Patterns and General Rule

Derive the general rule for figure number(n) and the number of match sticks (s)

• s= 5n -1

• s= 5n + 1

• n = 5s -1

• n = 4s

Derive the general rule for stage number(s) and the number of match sticks (m)

• s= 4n -1

• s= 5m - 1

• m = 3s -1

• m = 3s +1

Complete the table for stage number(s) and the number of match sticks (m)

s : 1 2 3 4.....................

m : 4 ..................................

• s= 2 , m= 6

• s= 2 , m = 8

• s = 2, m = 7; s= 3 ,m = 11

• s = 2, m = 7; s= 3 ,m = 10

Complete the table

figure number( n) : 1 2 3 4

Number of triangles( t ) : 2 4 6 8

• n = 5 , t = 6

• n= 5, t = 7

• n= 5 , t = 10

• n = 5 , t = 11

Refer to the table

figure number( n) : 1 2 3 4

Number of triangles( t ) : 2 4 6 8

We , will verify the general rule for n =

• n = 5

• n= 4

• n= 3

• n = 2

Refer to the table

figure number( n) : 1 2 3 4

Number of match sticks( m ) : 4 7 10 ...................

We , will verify the general rule for n =

• n = 5

• n= 4

• n= 3

• n = 2

Derive the general rule number of triangles (t) in terms of figure number(n)

• t = n+ 1

• t = n+ 2

• t = 2n + 1

• t = 2s

Derive the general rule number of triangles (t) in terms of figure number(n)

• t = n+ 1

• t = n+ 2

• t = 2n + 1

• t = 2s

Complete the table for figure number ( n ) and number of match sticks( s)

n : 1 2 3 4 ...................

s : 6 11 16 .....................

• n = 4 , s = 20; n= 5 ,s = 25

• n = 4 , s = 19; n= 5 ,s = 23

• n = 4 , s = 18; n= 5 ,s = 24

• n = 4 , s = 21; n= 5 ,s = 26

Refer to the the table for figure number ( n ) and number of match sticks( s)

n : 1 2 3 4 ...................

s : 6 11 16 .....................

We will verify the general rule , by taking n =

• n = 1

• n = 2

• n = 4

• n = 1