. Explanation is a little difficult to understand, but includes critical components. Explanation is difficult to understand and is missing several components OR was not included. Mathematical Errors % of the steps and solutions have no Almost all (85-89%) of the steps and solutions have no Most (75-84%) of solutions have no More than 75% of solutions have 7

UNIT PLAN. Grade Level: Unit #: 7 Unit Name: Circles

UNIT PLAN. Grade Level: Unit #: 7 Unit Name: Circles UNIT PLAN Subject: Geometry Grade Level: 10-12 Unit #: 7 Unit Name: Circles Big Idea/Theme: The understanding of properties of circles, the lines that intersect them, and the use of their special segments