NCERT Solutions for Class 3 Maths Chapter 10 - Play With Patterns

1. Look around you and list three things in which you find some pattern.

Ans: The three things around me that are in patterns are as follows: 

a) The tiles in the washroom  

b) The window grills 

c) The wooden door of the class.

2. Draw some patterns which you have found around yourself. 

Ans:

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3. Given below are some patterns. Figure out the rule for each and continue the pattern.

a)

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Ans: The pattern followed in this picture:  Pink pots and blue pots are kept alternatively in series.

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b)

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Ans: The pattern which is followed in this picture is that B is written after double-A.

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c)

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Ans: The pattern followed in this picture: a flower with an odd number of petals from 1 to 5 is repeated.

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d)

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Ans: The pattern followed in this picture: Out of four triangles f a square, one triangle of blue colour is rotated anti-clockwise.

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d) 

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Ans: The pattern followed in this picture: The given pattern of a semicircle is rotated 90degree or perpendicular in a clockwise direction.

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e) Morning, afternoon, evening, night, morning, ________

Ans; The pattern followed here: A day is divided into 4 durations depending upon the position of the sun. And it is repeated again and again. Morning, afternoon, evening, night, morning, afternoon, evening, night.

4. Growing Patterns:

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Can you see the rule and continue the pattern?

Ans: It can be observed that in the $1st$  image, there is only a $1$ arrow head pointing in the upward direction. While 2nd image, there is only a $1$ arrow head and is pointing in the downward direction. Similarly in the $3rd$ image, there are only $2$ arrow heads pointing in the upward direction. In the $4^{th}$ image, there are only $2$ arrow heads pointing in the downward direction. As above. the arrowheads become $3^{rd}$ in the fifth and $6th$ image, pointing upward and downward alternately. So, in the $7^{th}$ and $8^{th}$ image of the pattern, there will be 4$4$arrowheads, pointing upward and downward alternately.

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5. Try these also

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Ans: 

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6. My Own Patterns:  Here is your space to make your own patterns:

Ans: Some of the patterns are:

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Ask your friends to continue the patterns made by you. 

Ans: 

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7. Number Patterns:

We have made some patterns with pictures. We can make patterns with numbers too. Like 

$21,41,61,81,101,121$

You know the next number, don’t you? This is a growing pattern. It can go on and on.

$21,41,61,81,101,121,141,161...$

Ans: In the above number pattern, the series is growing by $20$ .

$21,41,61,81,101,121,141,161,181,201,221,241$

8. A Look for the rules and continue these growing patterns:

a) $51,56,61,66,\_\_\_\_,\_\_\_\_\_$

Ans: Here each number is obtained by adding $5$ to the previous numbers, such as $51 + 5 = 56 + ,56 + 5 = 61$ .

So the required next two numbers are $66 + 5 = 71,71 + 5 = 76$ .

Therefore the pattern is 

$51,56,61,66,71,76$

b) $7,\_\_\_,21,28,35,\_\_\_,\_\_\_\_$

Ans: In this series the table is the multiple of $7$i.e.

$7 \times 1 = 7$

$7 \times 2 = 14$

$7 \times 3 = 21$

Therefore by following the above table, the required series is

$7,14,21,28,35,42,49$

c) $2,4,8,16,32,\_\_\_,\_\_\_,\_\_\_$

Ans; It can be written as: 

$2 \times 1 = 2$

$2 \times 2 = 4$

$2 \times 4 = 8$

$2 \times 8 = 16$

In this series we keep multiplying $2$ with the previous answer received to complete the pattern further.  

Therefore the series is $2,4,8,16,32,64,128$

d) $12A,13B,14C,\_\_\_\_,\_\_\_\_$

Ans: It can be observed that here each number increases by $1$ and alphabets are written in their order along with the increasing numbers.

