Quarter 4, Week 1: March 19th – 23rd

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TeacherFelicia Taylor
Subject AreaGeometry Honors
Grade Level8th
Week #28
Unit of Instruction8: 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)
Additional Resources

Nearpod:

  1. Geometry Nets and Three-Dimensional Figures Notes – Nearpod Code: BLFXE
  2. Cavalieri’s Principle of Area and Volume Notes – Nearpod Code:  ATQHE
  3. Volume of Prisms and Cylinders Notes – Nearpod Code:  EYUMR

Geometry Nation Videos:

  1. Section 14, Topic 1:  Geometry Nets and Three-Dimensional Figures
  2. Section 14, Topic 2:  Cavalieri’s Principle for Area
  3. Section 14, Topic 3:  Cavalieri’s Principle for Volume
  4. Section 14, Topic 4:  Volume of Prisms and Cylinders