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.

---------------------------
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.

------------------

No comments: