Worksheet Solution: Patterns in Mathematics | Mathematics (Maths) Class 6 PDF Download

Learning Pattern

Q1: Find out the missing numbers and figure out what the pattern rule is for each box 

Q2: What happens when you start adding up triangular numbers, i.e., take 1, 1 + 3, 1 + 3 + 6, 1 + 3 + 6 + 10, ... ? Which sequence do you get? Can you explain it using a picture of a triangle?
Solution:When you add up triangular numbers, you get the sequence of tetrahedral numbers (3D triangular numbers). For example:

• $1=11\; =\; 1$1=1
• $1+3=41\; +\; 3\; =\; 4$1+3=4
• $1+3+6=101\; +\; 3\; +\; 6\; =\; 10$1+3+6=10
• $1+3+6+10=201\; +\; 3\; +\; 6\; +\; 10\; =\; 20$1+3+6+10=20

These numbers can be visualized as a pyramid of dots arranged in triangular layers. 

Fill in the Blanks

Q1: A ________ polygon is a shape with all sides and angles equal.
Ans: regular
Solution: The term "regular" in geometry means that all sides and angles of the polygon are equal.

Q2: The sequence 1, 8, 27, 64, ... represents the ________ of numbers.
Ans: cubes
Solution: These numbers are the cubes of the natural numbers: $13,23,33,431^3,\; 2^3,\; 3^3,\; 4^3$13,23,33,43.

Q3: ________ numbers can be represented as dots forming a perfect square.
Ans: Square
Solution: Square numbers can be visualized by arranging dots in a grid where the number of rows equals the number of columns.

Q4: The pattern 2, 4, 6, 8, 10, ... is a sequence of ________ numbers.
Ans: even
Solution: This sequence is formed by adding 2 to the previous number, which creates a sequence of even numbers.

Q5: ________ numbers increase by the same amount each time, and this sequence is called counting numbers.
Ans: Natural
Solution: The natural or counting numbers increase by 1 each time: 1, 2, 3, 4, ...

True or False

Q1: The sequence 1, 4, 9, 16, 25, ... is an example of cube numbers.
Ans: False
Solution: This sequence is an example of square numbers, not cube numbers.

Q2: A regular pentagon has equal sides but different angles.
Ans: False
Solution: A regular pentagon has both equal sides and equal angles.

Q3: The sequence of odd numbers starts with 1, 3, 5, 7, ...
Ans: True
Solution: The odd number sequence starts with 1 and increases by 2 each time.

Q4: A shape sequence starting with a square and adding one side each time would form polygons with increasing numbers of sides.
Ans: True
Solution: This sequence would start with a square (4 sides), then a pentagon (5 sides), and so on, each with one more side.

Q5: The number 36 can be both a square number and a triangular number.
Ans: True
Solution: The number 36 is unique in that it can be represented both as a square number (6x6) and as a triangular number.