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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use a scale factor to predict a segment's length after a dilation. They compare corresponding lengths and explain the relationship using multiplication and ratios.
What Mastery Looks Like
- Given a segment length and scale factor, students can calculate the image length. From two corresponding lengths, they can find the scale factor and identify an enlargement, reduction, or unchanged image.
Common Misconceptions
- Students may add the scale factor to a length instead of multiplying. They may reverse the image-to-original ratio or think a factor below 1 produces a negative length.
How to Assess It
- Give this exit ticket: A 12 cm segment becomes 7.5 cm after dilation. Find the scale factor and state whether it is an enlargement or reduction.
Lesson moves
Ways to Teach It
Use grid paper and a chosen center to dilate a 6 cm segment by 1.5, then measure its image.
A student says a scale factor of 0.4 shortens every segment by 0.4 unit. Write a correction using an example.
Play matching cards: pair original lengths and scale factors with image lengths, then justify each match with an equation.
Compare a map distance with its enlarged photocopy, calculate the copy's scale factor, and predict another enlarged distance.
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Printable HSG-SRT.A.1b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-SRT.A.1b, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSG-SRT.A.1
Understanding dilations by center and scale factor supports seeing every segment length multiply by that scale factor.
- CCSS.Math.Content.7.G.A.1
Scale drawings give practice using scale factors to make lengths proportional, which carries directly into dilation changing segment lengths by a ratio.
- CCSS.Math.Content.7.RP.A.2
Scale factors use ratio reasoning from proportional relationships to describe how dilated segment lengths compare to original lengths.
Keep exploring
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.
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