Yakima WATERS Mini Lesson
Snowflake Symmetry
Targets and Assessment
WA Science Standards Addressed:
 6-8 INQC Recognize and interpret patterns
WA Math Standards Addressed:
 8.2.C Demonstrate that the sum of the angle
measures in a triangle is 180 degrees, and apply
this fact to determine the sum of the angle
measures of polygons & unknown angle
measures.
 8.2.D Represent & explain the effect of one or
more translations, rotations, or reflections of a
geometric figure on a coordinate plane.
Assessments:
 Students will demonstrate ability to find COR,
LOR, & BDE during powerpoint presentation
 Students will turn in the worksheets; and be
graded on accuracy
Lesson Parameters
Content Area: Pre-Algebra
Overview: Students will create snowflakes by cutting
square sheets of paper, then discover the rotations,
reflections, and translations of the Basic Design Element of
their original cuts.
Grade Level: 7-8
Suggested Time: Two 45 minute class periods
Special Materials:
 Powerpoint 2007, computer, projector, screen,
choice of meter stick, ruler or laser light
Learning Outcomes:
 Knowledge: Students will become more familiar with rotations, reflections, and translations in nature.
 Skill: Students will be able to locate and delineate the center of rotation (COR), line of reflection (LOR),
and basic design element (BDE) of a given object. Students will be able to compute the angle of
rotation.
Science/Math Concept Background: Spatial manipulation is an invaluable skill, yet one that is difficult to
translate into the classroom. This activity allows students to physically manipulate their snowflakes so that
they can more easily make the connection between reflections, rotations, and translations that only exist on a
two-dimensional plane to something that they can shape with their hands and physically experience the
reflection, rotation, and translation as they maneuver their snowflakes into position.
Materials: 7” X 7” square sheet of paper, scissors, 2 different colored pencils, ruler (materials are per student)
Procedure:
**Students should already have a basic knowledge of reflection, rotation, and translation.
1. Begin with the powerpoint presentation to gauge student familiarity with reflection, rotation, &
translation. Using a ruler, meter stick, or laser light, have students point out line of reflection, center
of rotation, & basic design elements as appropriate. While taking notes, students can also determine
angle of rotation for figures displaying rotational symmetry.
2. Hand out worksheets, using last powerpoint slide as an assessment of student understanding.
3. Many students will have made paper snowflakes in previous years. It is still a good idea to remind
them to fold in two different directions (horizontal/taco, vertical/hamburger) so that their BDE
repeats. Also, remind students to leave some portion of each of the edges uncut, so that snowflakes
remain intact and don’t fall apart.
4. For the translational symmetry section, look for simple repeating elements (triangles, circles, squares;
then work up to the BDE.)
5. Write, pair, share how different folds and BDE’s are exhibited throughout the classroom. Which are
the easiest to see reflection, rotation, and translation?
Key questions: Are there snowflakes that exhibit only reflection or rotation? Is it possible to exhibit
only one or the other? Why or why not?
Extension(s): Is there a relationship between the number of folds and the number of BDE’s repeated? What
about fold direction and rotation or reflection?
Teaching Tips: Help students to “see” reflection by folding snowflake in half in different directions along lines
of reflection. Help students to “see” rotation by having them rotate snowflakes on top of their outline
drawings, then note how far they have to rotate to get angle of rotation, or alternately, how many times the
snowflake lines up with the outline as they spin it 360°. (If it lines up 3 times, then 360÷3=120. Angle of
rotation = 120°).
Supplements:
See attached worksheet, and powerpoint presentation.
Author: Tiffany Bishop, Yakima WATERS Project, CWU, Winter 2011