PPT: Numbers and The Number System | Year 4 Mathematics IGCSE (Cambridge) - Class 4 PDF Download

 Page 1


Numbers and 
the Number 
System
Page 2


Numbers and 
the Number 
System
Counting and Sequences
C o u n t i n g
Counting is the systematic process of assigning numerical values to objects in a 
collection. It forms the foundation of mathematics and helps us understand 
quantity relationships. 
S e q u e n c e s
Sequences are ordered lists of numbers that follow specific patterns or rules. 
Common sequences include arithmetic (adding the same value) and geometric 
(multiplying by the same value).
Page 3


Numbers and 
the Number 
System
Counting and Sequences
C o u n t i n g
Counting is the systematic process of assigning numerical values to objects in a 
collection. It forms the foundation of mathematics and helps us understand 
quantity relationships. 
S e q u e n c e s
Sequences are ordered lists of numbers that follow specific patterns or rules. 
Common sequences include arithmetic (adding the same value) and geometric 
(multiplying by the same value).
Let's Solve
Q u e s t i o n
What is the next number in the sequence 7, 14, 
21, 28, ___?
Page 4


Numbers and 
the Number 
System
Counting and Sequences
C o u n t i n g
Counting is the systematic process of assigning numerical values to objects in a 
collection. It forms the foundation of mathematics and helps us understand 
quantity relationships. 
S e q u e n c e s
Sequences are ordered lists of numbers that follow specific patterns or rules. 
Common sequences include arithmetic (adding the same value) and geometric 
(multiplying by the same value).
Let's Solve
Q u e s t i o n
What is the next number in the sequence 7, 14, 
21, 28, ___?
Solution
Calculate the Difference
By examining the sequence 7, 14, 21, 28, we identified a constant difference of 7 
between each consecutive term. This pattern reveals an arithmetic sequence with a 
common difference of 7.
Apply the Pattern
To find the next number, we add 7 to the last known term: 28 + 7 = 35. This follows the 
established pattern and continues the sequence logically.
Verify the Solution
The complete sequence is now 7, 14, 21, 28, 35. We can verify this is correct by 
confirming that each term equals the previous term plus 7, maintaining the arithmetic 
pattern.
Page 5


Numbers and 
the Number 
System
Counting and Sequences
C o u n t i n g
Counting is the systematic process of assigning numerical values to objects in a 
collection. It forms the foundation of mathematics and helps us understand 
quantity relationships. 
S e q u e n c e s
Sequences are ordered lists of numbers that follow specific patterns or rules. 
Common sequences include arithmetic (adding the same value) and geometric 
(multiplying by the same value).
Let's Solve
Q u e s t i o n
What is the next number in the sequence 7, 14, 
21, 28, ___?
Solution
Calculate the Difference
By examining the sequence 7, 14, 21, 28, we identified a constant difference of 7 
between each consecutive term. This pattern reveals an arithmetic sequence with a 
common difference of 7.
Apply the Pattern
To find the next number, we add 7 to the last known term: 28 + 7 = 35. This follows the 
established pattern and continues the sequence logically.
Verify the Solution
The complete sequence is now 7, 14, 21, 28, 35. We can verify this is correct by 
confirming that each term equals the previous term plus 7, maintaining the arithmetic 
pattern.
Q u e s t i o n
In the sequence 2, _, 6, 8, 10, we need to 
determine what number belongs in the blank 
space.