Secondary Mathematics II
Educational Links

Strand: GEOMETRY - Geometric Measurement and Dimension (G.GMD)

Explain volume formulas and use them to solve problems (Standards G.GMD.1, 3).

Standard G.GMD.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. Informal arguments for area formulas can make use of the way in which area scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k² times the area of the first. Use dissection arguments, Cavalieri's principle, and informal limit arguments.

• Area of a circle
  This purpose of this task is to develop an understanding of the formula for the area of the circle.
• Calculating Volumes of Compound Objects
  This lesson unit is intended to help educators assess how well students solve problems involving measurement.
• Circle Problems - Radius, Diameter, Circumference and Area
  This lesson asks students to calculate problems involving the radius, diameter, circumference and area of circles.
• Cylinders and Prisms
  Students will look at prisms and cylinders and measure their surface areas and volumes in this lesson.
• Module 7: Circles from a Geometric Perspective - Student Edition (Math 2)
  The Mathematics Vision Project, Secondary Math Two Module 7, Circles: A Geometric Perspective, is composed of four learning cycles. In the first learning cycle, students use rotations and perpendicular bisectors to find the center of a circle. The second learning cycle in Module 7 builds on the circle relationships that students have learned so far in the module to develop a formula for the perimeter and area of a regular polygon. The third learning cycle addresses relationships among central angles, radii, arcs, and sectors. Students calculate arc length and the area of a sector. The final learning cycle in Module 7 is an intuitive approach to volume of prisms, pyramids, and cylinders.
• Module 7: Circles from a Geometric Perspective - Teacher Edition (Math 2)
  The Mathematics Vision Project, Secondary Math Two Module 7, Circles: A Geometric Perspective, is composed of four learning cycles. In the first learning cycle, students use rotations and perpendicular bisectors to find the center of a circle. The second learning cycle in Module 7 builds on the circle relationships that students have learned so far in the module to develop a formula for the perimeter and area of a regular polygon. The third learning cycle addresses relationships among central angles, radii, arcs, and sectors. Students calculate arc length and the area of a sector. The final learning cycle in Module 7 is an intuitive approach to volume of prisms, pyramids, and cylinders.
• Student Task: Bestsize Cans
  In this task, the student must design a cylindrical drink can that uses the least aluminum for a given volume of drink
• Student Task: Funsize Cans
  In this task, students must design a cylindrical drink can that uses the least aluminum for a given volume of drink.
• Student Task: Glasses
  In this task, students will find the volumes of different shaped drinking glasses.
• Student Task: Propane Tanks
  In this task, students must work out how much you need to change the radius of a propane gas tank in order to double its capacity.
• Volume formulas for cylinders and prisms
  The goal of this task is to establish formulas for volumes of right prisms and cylinders.
• Volume of a Special Pyramid
  The goal of this task is to calculate the volume of a particular pyramid with square base, which is easily reasoned by viewing it as one sixth of a cube.

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http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

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