Florida B.E.S.T. MA.912.GR.6.5
The Standard
Apply transformations to prove that all circles are similar.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students map one circle onto another with a translation and a dilation. They identify the centers, radii, and scale factor, then explain why the transformation sequence shows similarity.
What Mastery Looks Like
- Given any two circles, a student can translate one center onto the other and dilate by the ratio of the radii. The student explains why the sequence maps every point on one circle to the other.
Common Misconceptions
- Students may think circles with different radii are not similar because they are not congruent. They may reverse the radius ratio or claim that a translation changes a circle's size.
How to Assess It
- Give Circle A with center (2, -1) and radius 3, and Circle B with center (-4, 5) and radius 7. Ask students to name a transformation sequence mapping A onto B and justify the scale factor.
Lesson moves
Ways to Teach It
On grid paper, students draw two circles, translate one center onto the other, then dilate using the ratio of their radii.
Ask students to write: Why are circles with radii 3 and 8 similar but not congruent?
Give teams transformation cards and circle cards, then have them race to match each circle pair with a valid translation and dilation.
Compare two printed versions of one circular logo, then calculate the scale factor from their diameters and explain why shape is preserved.
Free download
Printable MA.912.GR.6.5 Worksheet
A ready-to-print activity worksheet aligned to MA.912.GR.6.5, 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 worksheetKeep exploring
Related Standards
- MA.912.GR.2
Apply properties of transformations to describe congruence or similarity.
- MA.912.GR.6
Use properties and theorems related to circles.
- MA.912.GR.2.8
Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.
- MA.912.GR.2.9
Justify the criteria for triangle similarity using the definition of similarity in terms of non-rigid transformations.
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.