1. Geom etry M ., Ani P
., &
. , Daisy
A shley E
Ge rald B.,
T.
Ra mman

2. Introduction
A key benefit to studying geometry is that it develops
spatial sense, or the ability to mentally visualize
objects and spatial relationships. People with good
spatial sense are able to use geometric ideas to
describe analyze their world. Spatial sense is best
developed by consistent participation in rich
experiences with shape and spatial relationships.
Over time, these experiences lead to a heightened
ability to articulate and appreciated geometric ideas
in art, nature and architecture.

3. Big Ideas
• What makes shapes alike and different can be determined by
geometric properties. For example, shapes have sides that are
parallel, perpendicular, or neither; they have line symmetry,
rotational symmetry, or neither; they are similar, congruent, or
neither.
Shapes can be moved in a plane or in space. These changes can
be described in terms of translation (slides), reflections (flips),
and rotations (turns).

4. Geometric Properties

5. Example of Teaching and Learning for
Geometric Properties

6. Translation, Reflection, & Rotation

7. Example of Teaching and Learning for
Translation, Reflection, and Rotation

8. Third Big Idea

9. Example of Teaching and Learning for Third
Big Idea

10. Appl
et #1
Tessellation Creator
• A tessellation is a repeating pattern of polygons
that covers a plane with no gaps or overlaps.
This applet is a virtual interactive program which
allows for the manipulation of various polygons.
These shapes can be rotated and placed in a
workspace to form tessellations.
• http://illuminations.nctm.org/ActivityDetail.aspx?ID=202
• Reviewed by Ramman Turner, Gerald Bolden
and Ashley Echang

11. How the applet works…
• Click-and-drag the shapes from the top menu to the
canvas below. If the sides of shapes are dragged close
to each other, those shapes will snap together. Click-
and-drag a rectangle around a group of shapes to glue
them together. Use the scroll bars along the right side
and bottom of the canvas to view different parts of the
canvas. Use buttons on the left sidebar to erase, rotate,
copy, separate or color the polygons. There are also
buttons for zooming in and out as the pattern grows.

12. Analysis

13. Evaluation of Applet
See criteria on pages 120 and 121 of EMSM

14. A Problem-Based Task
• Task: What shapes tessellate? If shapes can be
combined to make patterns that repeat and cover
the plane, then they tessellate. What patterns can
you find?
• Connection to the standards and/or big ideas:
This task is connected to Big Ideas #2: Shapes
can be moved in a plane or in space. These
changes can be described in terms of
translations, reflections, and rotations.

15. Questions to Ask to Assess and Advance
Student Thinking
• Launch (Task Set-Up):
Which of the shapes tessellate by themselves? Can you cover the plane
with just triangles? just squares? just pentagons?
• Explore (During Task Implementation):
Try to find a way to make a tessellation with just squares and octagons.
Which other combinations of shapes tessellate? Which of the shapes
tessellate by themselves? Find out all of the regular polygons that will
tessellate with themselves.
• Summarize (As students share findings, strategies, reasoning,
etc.):
Is there a way to tell if shapes with tessellate by looking at the properties
of those shapes? How? Hint: The length of the sides of all the shapes are
all the same. Only the angles are different. What are the angles in each

16. App
let #
2
Applet Name
Give picture and brief description of the Applet
Put link for applet and who reviewed the Applet

17. How does the Applet work?

18. Analysis of Applet
Strengths and Weaknesses

19. Evaluation of Applet

20. A Problem-Based Task

21. Questions to ask to Assess and Advance
Student Thinking

22. Online Reflection Questions

23. National Standards by Grade
Our groups first standard
K-2 standard
3-5

24. National Standards by Grade
Our second standard
K-2
3-5

25. National Standards by Grade
Our third standard
K-2
3-5