plane graph
For the problem that the conditions in the topic are abstract and it is not easy to write the answer directly according to the knowledge learned, you can draw a plan to help yourself think and solve the problem.
Example 1:
There are two natural numbers A and B. If A increases 12, and B remains the same, the product increases by 72. If a remains the same, b increases 12, and the product increases 120 to find the product of the original two numbers.
According to the abstract characteristics of topic conditions, we might as well borrow a rectangular diagram to transform conditions into the relationship between elements and products. Draw a rectangle first, where the length means A and the width means B. The area of this rectangle is the product of the original two numbers. As shown in the figure (1).
If a increases 12 according to the conditions, the length will be extended 12, and b will remain unchanged, as shown in Figure (2); Similarly, if a remains the same, so does the length. If b increases 12, the width will be extended by 12, as shown in Figure (3). It is not difficult to find from the figure:
The length (a) of the original rectangle is 120÷ 12 = 10.
The width (b) of the original rectangle is 72 ÷ 12 = 6.
Then the product of two numbers is 10× 6 = 60.
With the help of rectangular diagram, the conditions in the problem are clarified and the key to solving the problem is found.
Example 2:
The bottom of the trapezoid is 1.5 times that of the upper bottom. After the upper bottom is extended by 4 cm, the trapezoid becomes a parallelogram with an area of 60 cm 2. How many square centimeters was the original trapezoidal area?
Draw a picture according to the meaning of the question:
It can be seen from the figure that the difference between the upper and lower soles is 4cm, and this 4cm corresponds to 1.5- 1 = 0.5 times. So the upper bottom is 4 ÷ (1.5- 1) = 8 (cm), the lower bottom is 8 × 1.5 = 12 (cm), and the height is 60 ÷12 =.
stereograph
Some quadrature problems, combined with the content of the topic, draw a three-dimensional diagram, which makes the content of the topic intuitive and vivid, and is conducive to thinking and solving problems.
Example 1:
Cutting a cube into two cuboids increases the surface area by 8 square meters. What is the surface area of the original cube?
If you only rely on imagination, it will be even harder to do it. Drawing pictures according to the meaning of the problem can help us think and find out the solution to the problem. Draw a three-dimensional picture according to the meaning of the question:
It is not difficult to see from the figure that the surface area has increased by 8 square meters, but actually two square faces have been added, and the area of each face is 8 ÷ 2 = 4 (square meters). The original cube has six faces, that is, the surface area is 4× 6 = 24 (square meters).
Example 2:
Make a big cuboid with three cuboids 3cm long, 2cm wide and 1cm high. What is the surface area of this big cuboid?
According to the meaning of the topic, draw a three-dimensional diagram to illustrate that there are three kinds of big cuboids composed of three cuboids.
The length of (1) cuboid is 2× 3 =