Here is a suggested sequence for introducing multiplication facts, together with useful
strategies for working out unknown facts.
| a) |
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Tens with turn-arounds |
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All multiples of ten end in zero. |
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8 |
x |
10 |
= |
30 |
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(Turn-around: 10 x 3 = 30) |
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Most children learn these facts fairly easily. |
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| b) |
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Twos with turn-arounds |
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The number to be multiplied by two is doubled. |
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8 |
x |
2 |
= |
16 |
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Double 8 is 16 |
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(Turn-around: 2 x 8 = 16) |
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If all the tens and twos facts, together with their turn-arounds are known, about one-third of all basic multiplication facts are known. |
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| c) |
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Fives with turn-arounds and/or tens facts and halving |
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Answers to these facts always end in 5 or 0. If it is an even number of fi ves being considered, the answer will end in 0. |
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If it is an odd number of fives being considered, the answer will end in 5. |
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Use tens facts and halving. |
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One half of 60 is 30. |
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If all tens, twos and fives facts, together with their turn-arounds, are known, almost one-half of multiplication facts are known. |
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| d) |
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Ones with turn-arounds |
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One lot of any number is the number itself. |
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1 |
x |
7 |
= |
7 |
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(Turn-around: 7 x 1 = 7) |
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| e) |
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Zeros with turn-arounds |
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In the early stages, there needs to be a lot of practise at putting out ‘zero sets’ of a given number of objects. Later, your child should understand that any number multiplied by zero will give a result of zero. |
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4 |
x |
0 |
= |
0 |
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(Turn-around: 0 x 4 = 0) |
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| f) |
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Fours with turn-arounds |
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The answers to these facts will always be even numbers. Answers can be obtained by 'doubling doubles'. |
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3 |
x |
4 |
= |
? |
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4, 8, 12 (counting by fours) |
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Double 8 = 16; double 16 = 32 |
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4 |
x |
8 |
= |
32 |
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(Turn-around: 8 x 4 = 32) |
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| g) |
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Nines with turn-arounds |
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The digits in the answer always add to nine. |
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1 |
x |
9 |
= |
9 |
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0 |
+ |
9 |
= |
9 |
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2 |
x |
9 |
= |
18 |
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1 |
+ |
8 |
= |
9 |
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3 |
x |
9 |
= |
27 |
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2 |
+ |
7 |
= |
9 |
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4 |
x |
9 |
= |
36 |
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3 |
+ |
6 |
= |
9 |
(etc) |
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The tens digit in each two-digit answer is one less than the number of nines. |
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5 x 9 = 45 3 x 9 = 27 6 x 9 = 54 |
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After finding the first digit of an answer, it is possible to work out the second digit, as together they must add to nine. |
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7 |
x |
9 |
= |
6? |
'I can work out the tens digit because there are seven nines so the tens digit of the answer will be one less, which is six. |
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7 |
x |
9 |
= |
63 |
Together the two digits of the answer must total nine so the second digit must be three
(9 - 6 = 3).' |
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Another way of working out nines facts is to use tens facts and subtraction. |
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7 |
x |
9 |
= |
? |
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7 |
x |
10 |
= |
70 |
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(known fact) |
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7 |
x |
9 |
= |
70 |
- |
7 |
= |
63 |
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| h) |
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Square numbers |
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Given visual aids, most children discover these facts fairly easy to learn. |
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3 |
x |
3 |
= |
9 |
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2 |
x |
2 |
= |
4 |
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| i) |
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Remaining facts |
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If the preceding facts have been learned, only three facts and their turn-arounds remain. |
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6 |
x |
7 |
= |
42 |
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(Turn-around: 7 x 6 = 42) |
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6 |
x |
8 |
= |
48 |
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(Turn-around: 8 x 6 = 48) |
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8 |
x |
7 |
= |
56 |
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(Turn-around: 7 x 8 = 56) |
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Some strategies for solving these facts follow: |
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6 |
x |
7 |
= |
? |
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10 x 7 = 70 (known fact);
halve to find 5 x 7 (35);
add 1 x 7 (35 add 7 is 42) |
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6 |
x |
6 |
= |
36 |
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(known fact);
add 1 x 6 (36 + 6 = 42) |
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7 |
x |
7 |
= |
49 |
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(known fact);
subtract 1 x 7 (49 - 7 = 42) |
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3 |
x |
7 |
= |
21 |
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(known fact);
double for 6 x 7 (21 + 21 = 42) |
| and |
2
4 |
x |
7
7 |
=
= |
14
28 |
|
(known facts);
add products for 6 x 7
(14 + 28 = 42) |
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2 |
x |
7 |
= |
14 |
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(known fact);
add 14 + 14 + 14 i.e. 3 x (2 x 7) |
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6 |
x |
8 |
= |
? |
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10 x 8 = 80 (known fact);
halve to find 5 x 8 (40);
add 1 x 8 (40 add 8 is 48) |
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6 |
x |
6 |
= |
36 |
|
(known fact); add on 6 x 2 (12) |
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5 |
x |
8 |
= |
40 |
|
(known fact); add on 1 x 8 |
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3 |
x |
8 |
= |
24 |
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(known fact); double 24 |
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8 |
x |
7 |
= |
? |
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4 x 7 = 28 (known fact); double 28 |
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8 |
x |
8 |
= |
64 |
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(known fact); subtract 8 x 1 |
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2 |
x |
7 |
= |
14 |
|
(known fact);
add 14 + 14 + 14 i.e. 4 x (2 x 7) |
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10 |
x |
7 |
= |
70 |
|
(known fact);
subtract 14 i.e. (2 x 7) |
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7 |
x |
7 |
= |
49 |
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(known fact);
add 7 |
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| j) |
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Other strategies for solving basic multiplication facts |
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• Repeated addition |
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3 |
x |
7 |
= |
? |
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7, 14, 21 (counting by sevens) |
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• Counting on |
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2 |
x |
4 |
= |
? |
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4, 5, 6, 7, 8
(counting on from 4, noting groups of 4) |
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The counting on strategy is quite different when dealing with larger numbers (6, 7, 8, 9) and its use in these instances should be discouraged. |
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2D shapes, 3D objects, Nets
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