TEKS Math 8.3.C
The Standard
use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students represent a dilation from the origin with the rule (x, y) → (kx, ky), where k is a positive rational number. They use the rule to explain how the coordinates, side lengths, size, and orientation change.
What Mastery Looks Like
- A student writes the rule (x, y) → (kx, ky) and uses it to find every image coordinate. The student explains that lengths change by k while angle measures and shape stay the same.
Common Misconceptions
- Students may multiply only one coordinate or add the scale factor instead of multiplying. They may also think a factor between 0 and 1 creates a reflection or changes angle measures.
How to Assess It
- Give students triangle A(2, 1), B(4, 1), C(2, 3) and scale factor 1/2. Ask for the rule, image coordinates, and one sentence describing the change.
Lesson moves
Ways to Teach It
Plot a triangle on graph paper, then multiply each coordinate by 3/2 and connect the image points with a different color.
Ask students to explain in writing why a scale factor of 1/4 shrinks a figure without moving the center of dilation.
Run a card sort matching original coordinates, scale factors, algebraic rules, and image coordinates.
Use a digital photo grid to model enlarging or reducing an image, then connect pixel coordinates to the rule (x, y) → (kx, ky).
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Printable 8.3.C Worksheet
A ready-to-print activity worksheet aligned to 8.3.C, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 8.3.B
compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane
- 8.3
The student applies mathematical process standards to use proportional relationships to describe dilations
- 8.10.C
explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes o...
- 8.3.A
generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation
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