Click on the blue word to follow and walk side by side with parents all over the country.

-0 1-

What do you study in primary school mathematics?

Anyone who has studied mathematics knows the importance of the application of thinking mode in learning mathematics. Primary school mathematics mainly cultivates children's logical thinking ability, which is a process from image thinking to abstract thinking. If the foundation of primary school is not laid firmly, it will become more difficult for children to learn more complicated content after junior high school.

It can be said that the examination of questions is a preliminary perception of questions, especially applied questions, and understanding the meaning of questions determines your angle of examination and the way of thinking about problems. So this is an important part of doing the problem.

-02-

Solving the problem of "painting" in primary school mathematics is immediate.

Draw a picture according to the content of the exam, show the conditions and questions on the picture, concretize the abstract mathematical problems with the help of line drawing or physical drawing, restore the original appearance, and find the solution to the problem. You can find the answer at once from the picture, and you can also find your own mistakes quickly by drawing.

Many primary school students do application problems and only know how to look. They don't need draft paper. They just stare at them ... Can they see the flowers? I just read the topic, not the novel.

It is a crucial step to help children understand the meaning of the problem by drawing pictures.

Drawing and solving problems is a "golden key" for children to open the door to solving problems. Many problems can be solved quickly, such as geometric problems and distance problems. If it is difficult to draw an answer, it will be clear at a glance. Let's look at some chestnuts.

1, plan

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.

For example, there are two natural numbers A and B. If A increases 12 and B remains unchanged, 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.

For another example, 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 square cm. 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 4cm corresponds to 1.5-l=0.5-L = 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 =.

2. Polygons

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.

For example, cutting a cube into two cuboids will increase 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).

Another example is to make a big cuboid with three cuboids of 3 cm long, 2 cm wide and 1 cm high. What is the surface area of this big cuboid?

According to the meaning of the topic, draw a three-dimensional diagram to show that there are three situations in which three cuboids are spliced into a big cuboid:

(l) The rectangular body length is 2× 3 = 6 (cm), the width is 3 cm, and the height is 1 cm. The surface area is (6× 3+6×1+3×1)× 2 = 54 (square centimeter).

(2) The rectangular body length is 3× 3 = 9 (cm), the width is 2 cm, and the height is 1 cm. The surface area is (9× 2+9×1+2×1)× 2 = 58 (square centimeter).

(3) The length, width and height of a cuboid are 3cm, 2cm and 1x3 = 3 (cm) respectively. The surface area is (3× 2+3× 3+2× 3) × 2 = 42 (square centimeter).

There are three answers to this question, which can be used to examine the question and understand the meaning of the question by drawing pictures.

3. Analysis chart

For some application problems, in order to correctly examine the problems and analyze the quantitative relationship in the problems, the analysis diagram can be used to express the relationship between conditions and problems in the problems.

For example, Xinhua Middle School bought 8 tables and chairs and spent 8 17.6 yuan. The price of each table is 78.5 yuan, which is 62.7 yuan more expensive than each chair. How many chairs did you buy?

(l) How much does it cost to buy a chair? 817.6-78.5× 8 =189.6 yuan)

How much is each chair? 78.5-62.7 = 15.8 (yuan)

(3) How many chairs did you buy? 189.6÷ 15.8 = 12(Ba)

The comprehensive formula is:

(8 17.6-78.5×8)÷(78.5-62.7)

= 189.6÷ 15.8

= 12 (Ba)

A: I bought a 12 chair.

4. Line segment diagram

Some questions have many conditions, and the relationship between them is complex, so it is difficult to answer them at the moment. You can draw a line segment diagram to represent it and seek a breakthrough in solving problems.

For example, there are more than 30 sixth-grade graduates in bright primary school than the whole school. There are 360 freshmen in the new semester, which is now more than the total number of students in the original school. How many students are there in the school?

It can be clearly seen from the figure that (360-30) students correspond to (+) students in the whole school, and the number of students in the whole school is calculated by division. The formula is:

(360-30) ÷ (+) = 330 ÷ = 900 (person).

For another example, Party A and Party B walk in opposite directions from two places 88 kilometers apart at the same time, and meet at a place 4 kilometers away from the midpoint eight hours later. A is faster than B. How many kilometers do A and B travel per hour?

Draw a line segment according to the meaning of the question:

It can be clearly seen from the figure that the distance between each line of A and B within 8 hours is more than half of the whole journey of A and less than half of the whole journey of B, so that the speed of A and B can be calculated.

A Speed: (88 ÷ 2+4) ÷ 8 = 6 (km)

Speed B: (88 ÷ 2-4) ÷ 8 = 5 (km)

5, table diagram

For some problems, the list can not only distinguish the conditions and problems of the topic, but also facilitate the distinction and comparison, which plays a very good role in examining the topic.

For example, Xiaoming moved 15 bricks three times. According to this calculation, Xiao Ming moved four times again. * * * moved a few bricks?

According to the conditions and problems, an easy-to-understand table is listed, and the known conditions and problems can be clearly seen.

It is not difficult to see from the table that the number of pieces moved four times does not correspond to * * *. We must find out how many times a * * * has moved before we can find out how many pieces * * * has moved. The formula is:

15 ÷ 3× (3+4) = 35 (block)

Another idea is that the number of blocks moved four times, plus the original number of blocks, is the number of blocks moved by * * *. The formula is:

15 ÷ 3× 4+ 15 = 35 (block)

6. Ideas

Some problems are solved in different ways because of different angles of analysis. Through drawing, we can clearly see the thinking of solving problems and facilitate analysis and comparison.

For example, if you have a nickel, four dimes and eight dimes, you must take out eight dimes. How many grips can a * * * have?

On the surface, this problem is not difficult at all, but there is no need to repeat it. It is not easy to tell all the roads without missing them. You can list all the situations one by one and write down your thoughts.

From the chart, you can clearly see the different holding methods. There are seven ways to solve this problem without repeating it.

As can be seen from the above example, drawing helps to understand the meaning of the problem and plays a role in simplifying the complex. We might as well use it widely when solving problems.