We used the 5 X 5 ones for investigating possible squares:
How many differentsized squares are there? At first noone could find any other square than these ones:
Then I gave a clue: I twisted my board round 45°. Immediately, lots of the class saw some others:
and then we went home. It was only when I was checking out a book by Caleb Gattegno, who invented and popularised the geoboard, that I realised we'd all missed a few more. Can you see what they are?
To answer that question, we can label the pegs like I did with Year 5. Then we can name the square by the letters at the four corners:
A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

and, most interesting...
If the smallest square of nails has an area of 1, what is the area of the other squares?
We also asked the same questions of the triangles possible on the 3 X 3 geoboard (there are more).
That bottom right triangle, what is its area? How do you work that out?
Different students had different methods.
Here are some students talking about their thinking:
One pupil made an observation on method. She said, "If you don't know how to do something, split it into bits." Useful advice in this case.
If the smallest square of nails has an area of 1, what is the area of the other squares?
That bottom right triangle, what is its area? How do you work that out?
Different students had different methods.
Here are some students talking about their thinking:
One pupil made an observation on method. She said, "If you don't know how to do something, split it into bits." Useful advice in this case.
Great stuff  We are so used to using dynamic geometry for this stuff, that I have forgotten the physical advantages of the geoboard. Actually having to put the rubber band around the point does change this a little I think. Thanks for the post!
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