Virginia SOL 7.MG.4.c
The Standard
Identify and describe dilations in context including, but not limited to, scale drawings and graphic design.
Virginia Standards of Learning for Mathematics · The student will apply dilations of polygons in the coordinate plane.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether one polygon is a scaled copy of another in a drawing or design. They describe the scale factor and explain what changes and what stays the same.
What Mastery Looks Like
- Students recognize when a figure has been resized proportionally. They identify the scale factor and explain how corresponding lengths change while angle measures and overall shape stay the same.
Common Misconceptions
- Students may treat a dilation as adding the same amount to every side instead of multiplying by one scale factor. They may confuse a stretched image with a proportional resize. Some think dilations must enlarge figures or must be centered at the origin.
How to Assess It
- Exit ticket: A 3 cm by 5 cm logo becomes 7.5 cm by 12.5 cm. Is the change a dilation? Find the scale factor and justify.
Lesson moves
Ways to Teach It
Plot a triangle on grid paper, dilate it from the origin by a factor of 2, then measure and compare corresponding sides.
Show one proportionally resized logo and one stretched logo; ask students to write which is a dilation and support their choice with ratios.
Run a card sort matching original polygons, resized images, scale factors, and written descriptions of the changes.
Use a 1:50 classroom floor plan; students calculate actual wall lengths and explain how the scale factor connects the drawing to the room.
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Related Standards
- 7.MG.2.h
Apply proportional reasoning to solve problems in context including scale drawings. Scale factors shall have denominators no greater than 12 and decimals no les...
- 7.MG.4.b
Sketch the image of a dilation of a polygon limited to a scale factor of 1 4 , 1 2 , 2, 3, or 4. The center of the dilation will be the origin.
- 8.MG.3.g
Identify and describe transformations in context (e.g., tiling, fabric, wallpaper designs, art).
- 7.MG.4
The student will apply dilations of polygons in the coordinate plane.
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