By

Mrs. PUSHPA PRAKASH,

CLASS – IV MATHEMATICS

KV IAT GIRINAGAR, PUNE

5.Patterns

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Rows

Columns

5.1 Patterns on Hundred’s charts

Patterns of sums 1 + 2 + 3 + __ = 55 11 + 12 + 13 + _ = 155 21 + 22 + 23 + _ = 255 31 + 32 + 33 + _ = 355

:

: 91 + 92 +93 + _ = 955

Find some more patterns from the above chart.

Activity

5.2 Table Patterns

Here are some patterns of multiples of 2,3,4,5,… on a 6 X 6 grid of numbers.

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

19 20 21 22 23 24

25 26 27 28 29 30

31 32 33 34 35 36

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

19 20 21 22 23 24

25 26 27 28 29 30

31 32 33 34 35 36

Multiples of 2 Multiples of 3

5.2 Table PatternsHere are some patterns of multiples of 2,3,4,5,… on a 6 X 6 grid of numbers.

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

19 20 21 22 23 24

25 26 27 28 29 30

31 32 33 34 35 36

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

19 20 21 22 23 24

25 26 27 28 29 30

31 32 33 34 35 36

Take a few 10 x 10 grids of numbers.Obtain the patterns of the multiples of 2,3,4,5,6,7,8,9and10.Use one sheet for one number.

Activity

Multiples of 4

5.3 Number Patterns Arising out of Addition of Consecutive Numbers.

Three consecutive number1 + 2 + 3 = 62 + 3 + 4 = 93 + 4 + 5 =12

. .8 + 9 +10=27

Three consecutive numbers

The sums are multiples of 3. Also,

the sum is thrice the middle term.

Four consecutive numbers

1 + 2 + 3 + 4 = 10 2 + 3 + 4 + 5 = 14 3 + 4 + 5 + 6 = 18

. .

10 + 11 + 12 + 13 = 46

The sums increase in 4’s.All are are even numbers which are not theMultiples of 4.Also,the sum is twice

The sum of the two middle terms .

The sums are multiples of 5

1 + 2 + 3 + 4 + 5 = 15 2 + 3 + 4 + 5 + 6 = 20 3 + 4 + 5 + 6 + 7 = 25

. . 15 + 16 + 17 + 18 +19 = 85

Obtain the patterns in the sum of six, seven, eight, etc.,consecutive numbers.

Activity

Five consecutive numbers

From the pattern given above, find the sum of first(a) 10 odd numbers (b)13 odd numbers

(c)22 odd numbers

5.4 Adding odd numbers

1 + 3 = 4 (2 x 2)Ans.____1 + 3 + 5 = 9 (3 x 3)Ans.____

1 + 3 + 5 +7 = 16 (4 x 4)Ans.____1 + 3 + 5 + 7 + 9 = 25 (5 x 5)Ans.____

And so on.

How many numbers are added to get 4? What is 2 x 2 ?How many numbers are added to get 9? What is 3 x 3 ?How many numbers are added to get 16? What is 4 x 4 ?How many numbers are added to get 25? What is 5 x 5 ?

Activity