Download + 1 Complicated Linear Patterns

Starter Question
1. Write the next two numbers in the
sequence: 12, 13, 15, 18, 22, 27
2. Calculate the area of a rectangle with length
4m and breadth 8m
Area of a rectangle = l x b
=4x8
= 32 m2
3. Write the ratio of boys to girls in the class
4. Which is longer 0.5cm or 6mm?
0.5 cm = 0.5 x 10 = 5 mm
longer
Complicated Linear Patterns
A pattern is made using matchsticks:
1 triangle
2 triangles
3 triangles
3 matches
5 matches
7 matches
Number of
Triangles (T)
Number of
matches (M)
1
2
3
4
5
3
5
7
9
11
Complicated Linear Patterns
Number of
Triangles (T)
Number of
matches (M)
1
2
3
4
5
3
5
7
9
11
+2
+2
+2
+2
For every new triangle =>
the number of matchsticks rises by 2
Complicated Linear Patterns
Step 1:
In symbols we can begin to write
M = 2 x T
BUT look at the table:
Number of
Triangles (T)
Number of
matches (M)
1
2
3
4
5
3
5
7
9
11
M = 2 x T
M=5, T=2
2 x 2 = 5
Complicated Linear Patterns
Step 1:
In symbols we can begin to write:
M = 2 x T
Step 2:
We need a correction number to make
the pattern work
T = 2, M = 5
2 x 2 = 5
2 x 2 ++ ?1 = 5
Complicated Linear Patterns
Formula
M=2xT+1
Check:
Number of
Triangles (T)
Number of
matches (M)
1
2
3
4
5
3
5
7
9
11
Complicated Linear Patterns
Formula
M=2xT+1
Q) If there are 20 triangles how many
matches are there?
M=2xT+1
T=20
M = 2 x 20 + 1
M = 41
Complicated Linear Patterns
2 posts
3 posts
4 posts
1 support
2 supports
3 supports
Number of Posts
(P)
Number of
supports (S)
2
3
4
5
6
1
2
3
4
5
Simple Linear Patterns
Number of Posts
(P)
Number of
Supports (S)
2
3
4
5
6
1
2
3
4
5
+1
Step 1:
1 x P
S = ?
Step 2:
1
S = 1 x P -?
+1
+1
+1
Simple Linear Patterns
Number of Posts
(P)
Number of
Supports (S)
2
3
4
5
6
1
2
3
4
5
+1
Formula
S=1xP-1
S=P-1
+1
+1
+1
Simple Linear Patterns
Formula
S=P–1
Q) If there are 156 posts how many
supports are there?
S=P-1
P=156
S = 156 - 1
S = 155