Number sequences - drawing a diagram
From the book: "Draw a diagram that shows how the sequence of odd numbers can be used to produce the sequence of squares. The diagram can contain numbers, addition symbols, equal signs, and arrows, but it should not contain any words. Your goal is to draw the diagram so that anyone who knows how to add whole numbers can look at it and see the relationship between the numbers in the two sequences."
1, 3, 5, 7,... The sequence of odd numbers
1, 4, 9, 16,... The sequence of squares
Here is my answer. What do you think? Is this a clear diagram? Would you have done it differently?
Second part makes sense, but first part less clear
Those are interesting diagrams. I also think it is a good example of what CaptainBlack was trying to describe with his diagram. Is there a page of text accompanying your diagrams? I understand some parts of it, but some parts of it are difficult to understand -- particularly the equations surrounding the first diagram, such as 1/2n(n+1), 2n+1, etc. I understand that n=5, but for instance, if 2n+1=11, I don't understand how that answer relates to the rest of the diagram.
Unfortunately, I don't think I could have used symbols and squares such as these to illustrate my diagram. The book only wanted the diagram to contain numbers, addition symbols, equal signs, and arrows. Furthermore, the diagram needed to be understandable for a very general audience, "anyone who knows how to add whole numbers" according to the book, and "anyone who can look at it and see the relationship between the numbers in the two sequences." If more symbols were allowed, perhaps my attached diagram would be clearer?