One of the most challenging aspects of the New York State Geometry curriculum is the unit of Volume of different solid shapes. Students generally struggle with the proper use of the dimensions of the shapes and struggle with visualizing a three-dimensional shape on a two-dimensional piece of paper. This unit will explore the many different solid shapes that can be found in the real world. Similarly, you will gain a better understanding of the meaning of volume. By clicking on each tab (Formula, Area, Rect./Cube, Cylinder, Pyramid, Cone, Sphere, Final), you will be given an opportunity to explore each type of shape, the make-up of the shape, manipulate the dimensions of the shape, and consider what happens to the volume of each of the shapes as the dimensions change. Each tab is it’s own lesson EXCEPT for Vocab. The Vocab. tab is a tab where definitions are given to students. Short assignments will be assigned to monitor your skills and developement of understanding of volume. Your grade will be posted in SKEDULA as they are assigned and collected. Each student has their own personal Skedula account and can receive help from UAM guidance counselors if needed.
Steps For Each Lesson
The first lesson is under the "Formulas" tab. Student’s should watch first watch the Voki if one is present. This Voki will provide instructions as to the next steps. There will also be "Steps", where specific instructions will be given as to how to complete the lesson. There will be links to take you to the activity or assignment. These links will all be highlighted in the color light blue and will be underlined.
The specific standards that will be covered are highlighted in bold text and listed below.
G.G.11 - Know and apply that two prisms have equal volumes if their bases have equal areas and their altitudes are equal
G.G.12 - Know and apply that the volume of a prism is the product of the area of the base and the altitude
G.G.13 - Apply the properties of a regular pyramid, including: lateral edges are congruent; lateral faces are congruent isosceles triangles; volume of a pyramid equals one-third the product of the area of the base and the altitude
G.G.14 - Apply the properties of a cylinder, including: bases are congruent; volume equals the product of the area of the base and the altitude; lateral area of a right circular cylinder equals the product of an altitude and the circumference of the base
G.G.15 - Apply the properties of a right circular cone, including: lateral area equals one-half the product of the slant height and the circumference of its base; volume is one-third the product of the area of its base and its altitude
G.G.16 - Apply the properties of a sphere, including: the intersection of a plane and a sphere is a circle; a great circle is the largest circle that can be drawn on a sphere; two planes equidistant from the center of the sphere and intersecting the sphere do so in congruent circles; surface area is 4π r2; volume is 4/3 π r3
This reference sheet will be useful and is given to you on the NYS Geometry Regents Exam and also has it’s own tab labeled "Formulas". This is your first lesson and the starting point of this course.
There are multiple different assignments per lesson. The activities will serve as your participation grade while the assignments will serve as your Classwork. All assignments and activities a will have either a link to a blog, discussion board, a print out, or quiz/exam. These links will all be highlighted in the color light blue and will be underlined. All assignments which require e-mail should be sent to LazStamatis@gmail.com. All students will use VoiceThread, Wordpress, and Eyejot plus will need access to internet and a scanner/camera. Listed below are the assignments:
Assignment 1: "Formulas"
Assignment 2: "Area"
Assignment 3: "Volume of Rectangular Prism and Cube"
Assignment 4: "Volume of a Cylinder"
Assignment 5: "Volume of a Pyramid"
Assignment 6: "Volume of a Cone"
Assignment 7: "Volume of a Sphere"
Assignment 8: "Final Exam"
I would like to give a special thank you to three people who have helped me through out the creation of this course. Prof. Sistek-Chandler has aided the development of my website and critiqued my course to help improve the overall product. Mr. Paulo Fonseca for editing and aiding the development of my website and capstone. Finally, Mrs. Meg Johnson for checking the content of the course for accuracy and quality.