There is no related content of addition and subtraction on the grid paper in the textbook, which belongs to an expansion of primary school knowledge and paves the way for the following binary linear equation. The addition on the square paper is based on the binary linear equation x+y=a, and the subtraction is based on X-Y = A. We can see it intuitively by establishing a coordinate system on the square paper.

Classroom design

I. Investigation of the problem

15+7=? ?

We learned to add and subtract two digits as early as grade one, and we all know that the result of 15+7 is 22. Now, how do we calculate the result of 15+7 on the grid paper?

First of all, we might as well express it on the grid paper (15,7):

(1) Draw a dot first. It is marked with 15, and the left side is marked with 7, 15. The corresponding vertical lines are drawn with 7, and their intersection point is (15,7).

(2) Draw another line, and the intersection point is the diagonal line along the upper right and lower left.

What did you find?

We find that the intersection of this straight line and the upper left is 22, and the sum of 15 and 7 is also 22.

Is it a coincidence? If it's not a coincidence, why? So how do we prove it?

The coordinate of point D is (15,7), so OE=DF= 15.

DE=OF=7, because AB is diagonally connected, so ∠A=∠B=45? We get that the triangle BDE is an isosceles right triangle, we get ED=EB, so OB=DE+EF, and we get that the sum of the abscissa and ordinate here must be the intersection of this line and the boundary.

At the same time, we can also prove that the coordinate sum of any point on this line is 22 according to this method.

Subtraction in the grid:

Then how do we calculate 15-7= on the grid paper?

(1) We can use the addition line to calculate the subtraction.

Can we make a subtraction line according to the addition line we made above?

Let's draw a point (15,7), and the intersection points are connected along the upper left diagonal and along the lower right diagonal. The corresponding number we get is the difference between two numbers, which is 8.

Then how to prove it?

According to the above geometric method, it can be proved that the coordinates of the points with a difference of 8 are all on this line.

Solve practical problems:

There are 22 black rabbits, 4 fewer than white rabbits. How many black rabbits and white rabbits are there?

The sum of black rabbit and white rabbit is 22, and the difference between black rabbit and white rabbit is 4. We can draw an addition line with a sum of 22 and a subtraction line with a difference of 4 in a square diagram, and the two numbers corresponding to their intersections are the only number of white rabbits and black rabbits we need.

As shown in the figure below:

abstract

By adding and subtracting on square paper, we can find the law, perform simple operations according to the law, understand the relationship between numbers and shapes, further understand the mystery of the combination of numbers and shapes, and skillfully solve related application problems. This type of outward bound class plays a great role in stimulating children's interest in mathematics and embodies the charm of mathematics.