What are Miras?
Miras are red plastic forms in the shape of a “T” or "I" and approximately 4 to 5 inches deep. The short length of the “T” is used for stability as the Miras are always laid on their side with the “T” shape both on the paper and pointing straight up. The Mira is then to the user’s perspective a large red pane which is transparent and tinted red. The Mira has a bevel on each long side of a single face of the large pane. Regardless of which edge the Mira has been laid on to view the pane the bevelled edge must face the user. The reason for this is because the Mira bends light. The bevel compensates for that bend as it meets the work surface during use. The Mira works much like a mirror but with the simultaneous advantage of being able to see through. The result is being able to map one image over another. This is the basic purpose and use of the Mira, the true depth of conceptual ability the Mira provides is in how it is applied to a task.
How do Miras help students?
Miras help students in geometry with the concept of symmetry and reflections as a transformation in 2 two dimensional geometry. The Mira has the advantage over the mirror in that it allows students to continue to see their original image at all times. When using a mirror students lose sight of the complete original at whatever point they place the mirror. The Mira forces students to map one image over another to varied degrees but nevertheless, this mapping and moving of the Mira opens doors to conceptual understanding of reflections. Then once students understand how to use the Mira they are then able to go further by tracing their reflections. This is done by looking through the Mira and tracing the image in a surprisingly intuitive way. Once the Mira is removed the student as all of the components of the transformation left behind on paper.
How many are recommended?
When using Miras, given their size and range it is only beneficial if each student has their own. While cooperative learning can still utilize Miras, first each student needs to work with the tool to understand the concept at hand and then later combine their understanding with other students.
Sample Activities
1. Draw an image on your sheet. Using the Mira, reflect the image and draw what you see.
2. Using the Mira, draw the lines of symmetry of the following shapes: rectangle, parallelogram, hexagon, pentagon, circle, and a line.
3. Using the Mira and grid paper, draw a triangle anywhere on the sheet, making sure that the vertices of the triangle are situated on dots.
Draw a line anywhere on the sheet, and draw its reflection.
4. Which letters of the alphabet have lines of symmetry? Draw the lines of symmetry for each letter: A B C D E F G H I J K L M N O P Q R S T
U V W X Y Z.
5. How many designs can you create that have only one line of symmetry? Two? Three?
6. How many designs can you create that have no lines of symmetry?
7. Provide students with 3 x 3 grids. Students will colour in a few squares (not all), and make as many patterns with one line of symmetry.
8. How many different patterns can you make with one line of symmetry by shading in 3 small squares?
9. How many different patterns can you make with two lines of symmetry by shading in 4 small squares?
Recommended Websites
Reflections - http://mathforum.org/sum95/suzanne/rex.html
Symmetry and Congruence using the Mira - http://www.shawnee.edu/acad/ms/ENABLdocs/Summer08pdfs/MIRA%20Lesson%20Plan.pdf
Gains - http://www.edugains.ca/resourcesLNS/GuidestoEffectiveInstruction/GEI_Math_K-6_GeomSpatialSense_Gr4-6/Guide_Geometry_Spatial_Sense_456.pdf
Miras are red plastic forms in the shape of a “T” or "I" and approximately 4 to 5 inches deep. The short length of the “T” is used for stability as the Miras are always laid on their side with the “T” shape both on the paper and pointing straight up. The Mira is then to the user’s perspective a large red pane which is transparent and tinted red. The Mira has a bevel on each long side of a single face of the large pane. Regardless of which edge the Mira has been laid on to view the pane the bevelled edge must face the user. The reason for this is because the Mira bends light. The bevel compensates for that bend as it meets the work surface during use. The Mira works much like a mirror but with the simultaneous advantage of being able to see through. The result is being able to map one image over another. This is the basic purpose and use of the Mira, the true depth of conceptual ability the Mira provides is in how it is applied to a task.
How do Miras help students?
Miras help students in geometry with the concept of symmetry and reflections as a transformation in 2 two dimensional geometry. The Mira has the advantage over the mirror in that it allows students to continue to see their original image at all times. When using a mirror students lose sight of the complete original at whatever point they place the mirror. The Mira forces students to map one image over another to varied degrees but nevertheless, this mapping and moving of the Mira opens doors to conceptual understanding of reflections. Then once students understand how to use the Mira they are then able to go further by tracing their reflections. This is done by looking through the Mira and tracing the image in a surprisingly intuitive way. Once the Mira is removed the student as all of the components of the transformation left behind on paper.
How many are recommended?
When using Miras, given their size and range it is only beneficial if each student has their own. While cooperative learning can still utilize Miras, first each student needs to work with the tool to understand the concept at hand and then later combine their understanding with other students.
Sample Activities
1. Draw an image on your sheet. Using the Mira, reflect the image and draw what you see.
2. Using the Mira, draw the lines of symmetry of the following shapes: rectangle, parallelogram, hexagon, pentagon, circle, and a line.
3. Using the Mira and grid paper, draw a triangle anywhere on the sheet, making sure that the vertices of the triangle are situated on dots.
Draw a line anywhere on the sheet, and draw its reflection.
4. Which letters of the alphabet have lines of symmetry? Draw the lines of symmetry for each letter: A B C D E F G H I J K L M N O P Q R S T
U V W X Y Z.
5. How many designs can you create that have only one line of symmetry? Two? Three?
6. How many designs can you create that have no lines of symmetry?
7. Provide students with 3 x 3 grids. Students will colour in a few squares (not all), and make as many patterns with one line of symmetry.
8. How many different patterns can you make with one line of symmetry by shading in 3 small squares?
9. How many different patterns can you make with two lines of symmetry by shading in 4 small squares?
Recommended Websites
Reflections - http://mathforum.org/sum95/suzanne/rex.html
Symmetry and Congruence using the Mira - http://www.shawnee.edu/acad/ms/ENABLdocs/Summer08pdfs/MIRA%20Lesson%20Plan.pdf
Gains - http://www.edugains.ca/resourcesLNS/GuidestoEffectiveInstruction/GEI_Math_K-6_GeomSpatialSense_Gr4-6/Guide_Geometry_Spatial_Sense_456.pdf