This term our Maths Investigations have been focussed on
using arrays for multiplicative thinking (an array is a strategy for organising
countable units in large numbers and counting them efficiently). We have been using the ultimate array for this
investigation – a chess board!
The idea of the activity is to see how much of the 8 x 8
chess board can be covered by 1 queen.
How many squares can she cover?
What is the position that is most effective (covers the most amount of
squares)?
We discovered that you can cover a chess board entirely, all 64
squares covered, with only five queens!
We were then challenged to find out what the most amount of
squares that could be covered by 4, 3, 2 or 1 queen.
In week 5, we are looking at changing the board size (the
array size) and taking our investigation further onto "how many squares can be covered
by just one queen?". We have already
worked out the really easy ones …
On a chess board that is one by one, one queen can cover the
entire board (which is one square!) On a
two by two board, again, one queen can cover the whole board; in this case four
squares. When we first tried three by
three we thought that one queen covered seven squares. This was because we were still placing the
queen in the corner! Once we had
remembered that we could position the queen anywhere on the board we worked out
a way to cover the whole board, nine squares!
So the results so far are looking like this:-
|
Size
of the board
|
2 by 2
|
3 by 3
|
4 by 4
|
5 by 5
|
6 by 6
|
7 by 7
|
8 by 8
(Normal board)
|
|
Amount
of squares covered
|
4
|
9
|
12
|
17
|
20
|
25
|
28
|
Drawing the different sized boards for working out
A 5 by 5 board: one queen covers 17 squares
A 6 by 6 board; one queen covers 20 squares
Initially we thought one queen on a three by three board would cover seven
But we forgot we could move the queen! Nine covered this time!
No comments:
Post a Comment