Virginia SOL 7.MG.4.a
The Standard
Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been dilated. Scale factors are limited to 1 4 , 1 2 , 2, 3, or 4. The center of the dilation will be the origin.
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 multiply each vertex’s x-coordinate and y-coordinate by the same scale factor. They plot the new vertices and connect them in corresponding order.
What Mastery Looks Like
- Students correctly multiply both coordinates of every vertex by the given scale factor. They plot and connect the image accurately, including when coordinates are negative or the scale factor is a fraction.
Common Misconceptions
- Students may add the scale factor instead of multiplying. They may multiply only one coordinate or treat one-half and one-fourth as enlargements. Negative coordinates often cause sign errors.
How to Assess It
- Exit ticket: Dilate triangle A(2, 4), B(6, 2), C(4, 8) by a scale factor of one-half. List the image coordinates and label the result an enlargement or reduction.
Lesson moves
Ways to Teach It
On a taped coordinate grid, place counters at polygon vertices, then move each counter along its origin ray using a scale-factor card.
Write and defend a coordinate rule for dilation, then explain how a fractional scale factor changes a polygon’s size and location.
Play a matching game with cards showing preimage coordinates, scale factors, and image coordinates, with students forming correct sets.
Resize a simple pixel-art logo on a coordinate grid, using a scale factor of two or one-half and recording every new vertex.
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Related Standards
- 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.b
Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been reflected over the x- or y-axis
- 8.MG.3.a
Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated vertically, horizontally, or a combination...
- 8.MG.3.c
Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated and reflected over the x- or y-axis or ref...
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