A' Number patterns'

1
A. Number patterns.

• Find the pattern for the first five even numbers
  plus eight.

Number
2 8 10
12 8 10
1st
6th
4 8 12
14 8 12
7th
2nd
6 8 14
16 8 14
3rd
8th
8 8 16
4th
Q Is there a more efficient method to find the
20th number?
10 8 18
5th
Q What is the 20th number in this pattern?
There are a number of ways to tackle this
problem. Maybe continue these calculations up to
the 20th number.
2
A. Number patterns.

• Find the pattern for the first five even numbers
  plus eight.

2 8 10
12 8 10
1st
6th
4 8 12
14 8 12
7th
2nd
6 8 14
16 8 14
3rd
8th
8 8 16
4th
Q Is there a more efficient method to find the
20th number?
10 8 18
5th
A The numbers are going up in twos.
Why?
3
A. Number patterns.

• Find the pattern for the first five even numbers
  plus eight.

2 8 10
12 8 20
1st
6th
4 8 12
14 8 22
7th
2nd
6 8 14
16 8 24
3rd
8th
8 8 16
4th
9th
26
10 8 18
5th
10th
28
Easy!
11th
30
12th
32
13th
34
So continue up to the 20th number.
14th
36
38
15th
16th
20th number 48
40
17th
42
18th
44
46
19th
4
Farmer Giles stared eagerly at this evenings
super and wondered.
Arrr, I reckons that lamb must be 5 kg. If
it take 25 minutes per kg plus 20 minutes extra
to warm up the oven. How long before I as
me supper on the table?
Time in minutes 5 25 20 145
minutes 2 hours 25 minutes
5
B. Finding rules for patterns.

• Look at the follow sequence of numbers

29
13
21
29
37
21
37
5
45
5
13
45
Find a rule to describe this sequence.
n
differences
1
It is easier to put numbers in a column.
Find the differences between the numbers
8
2
8
3
8
4
Give each a position number.
8
5
8
6
6
B. Finding rules for patterns.

• Look at the follow sequence of numbers

13
21
29
37
5
45
Find a rule to describe this sequence.
n
differences
Use a number machine to find the 3rd number.
The sequence is linked to the 8 times table.
5
1
8
2
13
8
8
3
24
21
3
8
29
4
8
However if we use a number machine 3 8 does not
produce the third number 21 in the sequence.
37
5
8
45
6
7
B. Finding rules for patterns.

• Look at the follow sequence of numbers

13
21
29
37
5
45
Find a rule to describe this sequence.
n
differences
The sequence is linked to the 8 times table.
5
1
8
2
13
- 3
8
8
3
4
29
21
21
3
8
29
4
8
Another operation is included in the number
machine -3 to give the desired number in the
sequence.
Check this number machine works with another
number in the sequence.
37
5
8
45
6