Joanne has taught middle school and high school science for more than ten years and has a master's degree in education.
By the end of this lesson, students will be able to:
- name and recognize the three different types of symmetry: reflection, rotational, and point
- identify a shape's line of symmetry
- identify a shape's order of rotation
- create an image with point symmetry using graph paper
- Copies of the quiz that accompanies the video lesson
- Construction paper with various polygons printed on it, one for each student
- Shapes should include an equilateral triangle, isosceles triangle, scalene triangle, square, rectangle, parallelogram, rhombus, pentagon, and hexagon
- 8.5 x 11 inch sheets of graph paper, folded or marked to show the four quadrants
- 8.5 x 11 inch sheets of white paper
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
- Line symmetry
- Line of symmetry
- Rotational symmetry
- Point symmetry
- Watch the video What is Symmetry in Math? - Definition & Concept. Have students take notes on important vocabulary terms, pausing as necessary to answer questions and clarity concepts.
- After the video, review the vocabulary terms with the class.
- Hand out copies of the quiz that accompanies the video. Have students work in pairs to complete the quiz.
- Distribute the materials and have students cut out each of the polygons.
- Have students fold the shapes in half to find the lines of symmetry.
- Are there any shapes that are asymmetric? How can you tell?
- Which shapes have more than one line of symmetry? How many do they have?
- For rational symmetry, have students choose four or five of the shapes (for example, the equilateral triangle, the scalene triangle, the square, the parallelogram and the hexagon). Students should then make a mark on one side of each shape to represent the 'top' of that shape. Then have students trace each of the shapes onto a piece of white paper.
- Have students place one of the shapes into its tracing, the 'top' side pointing up. If they are able to rotate the shape and have it 'fit' into back into its tracing before it turns all the way around, then the shape has rational symmetry. The amount of times that the shape 'fits' during one rotation represents that shape's order. Have students repeat this process for the other shapes.
- Which shapes show rotational symmetry? Which do not?
- For the shapes that do show rotational symmetry, what are their order of rotations?
- Finally, students will use their triangle to practice point symmetry. Ask students to trace the triangle into Quadrant I of their graph paper, ensuring that each point is at an intersection of the grid.
- Show students how to find the corresponding points in Quadrant III to show point symmetry. Have students graph the new image.
- Have students continue working with the graph showing point symmetry. This time, using rotational symmetry, graph the pre-image into Quadrants IV and II. Point out to students that point symmetry is the same as rotational symmetry of the 2nd order.
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