So the pattern is $12A,13B,14C,15D,16E$

9. Look at these growing patterns Find out what to add to each number to get the next one:  

a) $1,3,6,10,\_\_\_\_,\_\_\_\_\_,\_\_\_\_,\_\_\_\_,\_\_\_\_$

Ans; Here the first number is $1$

The pattern can be written as:

$1 + 2 = 3,3 + 3 = 6,6 + 4 = 10,10 + 5 = 15,15 + 6 = 21,21 + 7 = 28,28 + 8 = 36,36 + 9 = 45$

Therefore the number is $1,3,6,10,15,21,28,36,45$

b) $0,2,6,12,\_\_\_,\_\_\_\_,\_\_\_\_,\_\_\_\_,\_\_\_$

Ans; In this series, the pattern can be written as: 

$0 + 2 = 2,2 + 4 = 6,6 + 6 = 12,12 + 8 = 20,20 + 10 = 30,30 + 12 = 42,42 + 14 = 56,56 + 16 = 72$The new series is as follows:

$0,2,6,12,20,30,42,56,72$

c) $1,3,7,13,\_\_\_,\_\_\_,\_\_\_,\_\_\_,\_\_\_$

Ans: Following sequence is observed in this pattern:

$2 + 1 = 3,3 + 3 = 6,6 + 5 = 11,11 + 7 = 18$

The number which is added in each step is growing by $2$ .Hence the pattern is as follows:
\[1,{\text{ }}3,{\text{ }}7,{\text{ }}13,{\text{ }}21,{\text{ }}31,{\text{ }}43,{\text{ }}57,{\text{ }}73{\text{ }}\]

d) $2,3,6,11,18,\_\_\_,\_\_\_,\_\_\_,\_\_\_,\_\_\_$

Ans: In this the following sequence is observed in this pattern:
\[2{\text{ }} + {\text{ }}1{\text{ }} = {\text{ }}3,3{\text{ }} + {\text{ }}3{\text{ }} = {\text{ }}6,{\text{ }}6{\text{ }} + {\text{ }}5{\text{ }} = {\text{ }}11{\text{ ,}}11{\text{ }} + {\text{ }}7{\text{ }} = {\text{ }}18\]

The number which is added in each step is growing by $2$ . Hence the pattern is as follows:
\[2,{\text{ }}3,{\text{ }}6,{\text{ }}11,{\text{ }}18,{\text{ }}27,{\text{ }}38,{\text{ }}51,{\text{ }}66\]

10. Amrita and Paritosh are writing secret messages:
3W3H3E3R3E 3A3R3E 3Y303U
3 I3 N 3T3H3E 3C3A3N3T3E3E3N

Can you tell what they are trying to say?
Ans. Following are the secret messages:

Where are you?
In the canteen

11. There are two secret messages. Look at the patterns and find the hidden sentences.
1I2L204V5E6Y708U 

Ans: The message is:

I LOVE YOU

12. Even and Odd Number Patterns

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Half these numbers are in yellow. What patterns do you see in these numbers? Continue the same pattern and fill in the blank

$96,98,100,102,104,106,108,110,112,114$

How far can you continue this pattern?
Ans. This pattern can be continued endlessly.These numbers have a special name. They are called even numbers.

a) Do any of these even numbers end with $3$ or $5$?
Ans. None of the even numbers end with $3$ or $5$.

b) What do even numbers end with?
Ans. Even numbers end with \[2,{\text{ }}4,{\text{ }}6,{\text{ }}8\] or $10$

c) Look at the pattern of numbers in blue. Continue the pattern and fill in the blanks.
Ans. \[99,101,103,105,107,100,{\text{ }}111,{\text{ }}113,115\]

d) What do the numbers in blue end with?
Ans. The numbers in blue end with $1,3,5,7$ or $9$

e) Write all odd numbers between $400$ and $410$
Ans. \[\;401,{\text{ }}403,{\text{ }}405,{\text{ }}407,{\text{ }}409.\]

f) Write all even numbers between $155$ and $165$
Ans. \[156,158,160,162,164\]

g) If we add $1$ to any odd number we get an $\_\_\_\_\_$ (even/odd) number.
Ans. If we add $1$ to any odd number we get an even number.

h) If we add $1$  to any even number we get an _______(even/odd) number.
Ans. If we add $1$ to any even number we get an odd number.

i) What do you get if you add an even number to an odd number?
Ans. Odd number.

13. Adil has to arrange this list so that the names starting with A come first and then come those with B, C, D and so on. Number these names in the order in which they will come.

Sharada, Mahadevan, Tsering, Adil, Gurinder, Baichung, Harsha, Raja, Narayan Kavita, Warsha, Elvis, Jalaj

Ans: 

14. Which of the following names have the same pattern?  

Harsh, Anna, Kanak, Munna, Ongbi

Ans: Anna, Kanak and Munna are the names with the same pattern because all of them have repeated letters twice in these.

