There is no escape...believe it or not. Mathematics is everywhere.
Please write your ideas for introducing Geometry. I am interested in knowing some activities for initiating a lesson.
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My favorite "first day of geometry" activity is an investigation of polyominos. A polyomino is a two-dimensional shape formed by joining congruent squares edge-to-edge. The most trivial polyomino consists of just one square (it's called a monomino), and a polyomino consisting of two squares is called a domino. There is only one way to place two congruent squares together (2-D, edge-to-edge, no overlapping of interior points). Some students will probably look at two squares arranged "left and right", and another two squares arranged "top and bottom" and say "but these are different"...but they are not (those two arrangements are congruent). The question that drives this investigation is "how many different polyonimoes can you make out of 3-squares? 4 squares? 5 squares? n-squares?" These polyonimos are called the triominos, the tetronimos, and the pentominoes respectively. Solomon Golomb (a math professor at the University of Southern California) "invented" these polyominos when we was a high school students back in the 1950's. Try this investigation...it works for students of all ages and all ability levels.
If you use equilateral triangles rather than squares, the resulting shapes are called poly-iamonds (so, a shape made of two triangles is called a diamond, and so forth...).
Hands on way is to use surgical tube and dowls. or pencils.
In terms of instructions, I first make sure that students understand the definition of polyomino (the figures are all two-dimensional, the squares are all congruent, the squares can only be joined edge-to-edge). Then I ask them to make as many different triominos (3 squares) as they can. Students can use graph paper to record their results, and I have also had them use square pattern blocks and small square pieces of paper as manipulatives. Square Post-it notes ("sticky notes") work very well on the blackboard...students can place them on the board and them move them around to form new shapes.
Rashmi Kathuria said:
This is a good resource. What instructions did you give to students?
I found the best way to to teach is giving reason and room for the student to learn.
Without a reason, where is the value, why learn. where is the fun, alienation sets in
Without room to learn, students fight for freedom and empowerment, alienation sets in
When cruel is fun, alienation is in full swing.
When learning is fun, a self motivated student exists.
Rashmi, all of geometry seems to go back to the circle. I start with the circle and introduce it as unity (Whole) as well as a unit. Then we explore that properties of a 3-D circle by observation; not from books that only talk about circles as a symbol and a 2-D construction devise. We discover the dynamics of the circle and a number of basic geometry concepts and relationships from over 120 to be discovered in the first fold in half. Older students should know the vocabulary (good review to see if they are making the connections of what they know to what is in their hands) and with younger students (1st grade up ) you can introduce vocabulary to talk about what they are discovering through their own observations of what they are doing.
We do not understand folding circles and the information that is generated since we have a great deal of trouble seeing mathematics unless it is in a traditional and recognizable symbolic form, and that means drawing pictures of circles, not folding them. There is always amazement, at all ages, when students and teachers are folding circles seeing how easy all of these mathematical concepts and ideas are generated and that all the traditional constructions forms are inherent in the circle but not discernible from images or by cutting polygon pieces. This is fun because you are doing it for yourself not from a book written by, or a hands on exercise developed by, or something discovered a long time ago by... someone else. Folding circles requires a shifting from parts-to-whole thinking to a Whole-to-parts approach, in which we have no experience or tradition. Folding circles to learn serious math makes no sense as a concept; only when experiencing the folding do we begin to understand the depth and breath of the educational value of a simple paper circle and what a principled, sequential and consistent process of folding can reveal.
If you go to my website there is some basic folding instructions. that way you and your students can check it out:
http://www.wholemovement.com/index.php?option=com_content&view=...
Brad
Thanks Brad for this idea. In my Math lab class, students used circular paper plates for making icosahedron. It helped in creating interest in students for exploring and learning geometry. Also, students applied various geometry facts in making such objects.
Have you prepared some instruction sheets or hand outs for students? Pls share.
A colleague of mine (Warren Williams) recently had his geometry class carry out an activity that helped his students review for a final exam while having fun. The students were placed in small groups, and each group was asked to take pictures (using their cell phone cameras) of "geometric objects in the real world". Once each group had gathered a dozen or so images, they imported them into a PowerPoint presentation for the rest of the class.
Students took pictures of hubcaps on cars, windows, manhole covers, street lights, parts of buildings, fences, fire hydrants, telephone poles, flag poles...they surprised themselves at how much geometry was in the world around them.
I liked this activity for several reasons. It was open ended, it took geometry out of the textbook and into the world of the students, and it was very student centered. I'll try this with my class next year.
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