CCSS.Math.Content.HSG-SRT.A.1b
The standard
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Common Core State Standards for Mathematics · Understand similarity in terms of similarity transformations
What this standard means
Students need to understand that a dilation changes the length of a segment by multiplying it by the scale factor. If the scale factor is greater than 1, the image is longer. If it is between 0 and 1, the image is shorter. They should connect the picture, the measurements, and the multiplication.
Mastery looks like measuring or calculating an original and image segment, then explaining the scale factor in words and numbers. Students often get stuck when the center of dilation is not on the segment, or when a fraction scale factor feels like division instead of multiplication.
Ways to teach it
- Have students draw a segment on grid paper, choose a center, dilate both endpoints by scale factors 2 and 1/2, then measure both images.
- Ask students to explain why a scale factor of 3/4 makes every segment shorter, using a labeled diagram and one sentence.
- Show three original and image segment pairs, then have students find the scale factor and flag the one with an incorrect length.
- Use a phone map zoom example, where students compare a 2 cm road segment before and after zooming by a scale factor.
Plan a lesson for CCSS.Math.Content.HSG-SRT.A.1b
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Related standards
- CCSS.Math.Content.2.MD.A.4
Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
- CCSS.Math.Content.8.G.A.1a
Lines are taken to lines, and line segments to line segments of the same length.
- CCSS.Math.Content.HSG-SRT.A.1a
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- CCSS.Math.Content.HSG-SRT.A.1
Verify experimentally the properties of dilations given by a center and a scale factor: