MP6 – Mapping a Figure Onto Itself

21 Sep

How do you provide your students the opportunity to practice I can attend to precision?

Jill and I have worked on a leveled learning progression for MP6:

Level 4:

I can distinguish between necessary and sufficient language for definitions, conjectures, and conclusions.

Level 3:
I can attend to precision.

Level 2:
I can communicate my reasoning using proper mathematical vocabulary and symbols, and I can express my solution with units.

Level 1:
I can write in complete mathematical sentences using equality and inequality signs appropriately and consistently.


Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Our learning intention for the day was I can map a figure onto itself using transformations.

Performing a [sequence of] transformation[s] that will map rectangle ABCD onto itself is not the same thing as describing a [sequence of] transformation[s].

1 Rectangle 1.gif

2 Rectangle 2.gif

We practiced both, but we focused on describing.


I asked the student who listed several steps to share his work.

  1. rotate rectangle 180˚ about point A
  2. translate rectangle A’B’C’D’ right so that points A’ and B line up as points B’ and A. [What vector are you using?]
  3. Reflect rectangle A”B”C”D” onto rectangle ABCD to get it to reflect onto itself. [About what line are you reflecting?]

5 Screenshot 2016-08-29 09.14.58.png

What if we want to carry rectangle ABCD onto rectangle CDAB? How is this task different from just carrying rectangle ABCD onto itself?


What about mapping a regular pentagon onto itself?

8 09-21-2016 Image008.jpg

Many students suggested using a single rotation, but they didn’t note the center of rotation. How could you find the center of rotation for a single rotation to map the pentagon onto itself?

9 Screenshot 2016-08-30 17.08.44.png

This student used the intersection of the perpendicular bisectors to find the center of rotation, but didn’t know what angle to use for the rotation. How would you find an angle of rotation that would work?

10 Screenshot 2016-08-31 09.10.36.png

What can you do other than a single rotation?

11 Screenshot 2016-08-30 17.09.12.png

12 Screenshot 2016-08-30 17.09.04.png

This student reflected the pentagon about the perpendicular bisectors of one of the side of the pentagon.

13 Screenshot 2016-08-31 09.10.59.png

The descriptions students gave made it obvious that we needed more work on describing. The next day, we took some of the descriptions and critiqued them. Which students have attended to precision?



It’s good work to distinguish precision from knowing what someone means as we learn to attend to precision. And so the journey continues …

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Posted by on September 21, 2016 in Geometry, Rigid Motions


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