Multiple Methods

Hope you all had a great week, I thought it will be a good idea to describe part of my first day of masters. For those of you that don’t know, I have started my Master in Education ( PGDE for Secondary Teacher – Mathematics) and I enjoy it so far, even if it is extremely tiring. In the future I will write more about my experiences and knowledge gained at this program.

An interesting thing about this master is the fact that there is one course per semester for everyone, doesn’t matter if they what to be an English teacher, a math teacher or a geography teacher. In this course everyone learns general things about the Scottish Educational System and some things about child psychology and development. One of the first courses was about different methods a child understands, perceives and solves a problem in general. As an easy example they have used a math problem. Here is the problem:

Find the number of  orange squares from the following image: 


It is quite important to try and solve it by yourself before reading further. The answer is not extremely important, but just for your peace of mind the answer is 36. The interesting part comes next. The teacher asked the audience ( us, approx 200 students) to explain HOW we did it. After approximately half an hour we got to 5 different interesting methods (thought I believe there are more). And I wanted to share them with you:

1. 10 x 2 + 8 x 2 = 36 and here is the drawing/diagram for easy understanding:

border-problemt9t7i border-problemt9t7i7u65

2. 9 x 4 = 36 with the diagram:


3. 8 x 4 + 4 = 36 with diagram:


4. 4 x 10 – 4 = 36 with the following diagram:


5. 10 x 10 – 8 x 8 = 100 – 64 = 36 this method is all about areas: they did the area of the whole grid ( 10 x 10 ) and subtracted the area of the white part ( 8 x 8 ).

I have found the exercise extremely interesting and I enjoyed hearing everyone explaining their method. As a math lover this was wonderful. Let me know in the comment box bellow which of the above methods you have used when you solved the problem yourself, just in case you want to know I have used method 1. If you did it differently, let me know. 

Thank you for reading. Hope you enjoyed it. And for those interested, please don’t forget about my new project:

The project is called “Math Class Everywhere” and the idea is to describe a math class from different countries in the world. Thus I am looking for people from as many countries as possible to describe their experience in a math class. Everything will be anonymous and I don’t want to criticize things, just to describe and understand different countries’ concepts about teaching mathematics. If you would like to get involved let a comment bellow or send me an email at It would be wonderful if you would like to help ^_^

Thank you for your help and support. Have a wonderful weekend. You can find me on FacebookTumblr, Google+,  TwitterInstagram and Lettrs, I will try to post there as often as possible. Don’t forget that maths is everywhere! Enjoy! 

4 thoughts on “Multiple Methods

Add yours

  1. I used the second method (9*4). If there were less squares in the line I would probably use the method 4 but when I had to count the number of squeres (didn’t see 10 at the moment I looked at the main square), I knew that I have to count one less and multiply it four times. But yes the article is very nice and I enjoyed reading it.

    Liked by 1 person

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