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.
Lesson 1. Triangles Part 1 Part 2
Lesson 2. Quadrilaterals Part 1 Part 2 Part 3
Lesson 3. Polygons Part 1 Part 2
Lesson 4. 3 D Figures Part 1 Part 2 Part 3 Part 4 Part 5
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
Lesson 6. Similar Figures Part 1 Part 2 Part 3 Part 4
3. Identify different forms of symmetry, translations, rotations, and reflections.
Lesson 7. Symmetry Part 1 Part 2 Part 3 Part 4 Part 5
Lesson 8. Translation Part 1 Part 2 Part 3 Part 4
Lesson 9. Rotation Part 1 Part 2 Part 3 Part 4 Part 5
Lesson 10. Reflection Part 1 Part 2 Part 3 Part 4
4. Understand the Pythagorean theorem and its converse.
Lesson 11. Pythagorean Theorem Part 1 Part 2 Part 3 Part 4
Lesson 12. Converse of Pythagorean Theorem Part 1 Part 2 Part 3
Lesson 13. Proofs of Pythagorean Theorem Part 1 Part 2 Part 3
Lesson 14. Problems Part 1 Part 2 Part 3 Part 4
5. Work with properties of parallel lines.
Lesson 15. Parallel Lines
Lesson 16. Parallel Lines
Lesson 17. Parallel Lines
Lesson 18. Problems Part 1 Part 2 Part 3 Part 4 Part 5
Lesson 19. Interior Angle Sum of a Triangle Theorem Part 1 Part 2 Part 3
Lesson 20. Exterior Angle of a Triangle Part 1 Part 2 Part 3 Part 4
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
Lesson 22. Problems
Lesson 23. Problems
Lesson 24. Problems
Lesson 25. Problems
Lesson 26. Problems Problems 2
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
Lesson 27. Nets Part 2 Part 3 Part 4 Part 5 Part 6 Part 7
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
Lesson 32. Problems
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
Lesson 34. Measuring angles Part 1 Part 2 Part 3 Part 4
Lesson 35. Perimeter of polygons Part 1 Part 2 Part 3
Lesson 36. Area of polygons Part 1 Part 2
Lesson 37. Surface area of 3D objects Part 1 Part 2 Part 3
Lesson 38. Volume of Solids Part 1 Part 2 Part 3 Part 4
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
Lesson 40. Metric Conversion Areas and Volumes Part 1 Part 2 Part 3 Part 4
Lesson 41. Dimensional Analysis Part 1 Part 2 Part 3 Part 4
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
Lesson 43. Perimeter problems Part 1 Part 2 Part 3 Part 4 Part 5 Part 6
Lesson 44. Area formulas Part 1 Part 2 Part 3
Lesson 45. Area problems Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7 Part 8
Lesson 46. Surface area formulas
Lesson 47. Surface area problems Part 1 Part 2 Part 3 Part 4 Part 5 Part 6
Lesson 48. Volume formulas
Lesson 49. Volume problems Part 1 Part 2 Part 3 Part 4 Part 5
12. Relate proportional reasoning to the construction of scale drawings or models.
Lesson 50. Scale factor
Lesson 51. Scale factor
Lesson 52. Scale factor
Lesson 53. Scale factor
Lesson 54. Scale factor
13. Use measures such as miles per hour to analyze and solve problems.
Lesson 56. Problems
Lesson 57. Unit rate problems
Lesson 58. Problems
Lesson 59. Problems
Assessment
CSET Math Subtest II Geometry & Measurement Questions: 12-13, 18, and 19.
Good multiple choice items for review: Work through problems that deal with geometry and measurement.
NY Grade 3 State Test Questions
NY Grade 4 State Test Questions
NY Grade 5 State Test Questions
NY Grade 6 State Test Questions
NY Grade 7 State Test Questions
NY Grade 8 State Test Questions
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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Access the Illustrative Mathematics Project website. Open the Content Standards page. Open the Grades 1-5 Geometry and Measurement & Data pages and the Grades 6-8 Geometry page and solve the tasks associated with the measurement and geometry content standards.