| a) |
|
Count-on addition |
| |
|
Count on 1, 2 or 3 from any number. |
| |
|
|
6 |
+ |
2 |
= |
6, 7, 8 |
| |
|
(extension) |
321 |
+ |
3 |
= |
321, 322, 323, 324 |
| |
|
Always start with the larger number and add on. |
| |
| b) |
|
Add zero |
| |
|
The answer is always non-zero number. |
| |
|
|
0 |
+ |
12 |
= |
12 |
| |
|
(extension) |
129 |
+ |
0 |
= |
129 |
| |
| c) |
|
Turn-around fact |
| |
|
|
6 |
+ |
7 |
= |
13 |
|
therefore |
7 |
+ |
6 |
= |
13 |
| |
|
(extension) |
60 |
+ |
70 |
= |
130 |
|
therefore |
70 |
+ |
60 |
= |
130 |
| |
|
|
600 |
+ |
700 |
= |
1300 |
|
therefore |
700 |
+ |
600 |
= |
1300 |
| |
| d) |
|
Doubles |
| |
|
Basic facts doubles (0 + 0, 1 + 1, ... 9 + 9) are useful and need to be learnt. |
| |
|
Extension of these facts should be achieved as mental mathematics skills
develop. |
| |
|
For example: 10 + 10, 11 + 11 ... |
| |
| e) |
|
Double plus one (and turn around) |
| |
|
To use this strategy, double facts must be known. The strategy should be used for
facts that are one more than the doubles facts. |
| |
|
|
7 |
+ |
8 |
= |
? |
| |
|
|
7 |
+ |
7 |
= |
14 |
|
(known fact) |
| |
|
|
7 |
+ |
8 |
= |
14 |
|
+ 1 |
| |
|
|
7 |
+ |
8 |
= |
15 |
| |
|
If |
7 |
+ |
8 |
= |
15 |
| |
|
|
8 |
+ |
7 |
= |
15 |
|
(turn around) |
| |
|
(extension) |
25 |
+ |
26 |
= |
? |
|
| |
|
|
25 |
+ |
25 |
= |
50 |
|
(known double) |
| |
|
|
25 |
+ |
26 |
= |
50 |
|
+ 1 |
| |
|
|
25 |
+ |
26 |
= |
51 |
| |
| f) |
|
Double plus two (with turn-around) |
| |
|
To use this strategy, double facts must be known. The strategy should be used for
facts that are two more than the doubles facts. |
| |
|
|
5 |
+ |
7 |
= |
? |
| |
|
|
5 |
+ |
5 |
= |
10 |
|
(known double) |
| |
|
|
5 |
+ |
7 |
= |
10 |
|
+ 2 |
| |
|
|
5 |
+ |
7 |
= |
12 |
|
+ 2 |
| |
|
If |
5 |
+ |
7 |
= |
12 |
| |
|
|
7 |
+ |
5 |
= |
12 |
|
(turn around) |
| |
|
(extension) |
45 |
+ |
47 |
= |
? |
|
| |
|
|
45 |
+ |
45 |
= |
90 |
|
(known double) |
| |
|
|
45 |
+ |
45 |
= |
90 |
|
+ 2 |
| |
|
|
45 |
+ |
47 |
= |
92 |
| |
| g) |
|
Use ten |
| |
|
This is a useful strategy whenever its necessary to find the sum of two numbers,
one of which is 9 or 11. |
| |
|
If one number is 9, 1 is added to make 10 for ease of calculation. |
| |
|
After the calculation has been made the 1 is subtracted. |
| |
|
|
9 |
+ |
5 |
= |
? |
| |
|
|
10 |
+ |
5 |
= |
15 |
| |
|
|
9 |
+ |
5 |
= |
15 |
|
- 1 |
| |
|
|
9 |
