MMA.MATH.6.B

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) #dok2
  • apply (concepts of surface area and volume to real-world fields) #dok3
Learning Targets
  • I can identify a scale factor between two similar objects. #dok1
  • I can define proportional and non-proportional changes in geometric contexts. #dok1
  • I can use a scale factor to calculate surface area and volume for two-dimensional and three-dimensional objects. #dok2
  • I can analyze how changes in dimensions affect surface area and volume proportionally and non-proportionally. #dok2
  • I can model real-world situations where scale factors impact area and volume, such as in engineering or architecture fields. #dok3
  • I can justify whether changes in measurements lead to proportional or non-proportional changes in surface area and volume. #dok3
Big Ideas
  • Changing the scale of an object does not always result in proportional changes to both its surface area and volume.
  • Understanding the effects of scale factors is essential for real-world applications in architecture, engineering, and other fields.
Essential Questions
  • How does using a scale factor to change the dimensions of an object affect its surface area and volume?
  • What is the difference between proportional and non-proportional changes in geometric measurements?
  • In what real-world situations do scale factors play a critical role in design and analysis?
  • Why is it important to understand how scale factors influence surface area and volume in fields like engineering or architecture?
  • How can you determine whether a change in dimensions will result in a proportional change in surface area or volume?