Patterns
A pattern is referred to as the arrangement of shapes, numbers, and colours which are in repetition.
Number patterns, image patterns, logic patterns, word patterns, and so on are all examples of patterns in mathematics.
Image Patterns / Shapes Pattern
Image Pattern is referred to as the sequence followed by a certain group of objects/shapes.
For example, In the below image, we can see that the umbrellas follow a pattern. The umbrella is pointing down, then left, then up, and then back to the right. As a result, the following pattern can be observed:
Shape pattern
Number Patterns
A list of numbers follows a specific sequence based on a rule. Such as algebraic or arithmetic, geometric, and the Fibonacci pattern.
Shape pattern of mangoes
Arithmetic or Algebraic Patterns
Using addition or subtraction we can find the missing number in a sequence.
The difference between the first and second numbers in the below figure is +3.
Arithmetic Progression
Solved Example 1: Complete the following number patterns?
5, 10,15 , __, __, __
Ans. First Digit = 5
Second Digit = 5 + 5 = 10
Third Digit = 10 + 5 = 15
Clearly, we will add 5 to the preceding digits respectively to find the rest of the digits.
Fourth Digit = 15 + 5 = 20
Similarly , Fifth Digit = 20 + 5 = 25
Sixth Digit = 25 + 5 = 30
Hence the pattern is 5,10,15,20,25,30.
Geometric Series Pattern
A geometric pattern is a series of numbers formed by multiplying and dividing them.
Example: Here multiply each term by 2 to get the next term.
Geometric series
Solved Example 1: Complete the following number patterns?
10, 100,1000 , __, __, __
Ans. First Digit = 10
Second Digit = 10 × 10 = 100
Third Digit = 100 × 10 = 1000
Clearly, we will multiply 10 by the preceding digits respectively to find the rest of the digits.
Fourth Digit = 1000 × 10 = 10000
Similarly , Fifth Digit = 10000 × 10 = 100000
Sixth Digit = 100000 × 10 = 1000000
Hence the pattern is 10,100,1000,10000,100000,1000000.
Fibonacci Pattern
The Fibonacci Pattern is a number sequence in which each consecutive number is obtained by adding the two preceding numbers together.
Fibonacci Pattern
Equal Numbers
When two or more quantities are exactly the same, we can say they are equal.
In number patterns, if there is an equal sign(=) in the pattern, then LHS and RHS will have the same numbers.
Solved Examples 1: Find the missing numbers in the following pattern: 10, 20, _ = 10, _, 15.
Ans: As you can see, there are two numbers in the LHS: 10 and 20.
And in RHS: 10 and 15
As there is an equal sign it means both sides will have the same numbers.
So the missing numbers in the LHS = 15
And, the missing number in the RHS = 20
Numbers in LHS: 10, 20, 15
Numbers in RHS: 10, 20, 15
Numbers in LHS = Numbers in RHS
Therefore LHS = RHS
Solved Examples 2. Check whether LHS is equal to RHS: 15+ _ + _ = 30 + 20 + 15 ?
Ans: As you can see, there are three numbers in the RHS: 30 + 20 + 15.
And in LHS only 15
As there is an equal sign it means both sides will have the same numbers.
So the missing numbers will be the numbers that are in the RHS i.e, 30 and 20
So, missing numbers in LHS will be 15 + 30 + 20
If you add both LHS and RHS we get,
LHS: 15 + 30 + 20 = 65
RHS: 30 + 20 + 15 = 65
Therefore LHS = RHS
Palindrome
Special words/numbers which remain the same when reversed.
For example, 99 when reversed remains 99; 101, when reversed, remains 101.
Fun with Odd Numbers
Integers that do not appear in the table of two are known as odd numbers.
Note: When we add the first n odd numbers, we will get the sum as n × n, where (n) is the number of odd numbers taken at a time.
Solved Example 1: Let us find the sum of the first 3 odd numbers.
Ans: First 3 odd numbers: 1,3, 5. Here n = 3
Adding 1+3+5 we get 9.
Also, we know that When we add first n odd numbers,
we will get the sum as n × n.
Sum of first 3 odd numbers = n × n i.e. 3 × 3 = 9
So, the Sum of the first 3 odd numbers is 9.
Solved Example 2: Find the sum of the first 6 odd numbers.
Ans: First 6 odd numbers: 1,3, 5,7,9,11. Here n = 6
Adding 1+3+5+7+9+11 we get 36.
Also, we know that when we add first n odd numbers,
we will get the sum as n × n.
Sum of first 6 odd numbers = n × n i.e. 6 × 6 = 36
So, the Sum of the first 6 odd numbers is 36.
Practice Questions:
Q1. Complete the following number patterns?
20, 30, 40 , __, __, __
3, 5, 7 , __, __, __
Ans:
50, 60, 70
9, 11, 13
Q2. Find the sum of the first 11 odd numbers.
Ans.
121
Q3. Find the missing numbers in the following pattern: 10, 20, _, 40, 50 = 10, _, 30,_,_.
Ans.
Missing numbers in LHS = 30
Missing numbers in RHS = 20,40 and 50.
Importance of CBSE Class 5 Maths Chapter 7 Can You See the Pattern
This chapter will progress to the next level where you can identify the patterns and follow the changes in the designs.
You will learn how to rotate an image or a shape to find the next shape or phase of a sequence. These types of problems related to patterns do not follow any particular mathematical concept. In fact, you will not need any mathematical operations to do. All you will learn is to identify the patterns, check the sequential flow of these patterns, and solve the questions.
This chapter promotes logical thinking among students. If you follow the Can You See The Pattern summary, you will clearly understand the objective of this chapter.
You will learn at what angle the patterns, designs, images, letters, numbers, etc., need to be rotated to find the answers to such questions.
Benefits of Can You See The Pattern Class 5 Worksheets and Revision Notes
Our subject experts have come up with a concise summary of all the fundamental concepts taught in this chapter. It will help you to grab these concepts easily and accurately solve the questions.
This chapter enhances the development of your aptitude. Your logical reasoning skills to look for a pattern will increase considerably once you start practising this chapter. To support this development, you will need to practice the worksheets and revision notes.
Learn how the number patterns are changing by checking the solutions and explanations provided by our subject experts.
Prepare for your exam by using the revision notes to revise the concepts you have studied in this chapter, quickly.
Easy Exam Preparation with Class 5 Maths Chapter 7 Worksheets and Revision Notes
Download these revision notes and worksheets for free from Vedantu and learn how the experts have solved magic squares and hexagons problems. Follow the steps used by the experts and solve the worksheets to find out how good you are at solving these questions. Practice the sums thoroughly to score well in the exams.
Conclusion
Vedantu's free PDF notes on CBSE Class 5 Maths Chapter 7, "Can You See the Pattern," are a valuable educational resource for young learners. These notes offer a comprehensive understanding of mathematical patterns, aligning seamlessly with the CBSE curriculum. Vedantu's commitment to providing accessible educational content empowers students to grasp the complexities of patterns in mathematics with ease. These notes simplify intricate mathematical concepts, encourage critical thinking, and foster a deeper appreciation for the role of patterns in problem-solving and mathematics as a whole. By utilising these resources, students can enhance their mathematical skills, pattern recognition abilities, and overall academic performance, instilling in them a lifelong fascination for the beauty and utility of patterns in mathematics.