Learning to count and factorize

Group 1

Not learning to count 1, 2, 3, 4, 5, 6, ... learning to count figures!

Students in the morning class learned how to solve problems that involve counting the number of shapes in a given figure. For example, how many squares are in the following figures?

a.
┌─┐
└─┘

b.
┌─┬─┐
├─┼─┤
└─┴─┘

c.
┌─┬─┬─┐
├─┼─┼─┤
├─┼─┼─┤
└─┴─┴─┘

The answers are 1, 5, and 14. The students learned that these numbers can be broken down into 1, 1+4, and 1+4+9. They look like the sum of square numbers! And indeed it could be proven that this is the correct way to find the number of squares in squares of any size.

The students learned similar techniques for more types of figures.

Group 3

Today, the group learned advanced techniques for factoring, which is simplifying an expression into a product of smaller expressions. First, they went over some fundamental algebraic factoring techniques. Then, they learned a special technique called Simon's Favorite Factoring Trick (or SFFT for short).