 ### 7. Can You See the Pattern?

Isha, your skirt is beautiful!

My mother made this pattern

I have seen the same block making a different pattern on a kurta.

How was it different?

In your skirt, the rule of the pattern is: one up, one down. Then this is repeated.

But in my brother’s kurta, it is once up, then takes a ¼ turn every time. The rule is to repeat it with a clockwise turn.

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

Also make your own rule.

In Math-Magic Class IV (page 107- 108) , children have seen how one motif is used in 3 different ways and in Class III (page 145), the same sequence of motifs is repeated. Discuss how the motif here turns clockwise.

## 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)

b)

Encourage children to think of other alternatives. Answers obtained by anticlockwise turns should also be accepted and discussed.

c)

d)

2) See this pattern

a)

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

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

b)

c)

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

 a) Rule: _____ () () b) Rule: _____ () () c) Rule: _____ () () d) Rule: _____ () ()

### Look for a Pattern

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

a)

b)

c)

d)

## 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.

 49 46 52 47

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

Rule: The total of each side is 75.

 25

You can see Math-Magic Class IV (page 11) for similar magic patterns.

## Magic Hexagons

Look at the patterns of numbers in hexagons.

Each side has 2 circles and 1 box.

You get the number in each box by multiplying the numbers in the circles next to it.

Look at the number 65 in the box.

Which are the circles next to it?

Can you see how the rule works?

1. Use the same rule to fill the hexagons below.

Now you also make your own magic hexagons.

You can discuss that a hexagon is a six-sided closed figure, but this is not to be evaluated.

### Numbers and Numbers

24+19+37=37+24+19

215+120+600=600+215+120

* Are they equal?

* Fill in the blank spaces in the same way.

a) 14 + _____ + _____ = 34 + 14 + 20

b) _____ +42 + _____ = 65 + _____ + 80

c) 200 + 300 + _____ + = _____ 400 +

d) _____ + _____ + _____ = _____ + _____ +

* Now, look at this — 48 X 13 = 13 X 48

Check if it is true or not.

### Left Right — Same to Same

Can you see something special about 121?

What, it’s just a number!

See it is the same forward as well as backward.

Oh, yes! It is 1,2,1 from right to left also!

Discuss with students that changing the order of numbers does not make any difference to the sum.

Come, let’s see how to get such numbers.

Take a number, say 43

Then add them together 77

Now turn it back to front 34

77 is one such special number.

There are many such numbers.

You have reversed the number by writing it back to front.

Take another number 48

Now turn it back to front 84

Then add them together 132

Is this a special number? No! Why not?

OK, carry on with the number 132

Again turn it back to front 231

Then add the two together 363

Ah! 363 is a special number.

So we see that to get special numbers we sometime need more steps.

* Now you try and change these numbers into special numbers —

a) 28

b) 132

c) 273

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?

Now try and use words in a special way.

Special words/numbers which read the same both ways are called palindromes. Help children to read them from both the ends.

## Calendar Magic

Look at the calendar below.

Let us mark a 3X3 box (9 dates) on the calendar and see some magic.

I can quickly find the total of these numbers in the box.

The total is 99.

Won't that take some time?

Take the smallest number 3

Add 8 to it +8

= 11

Multiply it by 9

Total 99

Hey! Just take the middle number and multiply it by 9. See you can get the answer even faster.

Now you choose any 3X3 box from a calendar and find the total in the same way. Play this game with your family.

You can see Math-Magic Class III (page 105 -106) for other calendar tricks.

## Some more Number Patterns

1. 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?

12 X 2 + 3 = 27

12 X 3 + 3 = 39

12 X 4 + 3 = 51

12 X 5 + 3 = 63

12 X __ + 3 = __

__ X  7 + 3 = __

__ X __ + 3 = __

__ X __ + 3 = __

__ X __ + __ = __

Now try doing it with some other number and also take a different number to add at each step .

*  Look at the numbers below. Look for the pattern. Can you take it forward?

(9 – 1) ÷ 8 = 1

(987 – 3) ÷ 8 = 123

(98 – 2) ÷ 8 = 12

(9876 – 4) ÷ 8 = ____

(98765 – 5) ÷ 8 = ____

( ________–__ ) ÷ 8 = ____

( __________–__ ) ÷ 8 = ____

Encourage children to read aloud the numbers on the left hand side, even if they can not read them correctly. Some of the numbers are large. To help children read them, recall the concept of 1 lakh or 100 thousand.

What if someone gives you to add ten numbers together?

Oh! I can find it quickly.

Smart! How can you do that?

I can get the sum without adding.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

11 + 12 + _____ + _____ + _____ + _____ + _____ + _____ + _____ +20 = 155

21 + _____ + _____ + _____ + _____ + _____ + _____ + _____ + _____ +30 = _____

31+ _____ + _____ + _____ + _____ + _____ + _____ + _____ + _____ +40 = _____

41+ _____ + _____ + _____ + _____ + _____ + _____ + _____ + _____ +50 = _____

51 + _____ + _____ + _____ + _____ + _____ + _____ + _____ + _____ + 60 = 555

61 + _____ + _____ + _____ + _____ + _____ + _____ + _____ + _____ + 70 = _____

1. Did you notice some pattern in the answers?

## Fun with Odd Numbers

Take the first two odd numbers. Now add them, see what you get.

Now, at every step, add the next odd number.

1 + 3 = 4 = 2 X 2

1 + 3 + 5 = 9 = 3 X 3

1 + 3 + 5 + 7 = 16 = 4 X 4

1 + 3 + 5 + 7 + 9 = __ = __X__

1 + 3 + 5 + 7 + 9 + 11 = __ = __X__

1 + 3 + 5 + 7 + 9 + 11 + 13 = __ = __X__

How far can you go on?

When we add the first n odd numbers, we will get the sum as nXn . Children should be left free to add the numbers.

## Secret Number

Banno and Binod 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?

What is my secret number? _____

1. It is larger than half of 100

2. It is more than 6 tens and less than 7 tens

3. The tens digit is one more than the ones digit

4. Together the digits have a sum of 11

What is my secret number? _____

1. It is smaller than half of 100

2. It is more than 4 tens and less than 5 tens

3. The tens digit is two more than the ones digit

4. Together the digits have a sum of 6

* Write a set of clues for a secret number of your own. Then give it to a friend to guess your secret number.

## Number Surprises

a) Ask your friend rite — W down your A age. dd 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?

b) Take a number _____

Double it _______ X 2 = ______

Multiply by 5  _______ X 5 = ______

Divide your answer by 10 _______ X 10 = ______

c) Take a number _____

Double it  _________

Again double it  _______ X 2 = ______

Add the number you took first to the answer _____ + _____ = _____

Now again double it  _______ X 2 = ______

Divide by 10  _______ / 10 = ______

d) Look at this pattern of numbers and take it forward.

1 = 1 × 1

121 = 11 × 11

12321 = 111 × 111

1234321 = ?

* Now make your own number surprises.