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:

Post a Comment