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MP6 – Mapping a Parallelogram Onto Itself

22 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.

CCSS G-CO 3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

We continued working on our learning intention: I can map a figure onto itself using transformations.

Perform and describe a [sequence of] transformation[s] that will map parallelogram ABCD onto itself.

21 09-21-2016 Image009.jpg

22-screenshot-2016-08-31-10-01-1823-screenshot-2016-08-31-10-01-25

This task also requires students to practice I can look for and make use of structure. What auxiliary objects will be helpful in mapping the parallelogram onto itself?

The student who shared her work drew the diagonals of the parallelogram so that she could use the intersection of the diagonals as the center of rotation.

24 Screenshot 2016-08-31 09.13.49.png

Then she rotated the parallelogram 180˚ about that point.

25 Screenshot 2016-08-31 09.13.54.png

Could you use only reflections to carry a parallelogram onto itself?

You can. How can you describe the sequence of reflections to carry the parallelogram onto itself?

26 09-21-2016 Image001.jpg

How else could you carry a parallelogram onto itself?

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Posted by on September 22, 2016 in Geometry, Rigid Motions

 

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