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: Find out what type of pattern is represented by the given diagram and write number pattern for the same 

Ans:  The represented pattern is cube numbers 
Number pattern is 1, 3, 27, 64, ... and so on
Q3: Find out what type of pattern is represented by the given diagram and write  number pattern for the same 

Ans:  The represented pattern is of odd numbers 
Number pattern is 1, 3, 5, 7, 9, 11 ... and so on

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Fill in the Blanks

Q1: A ________ polygon is a shape with all sides and angles equal.
Ans: regular

 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

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

 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

 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

The natural or counting numbers increase by 1 each time: 1, 2, 3, 4, ...

Test: Patterns in Mathematics - 1

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True or False

Q1: The sequence 1, 4, 9, 16, 25, ... is an example of cube numbers.
Ans: False

This sequence is an example of square numbers, not cube numbers.

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

A regular pentagon has both equal sides and equal angles.

Q3: The sequence of odd numbers starts with 1, 3, 5, 7, ...
Ans: True

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

 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

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

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Word Problem

Q1: Riya is stacking books in a pyramid shape. The first row has 1 book, the second has 3, the third has 6. If she continues this pattern, how many books will be in the fifth row?

Ans: The books in each row follow a pattern:

• 1st row: 1
• 2nd row: 1 + 2 = 3
• 3rd row: 1 + 2 + 3 = 6
• 4th row: 1 + 2 + 3 + 4 = 10
• 5th row: 1 + 2 + 3 + 4 + 5 = 15

The fifth row will have 15 books.

 Q2: A honeycomb follows a hexagonal pattern. If the first row has 1 cell, the second has 7 cells, and the third has 19 cells, how many will be in the fourth row? 

Ans: The number of cells follows this pattern:

• 1st row = 1
• 2nd row = 1 + 6 = 7
• 3rd row = 7 + 12 = 19
• 4th row = 19 + 18 = 37

The fourth row will have 37 cells.

Q3: A school’s staircase follows a pattern: The first step has 2 tiles, the second has 4, the third has 6. How many tiles will be on the 10th step?

Ans: Each step increases by 2 tiles. The sequence follows:

• 1st step = 2
• 2nd step = 4
• 3rd step = 6
• 4th step = 8
• …
• 10th step = 2 × 10 = 20

The 10th step will have 20 tiles.

​Q4: Give a diagrammatic representation of triangular numbers.

Ans:

Q5: Represent 36 as both triangular and square numbers.

Ans: (i) 36 as triangular number 

(ii) 36 as square number 

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