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G-3D-1-2

Page history last edited by Brenda Butz 6 years, 2 months ago

G.3D.1.2 Use ratios of similar 3-dimensional figures to make conjectures, generalize, and to solve for unknown values such as angles, side lengths, perimeter of a face, area of a face, total surface area,and volume of the solids.


In a Nutshell

Similar 3 dimensional objects have certain relationships.  The corresponding side lengths are proportional.  The corresponding faces are similar.  The corresponding angles are congruent.  The ratio of the total areas of two similar solids is the square of the scale factor.  The ratio of the volumes of two similar solids is the cube of the scale factor.  All spheres are similar.

Student Actions

Teacher Actions

  • Develop deep and flexible conceptual understanding: Students will identify similar solids and use the relationships between them to solve problems.

  • Develop accurate and appropriate procedural fluency: Students will square the ratios of the side lengths to find the ratio of the areas of two similar solids and cube them to find the ratio of the volumes. Likewise students will take the cube root of the volumes to find the scale factor (ratio of side lengths).

  • Develop the ability to make conjectures, model, and generalize: Students will examine diagrams of solids and decide if they are similar. If two objects are similar, students will solve real world problems concerning surface area and volume.
  • Teachers will implement a variety of tasks involving real-world situations to promote reasoning and stimulate student problem solving.

  • Teachers will use and connect mathematical representations by providing many varied diagrams of solids for students to interpret.

  • Teachers will pose purposeful questions that require students to think about their world and applications of surface area an

Key Understandings

Misconceptions

  • Students understand how to use the various formulas for surface area and volume and the concepts of similarity to solve real world problems.

  • Students understand the relationships present in congruent or similar objects and can use those relationships to determine useful information about other figures or objects.

  • Students understand how to start with the formula for volume or surface area and solve for a missing dimension in a solid figure.

  • Students use the ratio of perimeters to solve for surface area or volume

  • Students cannot grasp that a pizza with a diameter that is twice the length of another has four times the area.

  • Students do not understand the difference in ratios of similar figures (perimeter, surface area and volume)

  • Students are not able to plug values into the formulas to solve for a missing value such as length, height, radius, etc.

OKMath Framework Introduction

Geometry Grade Introduction

 

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