Multiplication Methods | Long Multiplication, Chunking and Grid

Multiply big numbers by breaking them into parts is the easiest way, especially when working with non calculator papers.

Here, are illustrations on how to make calculations by using Long Multiplication, Multiplication by Chunking and Multiplication by Grid

Work out the value of 135 x 27

Method 1 - Long Multiplication by Chunking

             135
             x22
             -----
             270 .........multiply 2 x 135
         +2700..........put a 0 under 0, then multiply 2 x 135 and add the results
           ------
           2907
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Method 2 - Multiplication by Chunking

In 135, we have 100 + 30 + 5. Multiply each part by 22

           100 x 22 = 2200
             30 x 22 =   660...easy mental calculation, if 3 x 22 = 66, 30 x 22= 660  
               5 x 22      110
                              ------
                              2970     .......add 2200, 660 and 110 together       ...Happy now? :)
                            ---------

Method 3 - Multiplication by Grid

100   30   5
    0   20   2
---------------
      0      0      0               ....x 0
2000  600  100            ......x20
  200    60    10            ........x2
------------------
2200   660   110          .....add the number down
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    2970                           .....................Take the grand total (add across)       ......Get it? :( haha!
...............

Teachers' Note - it is important to use simple methods without diverting from traditional ones. However, introducing an optional method can help others students with difficulty in application of the other.

Students' Note - It is better to know two other methods that one.

How to Memorise Multiples of 9

This is the best and easiest technique I learnt in my first year of teaching. Could have been really helpful if I had known in back in Grade 2...

The idea is discovering the pattern in multiples of 9.


Source: PNG Teachers on Facebook

1 x 9 = 09
2 x 9 = 18
3 x 9 = 27
4 x 9 = 36
5 x 9 = 45
6 x 9 = 54

Do you see the pattern developing?
The tens increase from 0, 10, 20, 30, 40, 50....
Units decrease from 9, 8, 7, 6, 5, 4, ....

Now, you can smile :) and complete the rest...

7 x 9 =
8 x 9 =
9 x 9 =
10 x 9 =
11 x 9 =
12 x 9 =
13 x 9 =

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Hope this helps :)

Memorising Vs Collective Summation | 4x, x6, x7, x8, x12 & x 13

My Gr 2 headmaster in the village would let us out for recess if only we recite our multiplication tables. Those were the times. Here, is a strategy and if used properly can be very effective too.

I'd like to called it 'Collective Summation'. It uses the idea of patterns and simple multiplication & addition.

Students can easily recall the first 5 multiples of 4

4 x 1 = 4
4 x 2 = 8......I will us this to show the strategy
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20

Strategy 1
Key: remember the last multiple and add 4.

4 x 2 = 8

then 4 x 3 = 12 = 4 + 8
        4 x 4 = 16 = 4 + 12
        4 x 5 = 20 = 4 + 16

Instead of responsive recall of multiples of 4, what you are doing is actually working with what you know and adding a 4 to the subsequent number to get the next.

This strategy can be applied to hard-to-recall multiples in 6, 7, 8 and 13 times tables.

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Strategy 2

Using square numbers:

4 = 2 x 2
9 = 3 x 3
16 = 4 x 4
25 = 5 x 5
36 = 6 x 6
49 = 7 x 7
64 = 8 x 8
81 = 9 x 9
100 = 10 x 10
121 = 11 x 11
144 = 12 x 12
169 = 13 x 13

If you know, you can easily work out the multiples, when these numbers are doubled.
2 x 2 = 4            2 x 4 = 8 = 4 + 4

3 x 3 = 9            3 x 6 = 18 = 9 + 9
-----------------------------------------
16 = 4 x 4          4 x 8 = 32 = 16 + 16
25 = 5 x 5          5 x 10 = 50 = 25+ 25

36 = 6 x 6           6 x 12  = 72 = 36 + 36
49 = 7 x 7           7 x 14 = 58= 49 + 49

Got the idea? Now, try these

64 = 8 x 8              8 x 16 =
81 = 9 x 9              9 x 18 =

100 = 10 x 10              10 x 20 =
121 = 11 x 11              11 x 11 =

144 = 12 x 12              12 x 24 =
169 = 13 x 13               13 x 26 =

Teacher's Note: You may have a technique you have used in class over time - this is what I personally find useful. It can give your students confidence in you, too. (You know what I mean when you cannot do 12 x 24 in front of your student :))

Students' Note: You will find this useful when doing calculation involving 12 x 12, 12 x 24, 13 x 13 and 13x 26. It can save you lots of exam time.

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