MAFS.912.G-GMD.1.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)
MAFS.912.G-GMD.1.3: MODELING STANDARD Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
MAFS.912.G-GMD.2.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
|Learning Targets and Learning Criteria|
- identify the base for prisms, cylinders, pyramids, and cones.
- calculate the area of the base (B) for prisms, cylinders, pyramids, and cones.
- calculate the volume of a prism using the formula V = Bh and the volume of a cylinder V = πr2h, where B is the area of the base and h is height of the solid.
- defend the statement, “The formula for the volume of a cylinder (or cone) is basically the same as the formula for the volume of a prism (or pyramid).”
- explain that the volume of a pyramid (or cone) is 1/3 the volume of a prism (or cylinder) with the same base area and height. (Demonstrate rule for students, for example with liquids or bird seed.)
- use Cavalieri’s Principle to demonstrate that a right prism (or cylinder) and a slanted prism (or cylinder) have the same volume when the base areas and heights are the same.
- calculate the volume of a cylinder, pyramid, cone, and sphere and use the volume formulas to solve problems.
- find the volume when one or more dimensions are changed.
- identify the shapes of the two-dimensional cross-sections of three-dimensional objects.
- rotate a two-dimensional figure and identify the three-dimensional object that is formed.
- Complete the “Doodle Notes” pages (2) on Volume of Prisms in the envelope you picked up. In order to do this, go onto Gradebook and open the Answer Key file which is attached to the Volume of Prisms notes assignment. Use the first page to fill in the notes (first page). Then try the “Your Turn” page on your own and then check with the answer key. Please put these in your ISN as page 50 (both pages). (20 minutes)
- Complete the “Doodle Notes” page on Volume of Cylinders, Cones, and Spheres–only the Cylinder part for today because it goes with prisms. Again, you will find the answer key file in Gradebook attached to the Volume of Cylinders Notes assignment–do the same as above. These two pages will also go in your ISN as page 52–yes, I know I skipped page 51 (that will be on Tuesday). (10 minutes)
- Do IXL T.5 (Volume of Prisms and Cylinders) (30 minutes)
- Complete the “Doodle Notes” pages (2) on Volume of Pyramids. Again, in Gradebook, attached to the assignment Volume of Pyramids Notes, you will find the answer key. Use it to copy notes on the first page, then try the practice (Your Turn) on the second page and then check your answers on the answer key. Please put these two pages in your ISN as page 51. (20 minutes)
- Complete the Cone Part of the Volume of Cylinders, Cones, and Spheres (that you started already). (10 minutes)
- Do IXL T.6 (Volume of Pyramids and Cones) (30 minutes)
- All Geometry classes will have a Zoom meeting with Ms. Andreason at specific times listed below to discuss upcoming course work and procedures. You can go to the Zoom website (https://zoom.us) or download the free Zoom app on your phone, click on Join a Meeting and type in the meeting ID (7580487309)–you will use this same meeting ID every time we meet! You can connect through audio only if you don’t want to be on video. (40 minutes)
- Third period Geometry will meet from 10:00 am to 10:40 am
- Fifth period Geometry will meet from 11:00 am to 11:40 am
- Eighth period Geometry will meet from 12:00 noon to 12:40 pm
- Students will then watch the following video: https://www.youtube.com/watch?v=hlD_j3AtxGs (if this doesn’t work, go to Youtube and type in Math Shorts Episode 8 – Slicing Three Dimensional Figures) (the video is only a minute and a half long)
- Students will then do IXL H.4 and IXL H.5 (15 minutes)
- Today you are going to do a tutorial lesson on CPalms called “I Scream! You Scream! We All Scream for… Volume!” by going to the following (copy and paste into browser): https://www.floridastudents.org/PreviewResource/StudentResource/119329 (50 minutes)
- Complete the Sphere part of the Doodle Notes on Volume of Cylinders, Cones, and Spheres (10 minutes)
- Please place the copies of the handwritten notes in your ISN: Surface Area and Volume of Spheres will be page 53 and Surface Area Help will be page 54.
- Please do the worksheet: Volume of Rectangular Pyramid. You must write down what you multiplied clearly on the paper next to the figure–e.g. V = 1/3(13)(6)(14). That is your “work” and then put your answer in the space provided. (30 minutes)
- Please do the worksheet: Volume-Cone. Follow same directions as above. (30 minutes)
- Please take a picture of these two worksheets and share with me on Remind.
- IXL T.5 due by Friday, April 3.
- IXL T.6 due by Friday, April 3.
- “I Scream! You Scream! We All Scream for… Volume!” due by April 3.
- “Ninja Nancy Slices” due by April 3.
- IXL H.4 due by Friday, April 3.
- IXL H.5 due by Friday, April 3.
If you have questions, please message me on Remind and we will figure out the best way to get you help (message, phone call, Zoom meeting)! You are NOT alone!! We are in this together!!