directed number grid

this task is from Martin Wilson, in Harrogate
as he says, it's good for practice of directed number addition and subtraction because sometimes you are developing the grid forwards and sometimes backward
fibonacci like

a ppt is here

algebra can be used to explain a general rule

square fitting

interestingly, there are other representations

the smallest square filled with 21 squares of different sizes, discovered by AJW Duijvestijn in 1978 according to David Wells (in 'Curious and Interesting Geometry') is shown below

• the littlest square is 2 by 2
• the next littlest is 4 by 4
• the next littlest is 6 by 6
• and the next littlest is 7 by 7

what must each other size of square be?

a related task is to fit together squares with Fibonnacci numbers as the dimensions of their sides:

see also some work on expressions

fibonacci - going through

fibonacci patterns

fibonacci in nature

I'm not a huge fan of digging out maths from nature but this is a great little video

produced by Cristobal Vilo

fibonacci trapeziums (trapezoids)

how many triangles in the trapeziums?

how do these relate to the Fibonacci sequence?

does this pattern continue?

why is that?