Students proficient in this standard What do the Standards for Mathematical Practice mean in the context of the Conceptual Category: Geometry? Students proficient in this standard ·know that solving a problem doesn't always mean solving word problems ·look at a geometry problem from different perspectives-plane geometry, coordinate geometry, analytic geometry ·plan a solution pathway, rather than just jumping into a solution attempt ·check answers to see if they make sense especially in contextual problems ·understand other solution methods and can see similarities and differences in the methods of others to their own solution method

Students proficient in this standard ·have the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents ·have the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved ·pay attention to the units involved, checking that the final answer is not only numerically reasonable but that the operations used also produce the correct units for the final answer ·know and flexibly use different properties of objects What do the Standards for Mathematical Practice mean in the context of the Conceptual Category: Geometry?

Students proficient in this standard ·can listen to or read arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments ·can compare the effectiveness of two plausible arguments or proofs to distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in the argument or proof, explain what it is ·can understand and use stated assumptions, definitions, properties, postulates and previously established results in constructing solution methods, arguments, and proofs ·can write algebraic proofs to geometric theorems What do the Standards for Mathematical Practice mean in the context of the Conceptual Category: Geometry?

Students proficient in this standard ·can write equations to model problems in everyday life, society, and the workplace ·routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense ·use geometric models to represent algebraic operations(e.g. polynomial multiplication or completing the square) The following standards in the conceptual category of Geometry have been marked as modeling standards: ·Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems ·Use coordinates to compute perimeters of polygons and areas of triangles ·Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems ·Use geometric shapes, their measures, and their properties to describe objects ·Apply concepts of density based on area and volume in modeling situations ·Apply geometric methods to solve design problems What do the Standards for Mathematical Practice mean in the context of the Conceptual Category: Geometry?

Students proficient in this standard ·use estimation skills to estimate solutions to equations or results of computations ·use trigonometric tables or calculators when solving triangle trigonometry problems ·use compass and straight edge or computer software to perform constructions ·use rulers and protractors or computer software to make measurements ·use dynamic geometry software to explore and discover geometric software ·use physical models, patty paper, miras to explore geometric concepts What do the Standards for Mathematical Practice mean in the context of the Conceptual Category: Geometry?

Students proficient in this standard ·communicate precisely to others ·know precise definitions for geometric objects ·use mathematical terminology such as equal, similar, and congruent properly ·Use symbols like ≅ and = appropriately ·play close attention to units ·round appropriately based on the context of the problem What do the Standards for Mathematical Practice mean in the context of the Conceptual Category: Geometry?

Students proficient in this standard ·look closely to discern a pattern or structure ·can see complicated things, such a trapezoid, as single objects or as being composed of several objects(rectangle and two triangles) ·can see the similarities between the area formulas for trapezoids, rectangles, parallelograms, and triangles What do the Standards for Mathematical Practice mean in the context of the Conceptual Category: Geometry?

Students proficient in this standard ·notice if calculations are repeated, and look for both general methods and for shortcuts For example, after performing long division of polynomials multiple times, students may develop or at least understand synthetic division What do the Standards for Mathematical Practice mean in the context of the Conceptual Category: Geometry?

From the Common Core State Standards Document Conceptual Category Geometry Context Plane Euclidean Geometry Definitions and Proofs Geometric Transformations Symmetry

From the Common Core State Standards Document Conceptual Category Geometry Triangle Trigonometry Similarity Transformations Congruence

From the Common Core State Standards Document Conceptual Category Geometry Coordinate Geometry Equations Dynamic Analytic Geometric Transformations

From the Common Core State Standards Document Conceptual Category Geometry Domain Cluster

From the Common Core State Standards Document Conceptual Category Geometry Domain Cluster Standard

From the Common Core State Standards Document 8th grade standards Domain Cluster Standard

From the Common Core State Standards Document 8th Grade Standards Domain Cluster Standard

Ohio Department of Education Website Model Curriculum

Ohio Department of Education Website Model Curriculum

Ohio Department of Education Website Model Curriculum

Ohio Department of Education Website Model Curriculum

Ohio Department of Education Website Model Curriculum

Ohio Department of Education Website Resources

Ohio Department of Education Website Resources

Ohio Department of Education Website Resources

Ohio Department of Education Website Resources

Ohio Department of Education Website Resources

From Appendix A

From Appendix A Traditional Pathway

From Appendix A Integrated Pathway

From the PARCC Model Content Frameworks

From the PARCC Model Content Frameworks

From the PARCC Model Content Frameworks

From the PARCC Model Content Frameworks

From the PARCC Model Content Frameworks

Yes, it is a rectangle. Opposite sides are congruent Yes, it is a rectangle. Opposite sides are congruent. Consecutive sides are perpendicular as shown by slopes that are opposite reciprocals

Part II T'(-6,6) U'(2,10) V'(10,-6) W'(2,-10) Yes, it is a rectangle. Opposite sides are congruent. Consecutive sides are perpendicular as shown by slopes that are opposite reciprocals Yes, the rectangles are similar. Corresponding angles are congruent(right angles) and corresponding sides are in proportion with a scale factor of 2

Part III T'(-8,9) U'(0,13) V'(8,-3) W'(0,-7) Yes, it is a rectangle. Opposite sides are congruent. Consecutive sides are perpendicular as shown by slopes that are opposite reciprocals Yes, the rectangles are similar. Corresponding angles are congruent(right angles) and corresponding sides are in proportion with a scale factor of 2

Once it is established that x=ka, we know the triangles are similar by SSS

Angles are congruent

Repeat for other pairs of corresponding angles Showing when all 3 sets of corresponding sides are in proportion, the corresponding angles are congruent, implying trinagles are similar