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Symmetry

Here are several websites where kids can learn about symmetry interactively.  They include line symmetry, rotational symmetry, reflection, and congruency.  There are also detailed instructions for activities kids can do to practice using symmetry, such as origami and snowflake construction.
 
 
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Author/Host of Website BBC Schools
Type of Educational Content Website
Visit the website: BBC Bitesize Symmetry
Free
Grade Level Elementary (K-5)

BBC Bitesize Symmetry offers lessons, examples and practice for elementary age children in reflection and rotational symmetry.

 
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Author/Host of Website BBC Schools
Type of Educational Content Website
Visit the website: BBC Symmetry
Free
Grade Level Middle (6-8)

Here is a review (revision), activity and test on the concepts of line symmetry, regular polygons and rotational symmetry.  The activity interactive includes options for sound and subtitles.

 
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Author/Host of Website E-Lab/Harcourt School Publishers
Type of Educational Content Website
Visit the website: Bisecting Figures
Free
Grade Level Elementary (K-5)

From site: You will use a line of symmetry to bisect plane figures. You will discover that a line of symmetry has many important properties.

 
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Author/Host of Website Eric Mueller/Howe-to Software
Type of Educational Content Website
Visit the website: Drawing with Symmetry
Free
Grade Level Middle and High (6-12)

Students can increase their understanding of reflective, inverse and rotational symmetry by using the Drawing with Symmetry applet to draw using an X / Y axis plane.

 
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Author/Host of Website Annenberg Media
Type of Educational Content Website
Visit the website: Geometry Session 7: Symmetry
Lesson Plans or Teacher Info
Free
Grade Level Middle and High (6-12)

From site:  Symmetry is one of the most important ideas in mathematics. There can be symmetry in an algebraic calculation, in a proof, or in a geometric design. It's such a powerful idea that when it's used in solving a problem, we say that we exploit the symmetry of the situation. In this session, you will explore geometric versions of symmetry by creating designs and examining their properties.

 
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Author/Host of Website Dorsey, Hanifl, Kannel & Thomson
Type of Educational Content Website
Visit the website: Introduction to Symmetry
Lesson Plans or Teacher Info
Free
Grade Level Middle and High (6-12)

From site:  This site is designed for students and teachers interested in exploring symmetry (grades 7-12). It contains lesson plans, definitions, examples, activities, and links to other web sites. There are also some extension activities for those who would like a little challenge.

 
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Author/Host of Website Science U/Geometry Technologies
Type of Educational Content Website
Visit the website: Kali: Symmetric Sketching
Free
Grade Level Elementary and Middle (K-8)
Pick a color, pick a pattern, and draw your own symmetrical pattern.
 
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Author/Host of Website LINKS Learning
Type of Educational Content Website
Visit the website: Line Symmetry
Lesson Plans or Teacher Info
Parent/Guardian Information
Free
Grade Level Elementary (K-5)

This is an introduction to line symmetry.  It makes extensive use of graphics and pictures to illustrate the concepts.  The concepts include lines of symmetry and reflection, congruency, horizontal line, diagonal line, and vertical line symmetry.

This interactive introduction is useful for homeschooled students.  It's also helpful for students who missed the lesson on line symmetry in school, or didn't understand it when first presented.  It provides questions at the end to check for understanding, but it doesn't provide extended practice.

 
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Author/Host of Website Daniel & Jeanine Meyer
Type of Educational Content Website
Visit the website: Mathematical Thinking Through Origami
Lesson Plans or Teacher Info
Free
Grade Level All Ages (K-12)

From site:  On this site, we offer general and specific strategies for using activities based on origami to invoke mathematical thinking. Origami refers to the Japanese art of paper folding. Background is given on origami, including the development and critical aspects of the practice of origami in the United States. Next, we indicate how origami can relate to the current goals of K-12 mathematical education. General strategies are described that can be applied to any origami model. The basic strategy is for students to do the teaching. Then we describe in detail a variety of models. The examples include a variety of different computer-based techniques that students and hobbyists at all levels can use.

