Discover the relationship between problems with the data or vice versa. Are you able to find a clear relationship between the two? Consider the data, consider the question. Did you ever find a similar problem before?
For high school kids, 12 x 13 = ..... We can directly do about it. We multiply as usual. Is there another way? Why not try finding alternatives?
For small children, if he already knew the multiplication of two digit numbers with two digits? Is he already knew the multiplication of two digit numbers by one digit? Can you teach it in stages?
The third step. Carry out the plan. Check the step by step. Does each stage right? Can you prove the truth? Are there stages of this can be seen easily?
For high school kids, 12 x 13 = ... is computed by writing down tiered:
12
13
--- x
36
120
--- +
156
Are you sure every step of the above is true? Why?
For kindergarten children or early elementary school, depending on student ability. If children are familiar with multiplication 2 digits times two digits can be done by way of the above. But when children are new to multiplying two digits times one digit, we can depart from here.
12 x 13 = ...
12 x (10 + 3) = ...
(12 x 10) + (12 x 3) = ...
Watch out carefully! Do you send your child to do the calculation on top! The calculation above is only for us, adults. The kids just want to calculate your
12 x 10 = ...
Assure that the multiplication by 10 is easy. Just add a 0 behind it. So 12 added figures behind it. 12 x 10 = 120.
Try it, your child will love it.
Then ask your child count
12 x 3 = 36
Your child should have been able to multiply 12 by 3. If not, you can train him now.
After that, have the children add up 120 + 36 = ....
We get 120 + 36 = 156.
This is the final answer you want. Do the exercise with several different figures. Stay awake cheerful atmosphere of learning. Once the child is well above manner, introduce multiplicative multilevel way down like high school kids. Your kids will love it.
What's interesting is there are methods of Polya fourth step. Even though we have obtained a solution at the third step. In my opinion, the most important is the fourth step. The fourth step is generating much faster mathematical formula. Step four is also very important for small children learning.
Step four. Look back in full. How you can get the answer? Are you able to test the response? Can you test the argument? Can you get the results in a different way? Can you see just a glimpse? Can you use this result to how or other problems?
Both, for example 12 x 13 = ... can we get a solution using different ways?
Add 12 + 3 = 15 then multiply the 2 x 3 = 6
One obtains 156. (Complete)
Another example: 12 x 14 = .... Add 12 + 4 = 16 then multiply the 2 x 4 = 8
One obtains 168. (Complete)
Another example: 11 x 15 = ... Add 11 + 5 = 16 then multiply 1 x 5 = 5
One obtains 165. (Done).
Easy to do!
For junior high school kids already know that
(X + 2) (x + 3) =
x.x + (2x + 3x) + 2.3 =
Similarly how:
306 x 303 =
9 (from 3 × 3)
27 (from 6 × 3 + 3 × 3)
18 (from 6 × 3)
We obtained 92 718 answers.
Another example
207 x 304 = ...
6 (from 2 × 3)
29 (from 7 × 3 + 2 × 4)
28 (from 7 × 4)
We acquired 62 928.
