The origin of the region

The Nile River in ancient Egypt floods in July every year, and the flood gradually subsides in June165438+1October. The silt left after the flood formed fertile soil, which also brought the need for land retest. Geometry came into being in order to measure land. In fact, geometry originally meant "land survey". Land survey needs to make graphics the research object of mathematics. The amount of land, the size of the number is the area.

Regional teaching

① Build an area model in multiple experiences to understand the meaning of area.

Take a look: which is the bigger of the two pairs of footprints in the snow?

Touch: Find out which objects around you have faces and touch them with your hands. Comparing the surfaces of any two objects, we feel that the surfaces of the objects are large and small, and we feel that the surfaces cannot be separated from the body.

Painting: painting on the surface of an object, recognizing that the area is the size of the area.

Comparison: Compare the sizes of regular and irregular figures, and compare the enclosed and unsealed areas. Students realize that only a closed figure can have a definite area.

Spelling: Put the jigsaw puzzle together and make a square with seven pieces, so that students can understand the size of the surface and form a sense of unit.

② The understanding and application of area is gradually improved.

In the study of grades 3-6, students' understanding of plane, surface and surface size gradually deepens. (The area of rectangle and square is level 3-the area of parallelogram-the area of trapezoid-the area of triangle-the surface area of cuboid and cube is level 5-the area of circle-the side area of cylinder, and the surface area is level 6).

For the study of area, we need to understand and apply it in constant exploration, experience and practice.

intersecting surface

Cross-section includes cross-section, vertical cross-section, flat cross-section and inclined cross-section. The primary school stage is generally cross-sectional, that is, cut parallel to the bottom.

In normal teaching, teachers seldom organize a class. However, related problems often occur in practice, so it is still difficult for students to find the cross section. Teachers can design a series of mathematical activities to guide students to think deeply, experience and understand the meaning of sections in the activities.

Activity 1: concrete object, export part

Activity 2: Cut the cube and experience different sections formed by different cutting methods (cross cutting, longitudinal cutting and oblique cutting) of the same geometry.

Organize students to cut potatoes in groups, a few in each group. The question leads to, if you cut the cube at will, what shape will the cross section be after cutting? The cross section may be triangle, square, rectangle, trapezoid, pentagon and hexagon. The heptagon cannot be cut out because the cube has only six faces.

Guide students to find that the cross section obtained by cutting a cube from different angles may be a plane figure with different shapes, and the number of sides of the plane figure is determined by the number of faces on the cube surface through which the cross section passes.

superficial area

Definition: the quantity describing the surface area and its calculation formula.

The sum of the areas that all three-dimensional figures can touch is the surface area of this figure.

We often say that the surface area refers to a three-dimensional figure that can be touched in an ideal state, and the sum of the areas of each surface is calculated for each surface. After learning the surface areas of cuboids and cubes, students can expand their applications in the following situations.

(1) Find the sum of the surface areas you can see.

② Find the area combination of all exposed surfaces (several figures are stacked together).

(3) Cut a three-dimensional figure, and find the sum of the areas of the added surface and the sum of the areas of all three-dimensional figures after fireball cutting.

(4) Which way of packing is the most economical? (several identical objects are tied together)

Teaching concept of surface area;

① packaging teaching method

Can guide students to think like a three-dimensional figure and draw a bright coat. (You can draw or paste materials) How to wear this coat? In this process, students need to package three-dimensional graphics of several faces.

(2) The teaching design of turning solid into plane.

The plane development diagram of three-dimensional graphics is beneficial to the development of students' space concept. In class, it can help students understand the surface area of three-dimensional graphics in the mutual transformation between three-dimensional and two-dimensional, guide students to cut along the edge of three-dimensional graphics, transform three-dimensional graphics into plane graphics, guide students to observe graphics and find the three-dimensional graphics of unfolded plane graphics.

(3) Teaching design of changing plane into three-dimensional.

Provide some cardboard to the students, and then propose to make a dictation model of the original cuboid and cube together. In the process of doing it, students will find that they only need to prepare six rectangles with appropriate data to make a cuboid, and then enclose the six rectangles into a cuboid with tape in a certain way.