This document contains instructions for 5 math activities involving numbers: 1. Creating a "magic box" using addition of numbers in rows and columns. 2. Guessing a number by reversing digits, subtracting, and reversing the answer. 3. Determining a missing digit by adding digits, subtracting from the original number, and using divisibility by 9. 4. A probability activity using objects and counting possibilities. 5. Repeating a 3-digit number and dividing the result by 11, 1001.

1. Fun with Numbers

2. ACTIVITY NO. 1
MAGIC BOX

3. Reference: lesson no. 4. “Operations on Fractions”/pg 28/std 6th /Math/SCC

4. Let us try to make a magic square
with any number

5. 4 5 6 7
8 9 10 11
12 13 14 15
16 17 18 19

6. 4 5 6 7
8 9 10 11
12 13 14 15
16 17 18 19
5 6
8 11
12 15
17 18
Magic box

7. e.g. 16+ 11+15+4 = 46
Valid for all column and rows, also for diagonal
elements..
5 6
8 11
12 15
17 18
46 x 4 = 184 (sum of all the elements in the box)
4 x 4 Box

8. ACTIVITY NO. 2
Guessing a Number Without
Asking Anything

9. Take any three-digit number SAY 512
(but one in which the difference between the
extreme digits is not less than 2)
reverse the order of the digits SAY 215
Subtract the smaller number from the bigger
i.e 512 – 215 = 297
Add the result to itself, only written in
reverse order. 297 + 792 = ?
STEP 1
STEP 2
STEP 3
STEP 4

10. 1089
Let me Guess a Number Without Asking you all Anything
You all end up with same addition

11. Consequently, the difference
consists of the
following three
digits:
Number of hundreds: (a — c — 1),
number of tens: 9,
number of units: (10 + c — a).
We then do the following transformations:
99a - 99c = 99 (a - c)
= 100 (a - c) - (a - c)
= 100 (a - c) - 100 + 100 - 10 + 10 - a + c
= 100 (a - c - 1) + 90 + (10 - a + c).
= 100 (a - c - 1) + 10x9 + (10 - a + c).

12. ACTIVITY NO. 3
The Missing Digit

13. STEP 1: Take any multi-digit number,
say, 847.
STEP 2:
Add up these three digits
(8 + 4 + 7) = 19
Subtract the total from the original.
STEP 3:
The result will be:
847 - 19 = 828.

14. cross out any one of the three digits
Say, 8 2 8
the remaining number are: 8 2

15. Tell me the remaining ones.
I will tell the digit you has
crossed out,
Although I know neither the original nor
what you have done with it.

16. How is this explained?

17. If in the number 828 you crosses out the first digit (8)
and tells me the other two (2 and 8),
I added them and get 10.
The nearest number divisible by 9 is 18.
The missing number is consequently 8.

18. No matter what the number is,
if you
subtract from it the total number of its digits,
the balance will
always be divisible by 9.

19. Algebraically,
Let, abc = (100a + 10 b + c)STEP 1:
STEP 2:
Add up these three digits
(a + b + c)
STEP 3:
Subtract the total from the original.
(100a + 10 b + c) – (a + b + c) = 99a + 9b

20. As, abc = 100a + 10b + c - (a + b + c)
= 99a + 9b
= 9 (11a + b).
But, 9 (11a + b) is, of course, divisible by 9.
Therefore, when we subtract from a number the
sum total of its digits, the balance' is always
divisible by 9.

21. It may happen that the sum of the
digits you are told is divisible by 9,
That shows that the digit your friend
has crossed out is either 0 or 9,
and in that case
you have to say that the missing digit
is either 0 or 9.

22. Here is another version of the same trick:

23. STEP 1: Take any multi-digit number,
say, 8247.
STEP 2:
transposed in any way
Say, 4827 (or 2847,7872 and so on)
Subtract the total from the original.
STEP 3:
The result will be:
8247 - 4827 = 3420.

24. cross out any one of the three digits
Say, 3420
the remaining number are: 3 4 0

25. Tell me the remaining ones.
I will tell the digit you has
crossed out,
Although I know neither the original nor
what you have done with it.

26. ACTIVITY NO. 4
Who Has It?

27. This clever trick requires three little things
OBJECT: A
OBJECT: B
OBJECT: C

28. Remaining = 24 – 6 = 18

29. Remaining = 24 – 6 = 18
OBJECT: A
X1
OBJECT: B
X 2
OBJECT: C
X4
BA C
Remaining = 18 – 15 = 3

30. 6
5
4
3
2
1
2 3
TOTAL POSSIBILITIES
1
Person:
Patterns:

31. Remaining = 18 – 15 = 3
Patterns
Number of marbles taken Total
marbles
Total
marbles in
plate
acb 1 + 1 = 2 2 + 8 = 10 3 + 6 = 9 2+10+9 = 21 24-21 = 3
abc 1 + 1 = 2 2 + 4 = 6 3 + 12 = 15 2+6+15 = 23 24-23 = 1
bac 1+ 2 = 3 2+ 2 = 4 3 + 12 = 15 3+4+15 = 22 24-22 = 2
bca 1+ 2 = 3 2+ 8 = 10 3 + 3 = 6 3+10+6 = 19 24-19 = 5
cab 1+ 4 = 5 2+ 2 = 4 3 + 6 = 9 5+ 4+ 9 = 18 24-18 = 6
cba 1+ 4 = 5 2+ 4 = 6 3 + 3 = 9 5+ 6+ 9 = 20 24-20 = 4
Object A= x1 of its marbles
Object B= x2 of its marbles
Object C= x4 of its marbles

32. ACTIVITY NO. 5
COOL CALCULATION

33. TAKE ANY 3 DIGIT NUMBER
SAY 256
AGAIN REPEAT IT
256256

34. 𝟐𝟓𝟔𝟐𝟓𝟔 ÷ 𝟕 = 𝟑𝟔𝟔𝟎𝟖
𝟑𝟔𝟔𝟎𝟖 ÷ 𝟏𝟏 = 𝟑𝟑𝟐𝟖
𝟑𝟐𝟐𝟖 ÷ 𝟏𝟑 = 𝟐𝟓𝟔

35. 256256 = 256 x 1001
abcabc = abc x 1001
AS, 7 X 11 X 13 = 1001