3. Xiao Ming sets an octagon with matches, as shown in figure -| | | |-( 1). How many matches does it take to set 1 octagon? Pendulum 2

Setting an octagon requires 8 matchsticks, setting two octagons requires 15 matchsticks, and setting n octagons requires 8+7 matchsticks (n- 1) = 7n+ 1 matchsticks.

Analysis: It takes 8 sticks to put an octagon, 7 sticks to put two octagons and 7×2 sticks to put three octagons. We can find the rule according to the figure: if there is one more octagon, we use seven sticks; if there are n octagons, we need sticks: 8+7 (n- 1) = 7N+65438.

The law of building a square with matches

This special activity, building a square with matches, can help us better understand the composition of mathematics, especially geometry. The collocation with square can help us understand the "square" in geometry and further understand the concepts of shape, angle and symmetry.

When making a square with matches, we should first understand the materials needed to make a square with matches, such as a match, a piece of paper, a pair of scissors and so on. Since it is a square, these materials are of course related to squares. First of all, matches have two characteristics: equal corners and equal waist.

When we make a square with matches, we should use four matches on each side and try to make each side equal; In addition, paper is also essential for building squares. It can not only support matches, but also increase their stability. In addition, we have to use scissors to cut the matches flat to make the squares more tidy, so that the matches can be displayed more perfectly.

When a square is built with matches, the characteristics of the square can be embodied in different ways. For example, we can first build a square horizontally, then lay it flat on the paper, and cut the matches on the side into a symmetrical waist to make it square, so that it can be symmetrical left and right, or we can first build a square vertically, then lay it flat, and then cut the four corners into parallel with scissors to form a square, so that the whole will be more perfect and reflect the characteristics of a square.

In addition, in the process of building a square with matches, some knowledge of algorithms can also be involved, such as whether a square can be built by using the diagonal properties of matches, whether four foot matches can be connected by a certain operation method, and so on. These activities can cultivate students' scientific knowledge, improve their interest in learning mathematics and enhance their artistic cells.

To sum up, we can see that the matching box covers a lot of mathematical knowledge and is also a toy. If we can skillfully use it, we can better appreciate the fun of geometry, expand children's knowledge and cultivate children's mathematical thinking ability. In a word, it is very interesting to build a square with matches as long as we study hard. It can make us understand mathematics better and be good at it.