Florida B.E.S.T. MA.912.GR.4.3
The Standard
Extend previous understanding of scale drawings and scale factors to determine how dilations affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students determine how a dilation changes area, surface area, and volume. They connect a linear scale factor to squared measures and cubed measures.
What Mastery Looks Like
- Students use the square of the scale factor for area and surface area, and the cube for volume. They can work backward from an area or volume ratio to find the linear scale factor.
Common Misconceptions
- Students often multiply area, surface area, or volume by the linear scale factor. They may also confuse the square and cube relationships or apply scaling to only one dimension.
How to Assess It
- Give this exit ticket: “A solid is dilated by a scale factor of 3. State the factors for surface area and volume, and explain why.”
Lesson moves
Ways to Teach It
Use centimeter cubes to build 2-by-3-by-4 and 4-by-6-by-8 prisms, then compare surface area and volume.
Write and defend a rule for how doubling every length changes area, surface area, and volume.
Sort cards showing scale factors, area ratios, surface-area ratios, and volume ratios into matching sets.
Enlarge a 1:20 packaging prototype by a factor of 1.5, then calculate changes in cardboard use and capacity.
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Printable MA.912.GR.4.3 Worksheet
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Related Standards
- MA.912.GR.4.4
Solve mathematical and real-world problems involving the area of two-dimensional figures.
- MA.6.GR.2
Model and solve problems involving two-dimensional figures and three-dimensional figures.
- MA.7.GR.1.5
Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.
- MA.8.GR.2.2
Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship.
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