NCERT Solutions for Class 3 Maths Chapter 10 Play With Patterns

Students can practice and cross-check their answers with the NCERT Solutions for Class 3 Maths Chapter 10– Play with Patterns provided on Vedantu. If you are facing difficulties in understanding any topic, you can refer to these NCERT Solutions to develop your concepts. You can also take the help of our experienced teachers if you have any doubt relating to the topic, by signing up for the live classes.

In the NCERT Solutions for Class 3 Maths Chapter 10– Play with Patterns, students will learn how to recognize increasing and decreasing patterns in pictures and numbers. You will also be able to identify the rules for growing and reducing patterns and extend the patterns using rules.

We see patterns everywhere around us. They could be in the clothes that we wear or bed sheets or curtains in our homes or in the toys that we play with, etc. So what is the pattern? Patterns are created when figures, shapes, objects, etc. are arranged in a particular order and repeated over and over again. We must have seen different kinds of patterns in our daily life.

Let us look at the pattern below.

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This is a pattern.       

Maths is full of patterns. We find patterns in alphabets, numbers, shapes, etc. 

For Example: Let us see Table of 3.

3, 6, 9, 12, 15, 18, 21……. We are skipping each number by 3. 

Once you know the rule for a pattern you can continue with other similar patterns.

Growing and Reducing Patterns

Picture Patterns

A picture can be made by increasing or decreasing the number of objects in it.

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This is a growing pattern. In the above picture, the pattern keeps growing. It does not repeat. The rule followed in the pattern is: the number of stars is growing by 1 in each column.

Let us see the next picture.

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This is a reducing pattern. Now see the rule of the pattern followed in the above picture. In the first row, the lines are decreasing by 1 and in the second row, the lines are decreasing by 2.

Number Patterns

Increasing and decreasing patterns can be formed with numbers also.

Example: 21, 31, 41, 51, 61, ….. ? What will be the next number?

This is a growing pattern. The rule followed is that by adding 10 we obtain the next number to the previous number. 

So, the next number is: 61 + 10 = 71.

Let us see the reducing pattern.

Example: What is the next number in the pattern: 35, 28, 21, _______, 7?

This is a reducing pattern. The rule followed is that by subtracting 7 we obtain the next number from the previous number. 

So, the next number is: 21 – 7 = 14.

In Number patterns, we also have Even and Odd Number Patterns. The patterns that end with even numbers are even number patterns and the numbers that end with odd numbers are called odd numbers.

Secret Messages

How do you write a secret message? If you want to write a message to your friend and you don’t want anyone else to read the message then you can write the message in the code language. For example, we write the letters or the numbers following the rule of pattern, and later your friend can decode them. It is actually a lot of fun doing that.

What is happening in the above picture? Different signs or objects are assigned to the letters. You write the message in those signs, which is called coding. You decode the message by matching the signs with the letters.

What are the Benefits of using Vedantu for Class 3 Maths Chapter 10 - Play with Patterns?

Key Features of NCERT Solutions, These solutions are designed to help students achieve proficiency in their studies. They are crafted by experienced educators who excel in teaching Class 3 Maths. Some of the features include:

• Comprehensive explanations for each exercise and questions, promoting a deeper understanding of the subject.

• Clear and structured presentation for easy comprehension.

• Accurate answers aligned with the curriculum, boosting students' confidence in their knowledge.

• Visual aids like diagrams and illustrations to simplify complex concepts.

• Additional tips and insights to enhance students' performance.

• Chapter summaries for quick revision.

• Online accessibility and downloadable resources for flexible study and revision.

Conclusion

NCERT Solutions for Class 3 Maths Chapter 10 - Play With Patterns offer a foundational understanding of pattern recognition and application. These solutions empower young learners to grasp pattern formations, stimulating their logical and analytical thinking. With clear explanations and illustrative examples, students develop a keen eye for recognizing patterns in everyday scenarios. This chapter fosters critical skills, nurturing mathematical thinking and problem-solving abilities. NCERT Solutions serve as a guiding tool, encouraging students to explore, create, and comprehend the underlying concepts of patterns in an engaging and structured manner, laying a robust groundwork for their mathematical journey ahead.