Transcript Introductory PowerPoint

Finding position-to-term rules
Finding position-to-term rules
For the sequence:
5
9
13 17 21 ….
Finding position-to-term rules
For the sequence:
5
9
13 17 21 ….
Position number
1
2
3
4
5
Term
5
9
13
17
21
Finding position-to-term rules
For the sequence:
5
9
13 17 21 ….
Position number
1
2
3
4
5
Term
5
9
13
17
21
The rule for this sequence is
X4
Finding position-to-term rules
For the sequence:
5
9
13 17 21 ….
Position number
1
4
2
8
3
12
4
16
5
20
Term
5
9
13
17
21
The rule for this sequence is
X4
Finding position-to-term rules
For the sequence:
5
9
13 17 21 ….
Position number
1
4
2
8
3
12
4
16
5
20
Term
5
9
13
17
21
The rule for this sequence is
X4
+1
Finding position-to-term rules
For the sequence:
Position number
5
9
13 17 21 ….
1
2

Term
5
3
4

x 4 +1
9
13
5
17
21
Finding position-to-term rules
For the sequence:
5
9
13 17 21 ….
Position number
1
2

Term
5
3
9
13
5

x 4 +1
The formula for the nth term of the sequence is:
tn = 4n + 1
4
17
21
Find position-to-term rules for
these sequences:
1)
4
7
10
13
…..
2)
4
9
14
19
…..
3)
2
12
22
32
…..
4)
-13
-6
1
8
…..
5)
3
2
1
0
…..
Squares investigation
Squares investigation
Imagine a 3 x 3
square:
Squares investigation
Imagine a 3 x 3
square:
Colour the outside
red:
Squares investigation
Imagine a 3 x 3
square:
Colour the outside
red:
Squares investigation
How many of the
small squares have
 0 red sides?
 1 red side?
 2 red sides?
 3 red sides?
 4 red sides?
Squares investigation
Now change the size
of the starting
square to
 2x2?
 4x4?
 etc…
Squares investigation
How many of the small
squares now have
 0 red sides?
 1 red side?
 2 red sides?
 3 red sides?
 4 red sides?
INVESTIGATE!
Generalising from Diagrams
8 by 8
Generalising from Diagrams
20 by 20
50 by 50
100 by 100
n by n
2 red sides = ?
1 red side = ?
0 red sides = ?
Generalising from Diagram
20 by 30
50 by 40
90 by 50
a by b
2 red sides = ?
1 red side = ?
0 red sides = ?
Squares investigation
Put your results into a table! (If you need to)
Work methodically!
Spot patterns!
Try to find some general rules!