Polya. A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. . Polya.
A teacher of mathematics has a great opportunity.
If he fills his allotted time with drilling his students
in routine operations he
But if he challenges the curiosity of his students
by setting them problems proportionate to their
helps them to solve their problems with stimulating
he may give them a taste for, and some means of,
Incomplete understanding of the problem … is perhaps the most widespread deficiency in solving problems.... Some students rush into calculations and constructions without any plan or general idea; others wait clumsily for some idea to come and cannot do anything that would accelerate its coming.
Let’s look at some examples!!!
SHOCKING!!! It worked!
i = 3 j = 5 k = 7 i2 + j2 + k2 = 8 x 10 + 3 = 83
i = 2 j = 4 k = 6 i2 + j2 + k2 = 8 x 7 = 56
i = 3 j = 4 k = 5 i2 + j2 + k2 = 8 x 6 + 2 = 50
i = 4 j = 5 k = 6 i2 + j2 + k2 = 8 x 9 + 5 = 77
Written in positive terms...
Can we avoid doing 8 cases?
1. Even Even Even
2. Even Odd Even
3. Even Even Odd
4. Even Odd Odd
5. Odd Even Even
6. Odd Odd Even
7. Odd Even Odd
8. Odd Odd Odd
m=0, or 4
m=2 or 6