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Two- and Three-Dimensional Geometric Objects

 

1. Understand characteristics of common two- and three-dimensional figures, such as triangles (e.g., isosceles and right triangles), quadrilaterals, and spheres.

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Lesson 1. Triangles  Part 1  Part 2

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Lesson 2. Quadrilaterals   Part 1  Part 2  Part 3

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Lesson 3. Polygons  Part 1 Part 2

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Lesson 4. 3 D Figures  Part 1  Part 2  Part 3   Part 4  Part 5

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2. Draw conclusions based on the congruence, similarity, or lack thereof, of two figures.

 

Lesson 5. Congruent Figures  Part 1   Part 2   Part 3   Part 4

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Lesson 6. Similar Figures   Part 1   Part 2    Part 3   Part 4

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3. Identify different forms of symmetry, translations, rotations, and reflections.

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Lesson 7. Symmetry  Part 1   Part 2   Part 3   Part 4   Part 5

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Lesson 8. Translation  Part 1   Part 2   Part 3   Part 4

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Lesson 9. Rotation  Part 1   Part 2   Part 3   Part 4   Part 5

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Lesson 10. Reflection  Part 1   Part 2   Part 3   Part 4

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4. Understand the Pythagorean theorem and its converse.

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Lesson 11. Pythagorean Theorem  Part 1  Part 2  Part 3  Part 4

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Lesson 12. Converse of Pythagorean Theorem  Part 1  Part 2   Part 3

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Lesson 13. Proofs of Pythagorean Theorem  Part 1  Part 2   Part 3

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Lesson 14. Problems  Part 1  Part 2   Part 3   Part 4

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5. Work with properties of parallel lines.

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Lesson 15. Parallel Lines

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Lesson 16. Parallel Lines

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Lesson 17. Parallel Lines

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Lesson 18. Problems  Part 1  Part 2  Part 3  Part 4  Part 5  

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Lesson 19. Interior Angle Sum of a Triangle Theorem  Part 1  Part 2  Part 3  

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Lesson 20. Exterior Angle of a Triangle  Part 1  Part 2  Part 3  Part 4

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Representational Systems, Including Concrete Models, Drawings, and Coordinate Geometry

 

6. Use concrete representations, such as manipulatives, drawings, and coordinate geometry to represent geometric objects.

 

Lesson 21.  Coordinate Plane

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Lesson 22. Problems

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Lesson 23. Problems

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Lesson 24. Problems

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Lesson 25. Problems  

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Lesson 26. Problems   Problems 2

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7. Construct basic geometric figures using a compass and straightedge, and represent three-dimensional objects through two-dimensional drawings.

 

Lesson 26. Basic construction  Part 2   Part 3   Part 4   Part 5   Part 6   Part 7

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Lesson 27. Nets   Part 2  Part 3  Part 4  Part 5  Part 6    Part 7

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8. Combine and dissect two- and three- dimensional figures into familiar shapes, such as dissecting a parallelogram and rearranging the pieces to form a rectangle of equal area.

 

Lesson 31. Problems

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Lesson 32. Problems

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Techniques, Tools, and Formulas for Determining Measurements

 

9. Estimate and measure time, length, angles, perimeter, area, surface area, volume, weight/mass, and temperature through appropriate units and scales.

 

Lesson 33. Measuring length Part 1  Part 2  Part 3

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Lesson 34. Measuring angles  Part 1  Part 2  Part 3  Part 4

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Lesson 35. Perimeter of polygons Part 1  Part 2  Part 3

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Lesson 36. Area of polygons  Part 1  Part 2

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Lesson 37. Surface area of 3D objects Part 1  Part 2  Part 3

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Lesson 38. Volume of Solids  Part 1  Part 2  Part 3  Part 4

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10. Identify relationships between different measures within the metric or customary systems of measurements and estimate an equivalent measurement across the two systems.

 

Lesson 39. Metric System Conversion  Part 1   Part 2  Part 3  Part 4  Part 5

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Lesson 40. Metric Conversion Areas and Volumes  Part 1   Part 2  Part 3  Part 4

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Lesson 41. Dimensional Analysis  Part 1  Part 2  Part 3  Part 4

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11. Calculate perimeters and areas of two-dimensional objects and surface areas and volumes of three- dimensional objects, and use mathematics to solve real-world problems involving the volume of cones, cylinders, and spheres.

 

Lesson 42. Perimeter formulas  Part 1

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Lesson 43. Perimeter problems  Part 1  Part 2  Part 3   Part 4  Part 5  Part 6

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Lesson 44. Area formulas  Part 1  Part 2  Part 3

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Lesson 45. Area problems Part 1  Part 2  Part 3   Part 4  Part 5  Part 6  Part 7  Part 8

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Lesson 46. Surface area formulas

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Lesson 47. Surface area problems  Part 1  Part 2  Part 3  Part 4  Part 5  Part 6

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Lesson 48. Volume formulas

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Lesson 49. Volume problems  Part 1  Part 2  Part 3  Part 4  Part 5

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12. Relate proportional reasoning to the construction of scale drawings or models.

 

Lesson 50. Scale factor

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Lesson 51. Scale factor

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Lesson 52. Scale factor

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Lesson 53. Scale factor

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Lesson 54. Scale factor

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Lesson 55. Problems 1  2  3  

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13. Use measures such as miles per hour to analyze and solve problems.

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Lesson 56. Problems

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Lesson 57. Unit rate problems

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Lesson 58. Problems

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Lesson 59. Problems

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Lesson 60. Problems   Part 2

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Assessment

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CSET Math Subtest II Geometry & Measurement Questions: 12-13, 18, and 19.

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Good multiple choice items for review: Work through problems that deal with geometry and measurement.

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NY Grade 3 State Test Questions

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NY Grade 4 State Test Questions

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NY Grade 5 State Test Questions

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NY Grade 6 State Test Questions

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NY Grade 7 State Test Questions

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NY Grade 8 State Test Questions

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Good constructed response items: 

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  • Access the Mathematics Assessment Project website. Work through problems from the Grades 6 & 7 Tests for Middle School that deal with the measurement and geometry domain. You may also access the summative tasks page if you want to solve more problems.  

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