**NCERT Solutions for Class 3 Mathematics Chapter-10 Play With Patterns**

**Around Us**

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

**Answer:** Staircase, Zebra crossing, Railing in a balcony.

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

**Answer:**

**3.Can you see a pattern in the way each block is repeated?**

**Answer:** Yes, I can see that one block is placed upwards and the next is placed downwards.

**Practice Time**

**Given below are some patterns.**

**1. Figure out the rule for each and continue the pattern.**

**Answer:** (a) In this pattern; the colour of the pot changes from red to blue and then to red at each step.

(b) In this pattern A is written twice, followed by B written once.

AABAABAAB

(c)In this pattern; the number of petals increases from 1 to 3 and to 5. After that, this sequence is repeated.

(d)In this pattern the blue colour is moving anticlockwise in steps of one.

(e) In this pattern; the figure is rotating clockwise in steps of one.

(f) In this pattern; the sequence of morning, afternoon, evening, and night is repeated.

Morning, Afternoon, Evening, Night, Morning, Afternoon, Evening, Night

**Growing Patterns**

**1.Can you see the rule and continue the pattern?**

**Answer:** In this pattern; the number of marks in the oval is growing by one. After halfway mark the figure gets inverted.

**Number Patterns**

**1.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 series is growing by 20.**

**21, 41, 61, 81, 101,121, 141, 161, 181, **

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

**(a)51, 56, 61, 66,————– ,———— ,————- **

**(b)7,————- ,21,28,35,————- ,————- ,————- **

**(c)2, 4, 8, 16, 32,————- ,————- , ————- **

**(d)12 A, 13 B, 14 C,————- ,————- ,————-**

**Answer:** (a) 51, 56, 61, 66, 71, 76, 81, 86

(6) 7, 14, 21, 28,35, 42, 49, 56

(c) 2, 4, 8,16, 32, 64, 128, 256

(d) 12 A, 13 B, 14 C, 15 D, 16 E, 17 F.

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

**(a)1, 3, 6, 10,———- ,————- ,————– **

**(b)0, 2, 6, 12,———- ,———–,————– **

**(c)1, 3, 7, 13,————–,———–, ————-**

**(d)2, 3, 6, 11,18,———— ,———–,————-**

**Answer:** (a) Following sequence is observed in this pattern:

1 + 2 = 3 3 + 3 = 6 6 + 4=10

The number which is added in each step is growing by 1 Hence the pattern is as follows:

1, 3, 6,10, 15, 21, 28, 36, 45

(b)Following sequence is observed in this pattern:

0 + 2 = 2 2 + 4 = 6 6 + 6 = 12

The number which is added in each step is growing by 2.

Hence the pattern is as follows:

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

(c)Following sequence is observed in this pattern:

1 + 2 = 3

3+4=7

7 + 6 = 13

The number which is added in each step is growing by 2 Hence the pattern is as follows:

1, 3, 7, 13, 21, 31, 43, 57, 73 ’

(d) 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:

2, 3, 6, 11, 18, 27, 38, 51, 66

**Secret Messages**

**Amrita and Paritosh are writing secret messages:**

**3W3H3E3R3E 3A3R3E 3Y303U**

**3 I3 N 3T3H3E 3C3A3N3T3E3E3N**

**1.Can you tell what they are trying to say?**

**Answer:** Following are the secret messages: Where are you?

In the canteen

**3.There are two secret messages. Look at the patterns and find the hidden sentences.**

**1I2L204V5E6Y708U**

**Answer:** The message is: I LOVE YOU

**4.ATBHCIDSEBFOGOHKIIJSKFLUMN**

**Answer:** The message is:

THIS BOOK IS FUN

**5.Now you also make your own secret messages.**

**Answer:**1 I 2 L 3 O 4 V 5 E 6 I 7 N8D9I10A I LOVE INDIA

AMBACNDMEOFHGAHNILJIKVLEMSNAOTPDQERLS

HTI

MANMOHAN LIVES AT DELHI

**Even and Odd Number Patterns**

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

**96, 98,100,102,104,106, IQS, 110,112,114**

**1.How far can you continue this pattern?**

**Answer:** This pattern can be continued endlessly.

These numbers have a special name. They are called even numbers.

**2.Do any of these even numbers end with 3 or 5?**

**Answer:** None of the even numbers end with 3 or 5.

**3.What do even numbers end with?**

**Answer:** Even numbers end with 2, 4, 6, 8 or 10.

**4.Look at the pattern of numbers in blue. Continue the pattern and fill in the blanks.**

**Answer:** 99,101,103,105,107,100, 111, 113,115

**5.What do the numbers in blue end with?**

**Answer: **The numbers in blue end with 1, 3, 5, 7 or 9.

**6. Write all odd numbers between 400 and 410.**

**Answer:** 401, 403, 405, 407, 409.

**7. Write all even numbers between 155 and 165.**

**Answer:** 156,158,160,162,164.

**8.If we add 1 to any odd number we get an————(even/odd) number.**

**Answer:** If we add 1 to any odd number we get an even number.

**9.If we add’l to any even number we get an————(even/odd) number.**

**Answer:** If we add 1 to any even number we get an odd number.

**10. What do you get if you add an even number to an odd number?**

**Answer:** Odd number.

**Names in an Order**

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

**Jalaj is proud to have a special name. He says if you read it backwards it is still the same.**

**1.Which of the following names have the same pattern? **

**Harsh, Anna, Kanak, Munna, Ongbi**

**Answer:** Anna and Kanak.