Q1Written answer
2. What should come next?
(a)
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Solution:-
(b)
Solution:-
(c)
Solution:-
(d)
Solution:-
NCERT · Class 5 · Maths
Chapter 7: Can You See the Pattern?
Practice each question, then open the answer or worked solution.
Questions
14 questionsQ2Written answer
What should come next?
(a)
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Solution:-
(b)
Solution:-
(c)
Solution:-
(d)
Solution:-
Q3Written answer
See this pattern
(a)
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Solution:-
Q4Written answer
Using the same rule, take it forward till you get back to what you started with.
(a)
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Solution:-
(b)
Solution:-
Q5Written answer
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Solution:-
Q6Written answer
Mark that picture which is breaking the rule. Also, correct it.
(a)
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Solution:-
The below-marked picture breaks the rule.
(b)
Solution:-
The below-marked picture breaks the rule.
(c)
Solution:-
The below-marked picture breaks the rule.
(d)
Solution:-
The below-marked picture breaks the rule.
Q7Written answer
Magic Squares
Do you remember magic triangles? Come now, let’s make some magic squares.
(i) Fill this square using all the numbers from 46 to 54.
Rule: The total of each line is 150.
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Solution:-
From the question, it is given that the total of each line is equal to 150.
So, let us take the third row.
From the rule, + 52 + 47 = 150
+ 99 = 150
= 150 – 99
Therefore, the number in the first box in the third row = 51
Now, let us take the first column.
From the rule, + 46 + 51 = 150
+ 97 = 150
= 150 – 97
Therefore, the number in the first box in the first column = 53
Let us take the first row.
From the rule, 53 + + 49 = 150
+ 102 = 150
= 150 – 102
Therefore, the number in the second box in the first row = 48
Let us take the second column.
From the rule, 48 + + 52 = 150
+ 100 = 150
= 150 – 100
Therefore, the number in the second box in the second column = 50
Let us take the third column,
From the rule, 49 + + 47 = 15
+ 96 = 150
= 150 – 96
Therefore, the number in the second box in the third column = 54
(ii) Fill this square using all the numbers from 21 to 29.
Rule: The total of each side is 75.
Solution:-
From the question, it is given that the total of each line is equal to 75.
Q8Written answer
Magic Hexagons
Look at the patterns of numbers in 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?
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Solution:-
The circles next to 65 are 5 and 13.
The rule of this method is we get the number in each box by multiplying the numbers in the circles next to it.
(i) Use the same rule to fill the hexagons below.
(a)
Solution:-
11 × 9 = 99
11 × 6 = 66
6 × 17 = 102
17 × 7 = 119
9 × 12 = 108
12 × 7 = 84
(b)
Solution:-
4 × 16 = 64
16 × 8 = 128
8 × 8 = 64
13 × 8 = 104
13 × 6 = 78
Q9Written answer
Numbers and Numbers
(i) Are they equal?
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Solution:-
Yes, the mentioned equation are equal.
Let us consider the left-hand side (LHS) of the first equation = 24 + 19 + 37
LHS = 80
Now, the right-hand side (RHS) = 37 + 24 + 19
RHS = 80
By comparing LHS and RHS,
LHS = RHS
Then, consider second equation, LHS = 215 + 120 + 600
LHS = 935
Now, RHS = 600 + 215 + 120
= 935
By comparing LHS and RHS,
LHS = RHS
(ii) Fill in the blank spaces in the same way.
(a)
Solution:-
(b)
Solution:-
(c)
Solution:-
(iii) Now, look at this –
Check if it is true or not.
Solution:-
First, consider the left-hand side (LHS) = 48 × 13
LHS = 624
Now, consider the right-hand side (RHS) = 13 × 48
RHS = 624
By comparing LHS and RHS,
LHS = RHS
(iv) Now, you try and change these numbers into special numbers.
(a) 28
Solution:-
Take another number 28
Now, turn it back to front 82
Then, add them together 110
Is this a special number? No! Why not?
OK, carry on with the number 110
Again, turn it back to front 011
Then add the two together 121
Ah! 121 is a special number.
(b) 132
Solution:-
Take another number 132
Now, turn it back to front 231
Then add them together 363
Ah! 363 is a special number.
(c) 273
Solution:-
Take another number 273
Now, turn it back to front 372
Then add them together 645
Is this a special number? No! Why not?
OK, carry on with the number 645
Again, turn it back to front 546
Then add the two together 1191
Is this a special number? No! Why not?
OK, carry on with the number 1191
Again, turn it back to the front 1911
Then add the two together 3102
Is this a special number? No! Why not?
OK, carry on with the number 3102
Again, turn it back to the front 2013
Then add the two together 5115
Ah! 5115 is a special number.
(v) 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?
Solution:-
EYE, LEVEL, ROTATOR, NOON, REFER, TOP SPOT etc.
Q10Written answer
Some more Number Patterns
(i) 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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Worked solution
Solution:-
Let us check difference in the answer, 39 – 27 = 12, 51 – 39 = 12, 63 – 51 = 12,
75 – 63 = 12, 87 – 75 = 12, 99 – 87 = 12, 111 – 99 = 12
Therefore, the difference in the answer is the same at every step.
(ii) Look at the numbers below. Look for the pattern. Can you take it forward?
Solution:-
