Here are some exercises/puzzles for ESL kids to learn the following science/math/geometry ideas. You will not be able to do all 7 puzzles in one 50 min. class.

Introduce the following terms, new vocabulary. They take a while to explain to young 11 year olds but they catch the idea if teacher demonstrates.

upsidedown or inverted
reflected
clockwise (like a clock)
90 degrees (180 etc.)
bilateral (2-sided) symmetry like a split fish.
radial (as in radius) symmetry like the sun
vertical symmetry (up and down direction)
horizontal (as in horizon) symmetry
symmetry, symmetric, symmetrical (forms of the same word) Explain the sym part of the words if you wish. It is Latin and means together. Introduce the concept of mirror image.

Teacher can demonstrate these symmetries by cutting a banana and orange, apple etc. A banana is bilaterally symmetric through the vertical plane but not through the horizontal. The same is true of an apple as they both have a distinctive top and base. You can make disc sections of banana and these discs roughly show radial symmetry like most circular and round objects. Use a cucumber if not a banana.

Question 1. What capital letters, and numbers from 1 or 9, are vertically bilateral? You can phrase this differently by asking, "Which letters and numbers are mirror images (copies) if reflected or sliced down the middle?"

Answers: Withhold these from the students. Let them work them out. This is a good group work or homework exercise as long as all children understand the task from your class introduction.

0 1 and 8 are all bilaterally symmetric if cut vertically (simple form of 1, a simple stroke)

A H I M O T U V W X Y are the correct answers.

Question 2. Which numbers and letters show bilateral symmetry if cut horizontally? Students will be faster at this exercise and will work very fast to compete and finish.

Answers: 0 1 3 8
B C D E H I K O X

Question 3. What numbers and letters are radially symmetric? They can be cut through any radius.

Answers: Only zero and the letter O.

Note that N and Z and X can be split or reflected in some sections but not all radial sections unlike round and circular objects. Even a disc that is half white and half black cannot be sectioned or reflected equally in all radial lines. Draw this on the board and show the kids.

Question 4. Which letters remain the same when they fall over clockwise 90 degrees? Answer: Only O and X. And which letters form a different letter? Answer: H becomes I, N becomes Z and Z becomes N.

Question 5. Which small letters (in lower case) have a tail? The answer is q y p g. This question may not have much to do with symmetry but is important to note because when learning the alphabet many children do not draw the tail below the line, the correct traditional form. Instead children often try to cram the letters with tails on one line. This bad habit comes from some kids following some printed fonts which have this distortion. In the same vein some children try to use this printed aaaaaaaa instead of the simpler one.

Question 6. Which letters and numbers when inverted (turned upsidedown) remail the same? Answer: the number 0 1 3 8 and letters B C D E H I K O X. (Note that 6 become 9 but not vice versa)

Question 7. One final note. Ask the class if the letter S can be cut into two symmetrical halves. From the earlier exercises the answer is No but if the S were made of bread it could be cut through the edge like a bagel or doughnut making two halves. This is true for all the letters and numbers as they can all be sliced in the plane facing us, the plane of the page.

You can finish the class by reviewing the key words again and quizzing the kids orally or by giving them the chalk at the board. Then ask them about the symmetry of other objects in their world like people, houses, trees, a pencil. People are externally vertically symmetric but not when we look inside at the organs.

These lessons or puzzles in geometry and technical words will help kids think in different planes. Introduce the term plane if you feel like it and look for good planar illustrations for the class. Many children know how to draw in 3-D while others do not. Ask them how they do it and give them the chalk or marker to show the class. Teacher can get this started. The whole class runs better if kids are asked the puzzles above and individuals come up and draw answers on the board. This is group learning, in fact whole class learning.

Copyright: Robin T. Day August 16, 2008. Written in Ecuador.