How to Teach Congruence and Similarity
From second grade through sixth grade, elementary school students learn about congruent and similar shapes during math class. Math Open Reference defines congruent as "similar in size and shape" and similar as "the same shape, but can be different sizes." The article "Manipulatives: A Hands-on Approach to Math" shares results from a study which suggests that "spectacular results can be achieved when learning is taken off the chalkboard and literally put into the hands of the learners themselves." Use hands-on math manipulatives to teach the concepts of congruent and similar to elementary students.
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Things You'll Need
- Ruler
- Protractor
- Glue stick
- White softball
- Sheet of paper
- White baseball
- Overhead projector
- Transparent protractor
- Color pencils or markers
- 2 sheets white tag board
- 2 star shapes, different sizes
- Softball or baseball that isn't white
- Packets containing various similar and congruent geometric shapes
Instructions
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Hold up a baseball and a softball. Ask your students to tell you how the two balls are alike. Lead them in a discussion to determine that they have the same shape but are different sizes or similar. Hold up another ball, either a baseball or a softball but of a different color, with the matching white ball. Ask your students how the two balls are alike. Direct them to the idea that the two balls have the same shape and size during your discussion. They are congruent. Ask your students to give other examples of similar and congruent shapes. Write their correct answers on the chalkboard.
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Give your students two star patterns of different sizes and two sheets of white tag board. Label one paper "Congruent" and the other paper "Similar" with the color pencils. Ask them to draw shapes that demonstrate the name on the tag board. Do a visual check as the students work. Hang the tag boards from their desks or on the wall to remind them of the difference between congruent and similar.
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Give each student a packet of geometric shapes. Match the congruent shapes. Match the similar shapes. Glue the pairs to a sheet of paper and label each pair with the appropriate name.
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Teach older students to create similar and congruent shapes. Give them one shape with the angles and lengths named. Use an overhead projector and a transparent protractor and show them how to create similar and congruent copies of a triangle. Ask students to copy what you are doing on their own paper with their own protractors. Have students practice with other different shapes, including a different triangle.
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Tips & Warnings
Students benefit by having an understanding pf the sliding, rotating, reflecting and flipping of shapes before congruent and similar lessons.
Create more examples of similar by copying a picture on the copier. Set the machine to increase or decrease the size of the picture and make a second copy.
Create more examples of congruent by making to exact copies of the same item.
References
- Photo Credit coloured shapes image by Leslie Batchelder from Fotolia.com
