Because: the total number of flowerpots in the hollow square = (the number of flowerpots on each side of the outermost layer-the number of layers in the hollow square) ××××× the number of layers in the hollow square ×4.

The total number of 204 pots of flowers here is the total number of pots. Now, the number of pots on each side of the outer floor can be calculated from the total number of pots. You can refer to the previous hollow square diagram (the hollow square diagram on Exercise 1 in Lecture 27 of Olympic Daily Training) and deduce the answer from the above formula.

First, divide the total into four parts and find out how many potted flowers there are in each of the four color squares in the picture: 204÷4=5 1 (pots);

Divided into three layers, find the number of pots in each row of each color box in the picture: 5 1÷3= 17 (pots);

Finally, add three pots of flowers of another color to the same row in the figure, and find out how many pots are on each side of the outer layer: 17+3=20 (pots).

Lecture 27, Expanding and Improving, Exercise 1.

Title:

The students rehearsed group calisthenics and formed a phalanx. The solid square in the middle is female students, the outer three layers are male students, and the outermost two layers are female students. There are 108 boys in the known phalanx. How many girl students are there?

Analysis:

We can divide this group into three phalanxes: three-layer hollow phalanx for boys, solid phalanx for girls inside and two-layer hollow phalanx for girls outside. The number of female students is the sum of the number of two female phalanxes.

First, from the total number of boys, find out the number of boys outside the hollow square on the third floor:

108÷4÷3+3= 12 (person)

Because there are two fewer people on each side of each floor, so:

1. The number of girls in the real phalanx is 12-3×2=6 (people), and the total number is: 6×6=36 (people);

2. The number of female students on the outermost side of the hollow square on the second floor is 12+2×2= 16 (person), and the total number is: (16-2) × 2× 4 =12 (person).

The total number of girls is:112+36 =148 (people).

Lecture 27, expand and improve, exercise 2, practice every day in the Olympics.

Title:

A group of soldiers lined up in a three-story hollow phalanx, with nine more people. If you add a floor to the hollow part and there are seven people missing, how many soldiers are there in this group?

Analysis:

According to the meaning of the question, the total number of people on the lower floor of the hollow square is 9+7= 16 (people), and the number of people on each side is 16÷4+ 1=5 (people);

Therefore, the number of people on each side of the outermost layer of a three-layer hollow square is: 5+2×3= 1 1 (people), and the total number of people is: (1 1-3)×3×4=96 (people);

The total number of soldiers in this team is: 96+9= 105 (people).

Note: The two exercises developed in this lecture are more difficult. If children have difficulties in accepting it, they can ignore it and wait until senior students are exposed to the same type of exercises before re-learning.