Can You See The Pattern Class 5 JKBOSE Solutions

“Can You See The Pattern” is Chapter 7 from Merry Math V for students of Class 5th of JKBOSE. This post is about Can You See The Pattern. In a previous post, you read about Be My Multiple, I’ll Be Your Factor JKBOSE Solutions. Let’s get started:

Can You See The Pattern Class 5 JKBOSE Solutions

Page No. 104 Solutions

Now you use these two rules to make patterns with this  block,

Also, make your own rules.

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Turns and Patterns

Look at this block . We make three different rules to turn it clockwise and see the patterns.

Rule 1: Repeat it with a one-fourth turn.

Rule 2: Repeat it with a half-turn.

Rule 3: Repeat it with a three-fourth turn.

Practice Time

1. What should come next?

a)

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b)

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c)

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2. See this pattern

The rule of the pattern is – turning by 45° each time. Which will be the next?  Tick (🗸) the right one.

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4. Using the same rule, take it forward till you get back to what you started with.

(a)

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(b)

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5. Some patterns are given below on the left side of the red line. For 3. each pattern, write the rule. Then choose what comes next from the right side of the line and tick (🗸) it.

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Page No. 108 Solutions.

Look For a Pattern

Mark that picture which is breaking the rule. Also, correct it.

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Magic Squares

Do you remember magic triangles? Come now, let’s make some magic squares.

Fill this square using all the numbers from 46 to 54.

Rule: The total of each line is 150

Sol. From the question, it is given that the total of each line is equal to 150.

In the third row, two numbers are given so it is easy to find third number.

From the rule, __ + 52 + 47 = 150

___ + 99 = 150

___ = 150 – 99 = 51

Therefore, the number in the first box in the third row = 51

Now, in the first column numbers given are 46 and 51.

So, the third number is 150 – 46 + 51 = 53.

In the first row, the numbers given are 53 and 49.

So, the third number is 150 – 53 + 49 = 48.

In the second row, the numbers given are 48 and 52.

So, the third number is 150 – 52 + 48 = 50.

In the third column, the numbers given are 49 and 47.

So, the third number is 150 – 49 + 47 = 54.

Hence, the complete magic square is given as under:

Fill this square using all the numbers. from 21 to 29.

Rule: The total of each side is 75.

Ans. Let us write 24 in the first topmost box on the left side.

Taking the diagonal of the square, we have 24 + 25 = 49 and 75 – 49 = 26.

Therefore, write 26 at the end of the diagonal.

Now, write 28 in the first topmost right-hand side box.

Taking the diagonal of the square, we have 28 + 25 = 53 and 75 – 53 = 22.

Therefore, write 22 at the end of the diagonal.

In the first row, the required number is 75 – (24 + 28) = 23.

In the first column, the required number is 75 – (24 + 22) = 29.

In the second column, the required number is 75 – (25 + 23) = 27

In the second row, the required number is 75 – (29 + 25) = 21

The required square is

Magic Hexagons

Look at the pattern of numbers in the Hexagons.

Each side has 2 circles and 1 box.

Look at the number 65 in the box. Which are the circles next to it? Can you see how the rule works?

Ans. The circles next to 65 are 5 and 14.

(i) Use the same rule to fill the hexagons below.

(a) 

 

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(b) 

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Page No. 110 Solutions.

Are they equal?

Ans. Yes, they are equal.

24 + 19 + 37 = 37 + 24 + 19

80 = 80.

Fill in the blank spaces in the same way.

(a)

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(b)

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(c)

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Now, look at this____

Check if it is true or not.

On the LHS 48 × 13 = 624.

On the RHS 13 × 48 = 624.

By comparing LHS and RHS,

LHS = RHS.

So, it is true.

Page No. 111 Solutions.

Left Right – Same to Same

Now try and change these numbers into special numbers –

(a) 28

Ans. Given number = 28

Now, turn it back to front = 82

Then, add them together = 110

This is not a special number because it is not the same forward as well as backward.

OK, carry on with the number = 110

Again, turn it back to front = 011

Then add the two together = 121

121 is a special number. It is the same as forward or backwards.

(b) 132

Ans. Given number = 132

Now, turn it back to front = 231

Then, add them together = 363.

363 is a special number because it is the same forward as well as backward.

(c) 273

Ans. Given number = 273

Now, turn it back to front = 372

Then, add them together = 645.

It is not a special number. Now carry on with the number 645.

Again, turn it back to front = 546.

Then, add them together = 1191.

It is also not a special number. Now carry on with the number 1191.

Again, turn it back to the front = 1911

Then, add them together = 3102.

It is also not a special number. Now carry on with the number 3102.

Again, turn it back to the front = 2013.

Then, add them together = 5115.

5115 is a special number because it is the same forward as well as backward.

Now let’s use words in a special way.

Did you notice that it reads the same from both sides – right to left and left to right?

Ans. Eye, Level, Rotator, Refer, Noon etc.

Page No. 113 – 114 Solutions

Some More Number Patterns

Take any number. Now multiply it by 2, 3, 4…………… at every step. Also, add 3 to it at each step. Look at the difference in the answer. Is it the same at every step?

