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Middletown Public Schools Mathematics Unit Planning Organizer Grade/Course Geometry 16 instructional days (+4 reteaching/extension) Duration Subject Unit 3 Mathematics Polygons Big Idea One can draw reasonable conclusions from repeated observations, and it may be necessary to justify those conclusions using a logical argument. Logical arguments require a bank of pre-requisite concepts, skills and definitions and the ability to link them together, such that if one thing is true, another must be true. How does one make and support a reasonable conclusion regarding a problem? How do previous understandings impact the process of making a logical argument? Essential Question Mathematical Practices Practices in bold are to be emphasized in the unit. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Domain and Standards Overview Prove geometric theorems. Make geometric constructions. Geometry, Unit 3 Polygons 2014 1 Revised November 18, Priority and Supporting Common Core State Standards Bold Standards are Priority CC.9-12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; 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. Explanations and Examples Students may use geometric simulations (computer software or graphing calculator) to explore theorems about triangles. (See GSP Triangle Sum Lab) CC.9-12.G.CO.11 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. Students may use geometric simulations (computer software or graphing calculator) to explore theorems about parallelograms. CC.9-12.G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Students may use geometric software to make geometric constructions. (See Proving Quadrilateral Properties (1)) (See GSP Lab – Constructing Regular Polygons) Concepts What Students Need to Know ● theorems about triangles Skills What Students Need to Be Able to Do ● PROVE ● theorems about parallelograms ● PROVE Geometry, Unit 3 Polygons 2014 Bloom’s Taxonomy Levels Depth of Knowledge Levels 5 5 2 Revised November 18, Standard Learning Progressions The standards below represent prior knowledge and enrichment opportunities for standards in this unit. Pre-requisite Skills Accelerated Learning CC.9-12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; 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. CC.9-12.G.CO.11 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. CC.9-12.G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Geometry, Unit 3 Polygons 2014 Understand and apply the Pythagorean Theorem. 8.G.6-8 Use coordinates to prove simple geometric theorems algebraically. G.GPE.4-7 Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.1-3 Use coordinates to prove simple geometric theorems algebraically. G.GPE.4-7 Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.1-3 3 Revised November 18, Unit Assessments Performance Task Common Formative Assessment Geometry, Unit 3 Polygons 2014 G.CO.11 4 Revised November 18,