Transcript Lesson plan - chessboard problems (Powerpoint 2.2 Mb)

No of
aliens
Number
of
fingers
Number
of toes
Number
of legs
Number
of ribs
Number
of arms
1
2
3
4
5
6
7
8
9
10
Now to write the formulae!
Write formulae to show the number of each body part on n
aliens.
Copy and complete the following...
Fingers on n aliens = 6n
Toes on n aliens =
Legs on n aliens =
Ribs on n aliens =
Arms on n aliens =
How many squares can you find on a
chessboard?
Working systematically....
64
1 x 1 squares
49
2 x 2 squares
Can you see any
patterns?
PROVE that you are right!
Walt:
Explore different possibilities in order to solve
a problem.
Use our knowledge of the properties of
number in order to solve problems.
Use a symbol to stand for an unknown
number.
We found there are 204 squares
on a chessboard where the
length of
one side is 8 squares (8 x 8).
Imagine a new chessboard has been invented that has a
length of 25 squares (25 x 25).
How many squares are there in this new chessboard?!
Length of one
side (x)
1
2
3
4
5
6
7
8
9
10
Total number of
individual (1 x
1)squares
Total number of
squares (n)
Imagine your data is like a function machine.
Where... x = length of one side
n = total number of squares
You know the input (x) and the output (n), but what is happening in the function machine?
Can you spot any patterns in your data to help you solve the problem? Use your knowledge of the
properties of numbers to help you.
n = x(x +1)(2x +1)
6
n = total number of squares
x = length of one side
Can you work out from this the total number
of squares in a chessboard measuring 25 x
25 squares?