From zero to infinity

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from zero to infinity-min

Students hold an impression that Math facts and getting the correct answers is the essence of Mathematics. This has given birth to the idea that a fast recall of Math facts means that one is strong in the subject. We need to learn that there can be many different ways to get the solution and there can be even more than one solution! And from mistakes we can learn even more. Maybe textbooks have too many tasks showing one way to get one solution.

I have used the following example for the teachers during their in-service course and the target audience was Grade 5 students. I have a string that is tied to a loop. I asked four students in front of the class, each to keep it so that they are forming a rectangle. At the same time we talked together what are the qualities of a rectangle. Then I asked them to shape another rectangle. And third one! What is the perimeter of these rectangles? Students easily say – they have same length of perimeter. I asked them to form a new rectangle. Usually this is the moment when students begin to think, wonder if there can be more?

Someone from class may shout that form a square! And they begin to talk if square is a rectangle. Asking again to form a new rectangle they get excitedand always in the end they say regardless of the age that there are huge amount of rectangles. If the word infinity is not familiar, it is time to take it to use and also show how it is marked in Mathematics.

Of course it is good to have every now and then problems which have none, zero, two or more or even infinity amount of solutions. two students are working together. You present the students with a question (here task 1). Give them a brief amount of time to reflect and formulate their answer alone (one minute or so). Ask the students to pair up. Ask students to share their responses with one another. Experience showed that students manage well in task 1 and enjoy to share their findings with one 

Too often the teacher asks questions and only some students to raise their hands to answer. Then when the teacher asks them a question several students become disengaged. In this mode of instruction, the lesson becomes a dialogue between the teacher and a few pupils. In following exercises you can also use pair-share method,

where another. In task 2, they are very likely in need of each-other. They find solutions by using lines. Their mind can be fixed sharing the square with the line. If the pair finds only a couple of solutions you may form a group of four with two pairs. Most likely they discover to also use curve and polyline. Of course they can find solution also with line!

Tas k1. Divide a square into identical parts as many possible ways as
you can manage. For example:
Into three identical parts, using two lines. How many solutions you find?
Into four identical parts, using two lines. How many solutions you find?
Task2. Divide a square into two identical parts.
In task 2 the answer is infinite amount of solutions. It is essential to see
the center of the square and the symmetry of dividing lines go through
the center of the square.
When they study functions and equations they have problems which have
more than one solution. It is important to show that in Maths there can
be problems with variety of amount of solutions – just as in life.