MMA.MATH.7.D

Use scale factors with two-dimensional and three-dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields.

Mathematical Models with Applications · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
scale factorstwo-dimensional objectsthree-dimensional objectsproportional changesnon-proportional changessurface areavolumefields
Skills
  • use (scale factors with two-dimensional objects) #dok2
  • use (scale factors with three-dimensional objects) #dok2
  • demonstrate (proportional changes in surface area and volume) #dok2
  • demonstrate (non-proportional changes in surface area and volume) #dok3
  • apply (concepts of surface area and volume to real-world fields) #dok3
Learning Targets
  • I can identify scale factors for two-dimensional and three-dimensional objects. #dok1
  • I can describe proportional changes in surface area and volume resulting from scale factors. #dok2
  • I can apply scale factors to calculate new surface areas and volumes of scaled objects. #dok2
  • I can demonstrate non-proportional changes in surface area and volume compared to the original objects. #dok3
  • I can analyze and interpret the effects of scaling on surface area and volume in real-world contexts. #dok3
Big Ideas
  • Changing the scale of two- and three-dimensional objects affects their surface area and volume, and these changes are not always proportional to the scale factor.
  • Understanding how surface area and volume change with scaling has practical applications in various real-world fields, such as art, design, and engineering.
Essential Questions
  • How do scale factors affect the surface area and volume of two-dimensional and three-dimensional objects?
  • What is the difference between proportional and non-proportional changes in surface area and volume when scaling objects?
  • Why do changes in surface area and volume not always match the scale factor applied to the object's dimensions?
  • In what real-world situations is it important to understand the effects of scaling on surface area and volume?
  • How can we use mathematics to predict the outcomes of scaling in various applied fields?