5. 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

6. 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?

7. 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?

8. 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?

9. 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?

10. 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?

11. 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?

12. 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?

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

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

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

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

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

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

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

20. Ohio Department of Education Website
Model Curriculum

21. Ohio Department of Education Website
Model Curriculum

22. Ohio Department of Education Website
Model Curriculum

23. Ohio Department of Education Website
Model Curriculum

24. Ohio Department of Education Website
Model Curriculum

25. Ohio Department of Education Website
Resources

26. Ohio Department of Education Website
Resources

27. Ohio Department of Education Website
Resources

28. Ohio Department of Education Website
Resources

29. Ohio Department of Education Website
Resources

31. From Appendix A

32. From Appendix A
Traditional Pathway

33. From Appendix A
Integrated Pathway

35. From the PARCC Model Content Frameworks

36. From the PARCC Model Content Frameworks

37. From the PARCC Model Content Frameworks

38. From the PARCC Model Content Frameworks

39. From the PARCC Model Content Frameworks

60. 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

62. 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

64. 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

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

72. Angles are congruent

73. 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