+ |
5 |
= |
14 |
| |
|
(extension) |
252 |
+ |
9 |
= |
? |
| |
|
|
252 |
+ |
10 |
= |
262 |
| |
|
|
252 |
+ |
9 |
= |
262 |
|
- 1 |
| |
|
|
252 |
+ |
9 |
= |
261 |
| |
|
If one number is 11, 1 is subtracted to make 10. After the calculation has been
made, the 1 is added. |
| |
|
|
11 |
+ |
7 |
= |
? |
| |
|
|
10 |
+ |
7 |
= |
17 |
| |
|
|
11 |
+ |
7 |
= |
17 |
|
+ 1 |
| |
|
|
11 |
+ |
17 |
= |
18 |
| |
|
(extension) |
161 |
+ |
11 |
= |
? |
| |
|
|
161 |
+ |
10 |
= |
171 |
| |
|
|
161 |
+ |
11 |
= |
171 |
|
+ 1 |
| |
|
|
161 |
+ |
11 |
= |
172 |
| |
| h) |
|
Make ten or multiples of ten |
| |
|
This strategy is most useful when adding 7, 8 or 9 to a number. |
| |
|
| 6 + 9 = ? |
|
13 + 8 = ? |
|
27 + 7 = ? |
| 6 + (4 + 5) |
|
13 + (7 + 1) |
|
27 + (3 + 4) |
| (6 + 4) + 5 |
|
(13 + 7) + 1 |
|
(27 + 3) + 4 |
| 10 + 5 = 15 |
|
20 + 1 = 21 |
|
30 + 4 = 34 |
|
| |
|
Notice that in each case, the number other than 7, 8 or 9 determines how the 7,
8 or 9 will be regrouped. If the second example had been 14 + 8 = ?, 8 would be
regrouped as 6 + 2 and not 7 + 1. |
| |
|
| 14 + 8 = ? |
| 14 + (6 + 2) |
| (14 + 6) = 20 |
| 20 + 2 = 22 |
|
| |
| i) |
|
Number of strings |
| |
|
A string of numbers occurs when three or more numbers have to be totalled. |
| |
|
For example: 2 + 7 + 8 = ? 8 + 9 + 3 + 2 = ? |
| |
|
Here are some strategies that can be used to total a string of numbers. |
| |
|
Add to ten |
| |
|
6 + 8 + 4 = ? |
| |
|
6 + 4 = 10 or 4 + 6 = 10 (known fact) |
| |
|
then 10 + 8 = 18 |
| |
|
7 + 6 + 3 = ? |
| |
|
7 + 3 = 10 or 3 + 7 = 10 (known fact) |
| |
|
then 10 + 6 = 16 |
| |
|
Using doubles |
| |
|
7 + 3 + 7 = ? |
| |
|
7 + 7 = 14 (known fact) |
| |
|
then 14 + 3 = 17 |
| |
|
Using double plus one or double plus two |
| |
|
7 + 5 + 6 = ? 9 + 7 + 4 = ? |
| |
|
7 + 6 = 13 9 + 7 = 16 |
| |
|
13 + 5 = 18 16 + 4 = 20 |
| |
|
Using a known fact |
| |
|
4 + 3 + 6 = ? |
| |
|
4 + 3 = 7 (known fact) |
| |
|
7 + 6 = 13 (double plus one) |
| |
|
Using ten |
| |
|
11 + 6 + 2 = ? |
| |
|
10 + 6 = 16 (known fact) |
| |
|
11 + 6 = 16 + 1 |
| |
|
11 + 6 = 17 |
| |
|
17 + 2 = 19 |
| |
|
A combination of any of the above |
| |
|
9 + 5 + 4 = ? 9 + 5 + 4 = ? |
| |
|
5 + 4 = 9 (known fact) 10 + 5 = 15 |
| |
|
9 + 9 = 18 (double) 9 + 5 = 15 - 1 (use ten) |
| |
|
9 + 5 = 14 |
| |
|
14 + 4 = 18 |
| |
2D shapes, 3D objects, Nets
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