NCERT Solutions for Class 4 Mathematics Unit-10 Play With Patterns
In the magic box, 1, 2, and 3 is arranged in such a way that no number comes twice In any line.
In the magic box, there are 9 boxes and the digits from 1 to 9 are arranged in such a way that the sums of all line are equal.
In the magic pattern given here the number from 1 to 9 is used and the numbers ‘ on each line add up to 12.
This is a magic triangle. In the number from 1 to 6 are used. The sum of all sides are 9.
In secret message the numbers denoting the alphabet are used to form a message.
A = 1, B = 2, C = 3, D = 4, E = 5, F = 6, G = 7, H = 8,1 = 9, J = 10, K = 11, L = 12,
M = 13, N =14, O = 15, P = 16, Q = 17, R = 18, S = 19, T = 20, U = 21, V = 22, W = 23,
X = 24, Y = 25, Z = 26.
NCERT Textbook Page 108
1. Can you see how Tinu has made different patterns using the same block? Now
you too make 3 different patterns using
Ans.
Pattern-1
Pattern-2
Pattern-3
NCERT Textbook Page 109
1. Yamini has used her blocks to make a few patterns. Help her to take these patterns forward.
Ans. Do yourself.
2. We can also make patterns with numbers and letters. Below are a few examples. Can you take them forward?
Ans. Do yourself. ‘
3. Now write your own number patterns.
Ans. Do yourself.
4. Make a pattern without numbers.
Ans. Pattern without numbers is as follows:
NCERT Textbook Page 110
No Number Comes Twice
1. Now you try writing the letters-A, B, C in the box so that no letter comes twice in any line.
Ans.In the following pattern no letters repeat in a line.
NCERT Textbook Page 111
Magic Patterns
1. Now you fill these stars. Use numbers 1-9 and the
rule that the numbers on each line add up to 15.
Ans. The number from 1 to 9 are filled in the stars. Which added upto 15 in each line.
Magic Triangles
Look at this number pattern.
Rule: Numbers on each side of the triangle add up to
9. 3 + 4 + 2 = 9
2. See if the other sides-of the triangle also add up to 9.
Ans. Yes, numbers on the other sides of triangle add up to 9.
3 + 5 + 1 = 9 2 + 6 + 1 = 9
NCERT Textbook Page 112
1. Now use numbers 1-6 to make your own magic triangle.
Rule: Numbers on each side must add up to It
Ans.The numbers from 1—6 can be arranged as follows which will be added up to 10.
1 + 6 + 3 = 10 1 + 4 + 5 = 10 3 + 2 + 5 = 10
NCERT Textbook Page 113
1. Using the same rule, complete these number towers.
Ans. In the circle towers, numbers at the base is added and form the number of the above circle.
5 + 10 = 15 15 + 20 = 35 15 + 25 = 40
25 + 35 = 60 60 + 40 = 100
In the rectangle number tower:
1 + 2 = 3 2+3=5 3+4=7
4 + 5 = 9
In the third level
3 + 5 = 8 5 + 7 = 12 7 + 9 = 16
In the fourth level
8 + 12 = 20 12 + 16 = 28 On the fourth level (top)
20 + 28 = 48
The Same Sum Rule
1. Now you write any number and the three numbers after that. Make a pattern using the rule.
See if you get the same sum
Ans.The number using the same pattern is as follows:
NCERT Textbook Page 114
Patterns with Addition
1. Now you try to make such a pattern with 5 numbers in order.
Ans.
1 + 2 + 3 + 4 + 5 = 15 2 + 3 + 4 + 5 + 6 = 20
3 + 4 + 5 + 6 + 7 = 25 4 + 5 + 6 + 7 + 8 = 30
5 + 6 + 7 + 8 + 9 = 35
2. Does the sum grow by 5 each time?
Ans. Yes, the sum grows by 5 each time.
NCERT Textbook Page 115
Secret Messages
1. Complete this list of letters and numbers to help you.
Ans.
2. Teenu wants to write to his friend ‘Good Morning’. What will he write by using the same rule?
Ans. 7 15 15 4 13 15 18 14 9 14 7
3. If we change the rule and write 1 in place of ‘B’, 3 in place of ‘D’ and so on, then how, will we write ‘Let Us Dance’?
Ans.
Let Us Dance will be-11 4 19 20 18 3 26 1324
NCERT Textbook Page 116
More Secret Messages
Jaggu-You see, we have changed each letter by its next letter. That is, we write ‘G’ in place of ‘F’, ‘O’ in place of‘N’. So ‘YES’-becomes ‘ZFT’.
Kahuli-See what I have written-‘XF BSF GSJFOET?
1. What was Kahuli’s secret message?
Ans. New arrangement of letters for secret message is as follows:
Therefore, secret message written by Kahuli ‘
‘XF BSF GSJFOET’ will be-WE ARE FRIENDS
2. What did Shablu and Jaggu write?
Ans. Shablu’s secret message is-TFMMP! IPX BSF ZPV?’ And ‘XJMM ZPV QMBZ XJUI NF?’
Therefore
‘IFMMP! IPX BSF ZPV?’ will be – Hello! How are you?
And ‘XJMM ZPV QMBZ XJUI NF?’ will be – Will you play with me?
Jaggu’s secret message is-‘GJOF UIBOL ZPV. ZFT!’
This will become-Fine thank you. Yes!
3. Use the same rule to write-Meet me on the moon’.
Ans. The secret message for ‘Meet me on the moon’ will become-Nffu nf po uif nppo.
4. Make different rules and ask your friends to crack the secret message.
Ans. New rule-Write ‘A’ at the place of ‘C’, B at the place of‘D’ and so on. Following this rule the new key will be
Write the ‘I am going to play’ using this new rule This message will become-G yk emgle tm njyw.
NCERT Textbook Pages 117-119
1. Anisha is playing with this card. Draw what it will look like when upside down.
Ans. This card looks like as follows when keep upside down.
Floor Patterns
2. Have you ever seen a floor with tiles of these shapes?
Ans. No, I did not see this type of floor tiles.
(a) Now, you cover this floor with this tile.
Ans. For self attempt.
(b) Can you make such a floor design with a tile like a circle?
Try with this green tile without leaving a gap. Could you do it? Discuss with your friends.
Ans. For self attempt.
Now we cannot make the design without leaving a gap using circular tiles.
(c) Complete this tiling pattern.
Ans. For self attempt.
(d) Ramaiya has made a wall with his blocks. Can you complete this for him?
Ans. For self attempt.
(e) Renu began to paint this wall. Now you help her to complete it.
Ans. For self attempt.