ACTIVITIES TO INTRODUCE AND IDENTIFY THE TYPES OF SYMMETRY FOUND IN NATURE AND IN MATHEMATICAL SHAPES.
Zometool Kits (ARC)
Rectangular Hand mirrors
Overhead transparency sheets
Objects from nature with symmetry
Time needed –5 classes of approximately 45 mins.
Divide the class into teams of 3-4 students, and distribute Zome Kits and mirrors to each group. Introduce the students to the Zome pieces: struts come in three colors and each color has a particular hole it fits into on the nodes. Blue struts fit only into rectangular holes; yellow struts into triangular holes, and red struts into pentagonal holes. Making sure the strut goes all the way into its hole helps keep the model intact.
Allow students time to create with the Zome pieces. Ask each student to create a shape to begin the activity. When completed have them distinguish the difference between those that lie flat on the desk and those that rise above the desk surface. This will help them to understand 2 dimensional and 3 dimensional shapes. Introduce the word polygon, explaining that all the examples of 2D shapes in the classroom are polygons. Can anyone think of a 2D shape that would not be a polygon? (Circles) What do you think is the definition of a polygon?
Focus on an equilateral polygon created by a student yesterday or by yourself and ask students what makes it unique? Introduce the word equilateral. Have students return to their groups and ask each group create equilateral polygons with 3,4,5, and 6 sides.
To each shape’s correct name we can add the word equilateral because each of its sides is equal. Therefore we have created an equilateral triangle, an equilateral pentagon, an equilateral hexagon and a square.
Ask the students what they know about symmetry, and symmetrical. Discuss a definition and how we can tell if a shape or object has symmetry? Using their Zome shapes ask each group to investigate if the shape has a line of symmetry by using their mirrors. When the mirror is placed in position does its reflection complete the whole shape? Do any of the shapes have more than one line of symmetry? Have each group complete a chart from their findings using the headings:
TYPE OF POLYGON NUMBER OF SIDES NUMBER OF LINES
Do you see any pattern from your findings? (The number of sides and number of lines of symmetry will be the same.)
Natural objects or Pictures of natural objects on Transparency Sheets
Objects in nature often have lines of symmetry. In this activity we are going to check if shapes from nature have lines of symmetry. If an object has only one line of symmetry it is called bilateral. Divide students into groups. Distribute natural objects (shells, flowers, fruits, honeycomb, etc.) and hand mirrors to each group or copies of pictures of natural objects on transparency sheets. Pictures on overhead transparencies can be folded to test for symmetry or real objects can be tested using hand mirrors. Ask groups to chart their findings using the headings:
Object Bilateral Number of lines No symmetry
symmetry of symmetry
BOOK RESOURCE: The Butterfly Alphabet
WWW. LINKS: www.uea.ac.uk/edu/pgce/mball/symmetry.html
Today we are going to learn about a different type of symmetry. If an object or shape can be turned around a point a certain number of degrees and resemble its original shape it has rotational symmetry. Using two overhead transparency sheets, draw two equilateral triangles, one on each sheet, using different colored pens. Place the two triangles on top of each other on the overhead projector then rotate the top sheet till the triangle fits over the bottom one. CAN I ROTATE THE TOP TRIANGLE AGAIN AND HAVE IT REST ON TOP OF THE BOTTOM ONE? (Yes)
Repeat the procedure with an equilateral pentagon and hexagon. Can anyone name an object in nature that has rotational symmetry? Create a list of shapes in nature that have rotational symmetry. Have examples available.
DIVIDE THE CLASS INTO GROUPS OF 3-4. Have each group determine what capital letters of the alphabet have lines of symmetry or rotational symmetry. Chart their findings under the headings:
Letter No lines of symmetry Number of lines Rotational
of symmetry symmetry
Day 5 Computer Lab
The following is a site created by students to teach the different types of symmetry. It would be an excellent review of the week’s lessons on symmetry and has a valuable list of links, which provide an expanded understanding of symmetry.
Click on YEAR SIXES then the door to get to the lessons on symmetry.
The links can be access at the end of the lessons or at:
Activity 9 is another excellent review.
BOOK: Symmetry A Unifying Concept
By Istvan and Magdolna Hargittai
STANDARDS – Science and Technology
Students will communicate effectively in the applications of science and technology.
Funding for these lessons and materials which benefit the Area Resource Center were provided by the Colby Partnership for Science Education, the Howard Hughes Medical Institute, and Bell Atlantic.
Irene West China Middle School