**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.