# Quarter 4, Week 1: March 19th – 23rd

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Teacher Felicia Taylor Geometry Honors 8th 28 8: Three-Dimensional Measurements
Standard(s) Taught

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

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

I can:

• Volumes:
• 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.
Classroom Activities

Monday (2nd Period) / Tuesday (7th & 8th Periods)

• Go over Unit 8:  Three-Dimensional Measurements expectations, due dates, etc.
• Instruction:  Geometry Nets & Three-Dimensional Figures
• Quizlet Live – Geometry Nets & Three-Dimensional Figures Exit Ticket

Wednesday (All Classes – Early Release Day – 40 minute class)

• kahoot!  – Geometry Nets & Three-Dimensional Figures Bellringer
• Distribute Unit 8 Take Home Tests – Due in 3 weeks on Wednesday, April 11th
• Instruction:  Cavalieri’s Principle for Area and Volumes

Thursday (2nd Period) / Friday (7th & 8th Periods)

• Continue Instruction:  Cavalieri’s Principle for Area and Volumes
• Quizlet Live – Cavalieri’s Principle for Area and Volumes Exit Ticket
• Instruction:  Volume of Prisms and Cylinders
• Quizlet Live – Volume of Prisms and Cylinders
Assignments Due

Summatives

None

Formatives

1. Geometry Nets & Three-Dimensional Figures Exit Ticket –  due Monday, March 19th (2nd Period) / due Tuesday, March 20th (7th & 8th Periods)
2. Geometry Nets & Three-Dimensional Figures Bellringer – due Wednesday, March 21st
3. Cavalieri’s Principle for Area and Volumes Exit Ticket – due Thursday, March 22nd (2nd Period) / due Friday, March 23rd (7th & 8th Periods)
4. Volume of Prisms and Cylinders Exit Ticket – due Thursday, March 22nd (2nd Period) / due Friday, March 23rd (7th & 8th Periods)