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Yes, the difference is the same at every step. It is equal to 12 at every step.

(ii) Look at the numbers below. Look for the pattern. Can you take it forward?

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Smart Adding

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Did you notice some patterns in the answers?

Sol. Yes, there is a pattern in the addition of these numbers. The sum increases by 100 in every step.

Fun with Odd Numbers

Take the first two odd numbers. Now, add them, and see what you get. Now, at every step, add the next odd number. How far can you go on?

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How far can you go on?

Ans. The process can be continued for endless numbers.

Jaffar and Asiya were playing a guessing game by writing clues about a secret number. Each tried to guess the other’s secret number from the clues.

Can you guess their secret numbers?

It is larger than half of the 100

It is more than 6 tens and less than 7 tens

The tens digit is one more than the ones digit

Together the digits have a sum of 11

What is my secret number?

It is larger than half of 100, i.e. 50 ˂ 100

It is more than 6 tens and less than 7 tens, so the number lies between 60 and 70.

The tens digit is one more than the ones digit = 6 – 1 = 5

Together, the digits have a sum of 11 = 6 + 5 = 11

Therefore, the number is 65

 It is smaller than half of the 100

It is more than 4 tens and less than 5 tens

The tens digit is two more than the ones digit

Together, the digits have a sum of 6

It is smaller than half of 100 = number > 50

It is more than 4 tens and less than 5 tens = number lies between 40 and 50

The tens digit is two more than the ones digit = 4 – 2 = 2

Together, the digits have a sum of 6 = 4 + 2 = 6

Therefore, the number is 42

Number Surprises

2. a) Ask your friend to write down your age. Add 5 to it. Multiply the sum by 2. Subtract 10 from it. Next, divide it by 2. What do you get? Is your friend surprised?

Ans. Let us assume the age is 10.

Then, adding 5 to it, we get = 10 + 5 = 15

Multiply by 2, we get = 30

Subtract from 10, we get = 20

Divided by 2, we get = 10

Yes, my friend was really surprised.

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1 = 1 × 1

121 = 11 × 11

12321 = 111 × 111

1234321 = 1111 × 1111

123454321 = 11111 × 11111

12345654321 = 111111 × 111111

1234567654321 = 1111111 × 1111111

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Now Let Us Do These

1. Fill the 3 × 3 square using all the numbers from 1 to 9 so that the total of each row, column and diagonal is 15.

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2. Write the next number in the pattern:

1, 2, 4, 8, 16, ________________

Ans. 1, 2, 4, 8, 16, 32

1, 2, 3, 4, 9, 16, ______________

Ans. 1, 2, 3, 4, 9, 16, 27

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1, 2, 2, 4, 8, 32, ______________

Ans. 1, 2, 2, 4, 8, 32, 256.

3. Complete the pattern:

1 = 1 = 1 × 1

1 + 2 + 1 = 4 = 2 × 2

1 + 2 + 3 + 2 + 1 = 9 = 3 × 3

___ + ___ + ___ + 4 + ___ + ___ + ___ = 16 = 4 × 4

1 +2 + 3 + 4 + 5 + 4 + 3 + 2 +1 = ___ = ___ × ___

__ +__ + __ + __ + __ + __ + __ + __+ __ + __ + __ = 36 = __ × __

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1 = 1 = 1 × 1

1 + 2 + 1 = 4 = 2 × 2

1 + 2 + 3 + 2 + 1 = 9 = 3 × 3

1 + 2 + 3 + 4 + 3 + 2 + 1 = 16 = 4 × 4

1 +2 + 3 + 4 + 5 + 4 + 3 + 2 +1 = 25 = 5 × 5

1 +2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 +1 = 36 = 6 × 6

4. Fill in the blanks:

a) 4 + 7 + 9 = 7 + ___ + 9

b) 17 + 24 + 36 = 36 + 24 + ___

c) 9 + 11 + 21 = ___ + ___ + 9

d) 45 × 35 = 35 × ___

e) 45 + 35 = ___ + 45

Ans.

a) 4 + 7 + 9 = 7 + 4 + 9

b) 17 + 24 + 36 = 36 + 24 + 17

c) 9 + 11 + 21 = 21 + 11 + 9

d) 45 × 35 = 35 × 45

e) 45 + 35 = 35 + 45

5. Fill in the blanks:

0×1 ×2 +1 = 1 = 1 × 1 × 1

1 ×2 × 3 + 2 = 8 = 2 × 2 × 2

2 × 3 × 4 + 3 = 27 = 3 × 3 × 3

3 × 4 × 5 + 4 = 64 = 4 × 4 × 4

4 × 5 × 6 + 5 = 125 = __ × __ × __

__ × __ × __ + 6 = 216 = 6 × 6 × 6

__ × __ × __ + __ = 343 = __ × __ × __

Ans. 4 × 5 ×6 + 5 = 125 = 5 × 5 × 5

5 × 6 ×7 + 6 = 216 = 6 × 6 ×6

6 × 7 × 8 + 7 = 343 = 7 × 7 ×7

That’s it about Can You See The Pattern Class 5 JKBOSE Solutions. Hope you have found it useful. Do share your views about this post in the comment section below.