 
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Author/Host of Website Michael LaFosse/Peabody Essex Museum
Type of Educational Content Video
Visit the website: Polar Origami
Grade Level All Ages (K-12)

Polar Origami offers a series of 2-5 minute videos showing how to fold a variety of origami creatures.  The instructor tells a story that accompanies each creature while he is making it.

 
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Author/Host of Website HMH School Publishers
Type of Educational Content Website
Visit the website: Show Me Line Symmetry
Free
Grade Level Elementary (K-5)

This is a brief narrative demonstration of line symmetry and questions asking students to identify lines of symmetry in a few figures.

 
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Author/Host of Website Joe Edkins/demon.co.uk
Type of Educational Content Website
Visit the website: Symmetrical Patterns Online
Free
Grade Level Elementary and Middle (K-8)

From site:  This website is about symmetry. It has a couple of exercises for learning about reflective and rotational symmetry, and some examples to practise identifying symmetry. It also lets you design symmetrical picture online. It uses JavaScript to do this. This means that your finished symmetrical picture is not a conventional picture, so you can't save or print it in the normal way.

There are two simple exercises for learning about reflective and rotational symmetry. In each, you choose a shape (rotational) or letter (reflective) and think about whether it has the right sort of symmetry. Then you test it. The rotational symmetry page rotates the shape. If it isn't rotationally symmetrical, then it will be a different shape after being rotated. The reflective page draws a line, horizontal and vertical, rubs out half the chosen letter, and mirrors the remaining half the other side of the line. If it looks the same as the original letter, then it must have that sort of symmetry.

There is a page of examples of symmetry. They are small symbols and pictures of many different types of symmetry, and when you click on one, it tells you what the symmetry is. Like the exercises described above, it's best to think before clicking what the symmetry is, and then see if you're right. There are a couple of traps! To be truly symmetrical, the whole of the picture or symbol must rotate or reflect, and the colours must be the same.

 
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Author/Host of Website Jo Edkins
Type of Educational Content Website
Visit the website: Symmetry
Lesson Plans or Teacher Info
Free
Grade Level Elementary (K-5)

There are explanations of reflective and rotational symmetry, activities for practice identifying symmetry and activities for children to make their own symmetrical objects, including snowflakes.  For teachers, there is advice on using the exercises, and tips on downloading and printing the children's creations.

 
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Author/Host of Website Textile Museum/Math Forum @ Drexel
Type of Educational Content Website
Visit the website: Symmetry and Pattern of Oriental Carpets
Lesson Plans or Teacher Info
Free
Grade Level All Ages (K-12)

From site:  ORIENTAL CARPETS have long been appreciated for their beauty. That beauty is achieved through the choice of colors and designs, as well as by the manipulation of designs and colors to form pleasing patterns.

Patterns in Oriental carpets are never quite what you expect - a surprise here, a flourish there, a change of color, the flip or rotation of a design where you might not predict it. The more you look, the more variations you will find.

How can we explain this phenomenon? Is it the result of human choice, or human error?

The study of symmetry offers one approach to analyzing patterns in Oriental carpets. Through symmetry analysis we may identify areas of pattern that exhibit expected repetitions, and areas that vary from that expectation.

 
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Author/Host of Website Jill Britton
Type of Educational Content Website
Visit the website: Symmetry and Tessellations
Lesson Plans or Teacher Info
Free
Grade Level Elementary and Middle (K-8)
The author of "Investigating Patterns: Symmetry and Tessellations" offers dozens of activities in learning symmetry that correspond to her book.  Some of the areas explored are symmetry in the alphabet, inversions, faces, flags, quilts, rotation symmetry in hubcaps, tangrams, geometry and kirigami, shmuzzle puzzles and, of course, tessellations.  Try Activity 2, Photo Activity for Symmetry (in faces) -- what fun!
 
 
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LearningReviews.com is a directory of mostly free interactive K-12 educational resources for parents, teachers and students.  Fee-based resources included here are award-winning or highly rated by education and parent organizations.