英国开放题(适合各个年级的小学学生)
(一)Making mazes (制作迷宫)
Here is a very simple maze: (这是一个简单的迷宫:)
It was made on square 'dotty paper'.First you choose a size - this maze was 6 x 6, but you can use a larger size such as 10 x 10.
(可以在一个方形的点子图上制作,首先你要选择一个6×6大小的纸,但是你也可以用一个像10×10大小的纸)
Draw out the outside box leaving spaces for the start and finish. These can be wherever you like.
(画出外边的边框,但要给起点和终点留出空间,这可以是你喜欢的任何地方。)
Next draw the path, with plenty of false trails, going through every square. The pictures show how the maze was constructed.
(下一步就是画有许多错路的路线,要走过每一个方块。下图就是迷宫的建构过程。)
Remember to draw the path very faintly so it can be rubbed out at the end.
(注意要轻轻的画这些路线,最后好擦去。)
Next the 'walls' are put in wherever the paths do not go into the next square.
(下一步是在不需要走进下一个方格的地方加上墙。)
Finally the outer square is redrawn leaving gaps for the start and exit and the paths, both true and false, are rubbed out.
(最后,外边的方格可以重新画上,把起点、终点和路线留出来,不管对还是错,都要擦掉。)
Much more intricate mazes can be made this way by making the original square 10 x 10 or even larger. Remember that the paths must go into each square on the dotty paper once and once only because otherwise you might make a short cut. Two paths must never cross. The finished maze should have only one solution.
(再难的迷宫可以通过在原始的10×10或者更大的方格纸上制作。注意这些路线必须通过点子图的每一个方格,而且只能通过一次,否则的话,你就有可能走近路。两条路一定不能交叉。完成的迷宫应该只有一个解决方案。)What does make a maze harder to do?
(究竟是什么使制作迷宫这样困难呢?)
Does where the start and finish are in relation to each other make a difference?
(起点和终点的位置和它们的相互关系是否会使得结果不同?)
Do the number of false trails make it more complicated or is it only a question of size?
(是错路的次数的多少使得迷宫更复杂,还是它只是一个大小的问题?)
Make several mazes of the same size (you could do this with a group of maze- makers) and see which are the most difficult to do.
(制作同样大小的几个迷宫(你可以在一个迷宫制作小组制作),看一看哪一个最复杂。)
Perhaps you could make a circular maze in a similar way by first drawing a set of concentric circles with lines radiating through them.
(或许以相似的方式制作出圆形的迷宫,可以先画一些同心圆,在用一些直线穿过这些同心圆。)
Or you could try to make a maze with triangular or hexagonal cells or with curved lines.
Which of these do you think would make the maze most difficult to follow?
(或者你也可以试着用三角形、六边形和曲线来作一些迷宫。你认为哪一个迷宫最难走?)
You can make mazes that follow the alphabet like the one in this month's "Let Me Try". A maze like this can be made much larger, with many more false trails, and so much harder. Of course you could use many other shapes besides hexagons to make it from.
(你可以像这个月的"让我试一试"一样,按照字母表的顺序来制作迷宫。像这样的迷宫可以作得大一点,有更多的错路,当然你可以用六边形之外的其它形状来制作。)
Here is another different sort of maze. It is the same 6 x 6 size as the one we started with but has fewer walls. There are numbers in each of the cells. You go through adding all the numbers that you pass. You may not go through any cell more than once.
(下面是一个不同类型的迷宫,它与我们开始的6×6的迷宫大小一样,但墙更少一点。在每一个单位里都有一个数字。你要把你走过的数字全都加起来,每个单位格只能走一次。)
Can you find a way through in which the numbers add to exactly 100?
(你能走一条数字之和是100的路吗?)
Can you make up an even harder maze than this with numbers in it?
(你能作一个比有数字还难的迷宫吗?)
(二)Making Cuboids (制作立体图形)
Let's say you can only use two different lengths - 2 units and 4 units.
(你只能用两个不同长度的线段--一个是 两个单位长度,一个是四个单位长度。)
If you are using these lengths to make the sides of rectangles, how many different ones can you make? (Squares are just special rectangles!)
(如果你用这些线段去制长方形,你能制成几个不同的长方形?(正方形是特殊的长方形!))
There are 3 because two are the same - just rotated.
(有三个,因为有两个是一样的,只是翻过来了而已。)
But we are not making 2-dimensional rectangles! We are going to make 3-dimensional cuboids. Using just these 2 lengths as the edges of the cuboids how many different ones can you make? Here are two of them. How many more are there?
(但是我们不是在制作两维的长方形!我们要制作三维的立体图。就用这两个长度的线段作立方体的棱,能做多少个不同的立方体?这里已经有两个了,还有几个?)
It is a good idea to make them from squared paper and sticky tape, but you also need to find a way to record your results.This is one way to show the results above, making a list.
The smallest is
2 x 2 x 2
The middle sized one is
2 x 4 x 4
(用方形纸和胶布制作立体图形是一个好办法,但是你需要发现一个记录结果的方式。列表是一个显示上述结果的方式之一。
最小的是 2×2×2
中等大小的是 2×4×4)
You should find a way to record your results that makes sense to you.How can you make sure that your cuboids are not the same if rotated? How many different cuboids did you get?
(你应该发现一种适合你的记录结果的方式。你怎样能确定你的立体图形旋转以后还是不同的?你能得到多少个不同的立体图形?)
But what if we will have 3 different lengths: 2 units, 3 units and 4 units.
(但如果我们有三组不同长度的线段:两个单位长度的,三个单位长度的和四个单位长度的线段。)
How many different cuboids can you make now? Make them from squared paper and sticky tape.
Remember to record your results. Find a way of showing what they look like. Once they are made perhaps you can arrange them in order of size - but how will you work this out?
(你能得到几个不同的立体图形?用方形纸和胶带把它们制出来。注意要记录你的结果。找到一种显示结果的方式。一旦他们制成了,也许你能把它们按大小顺序排列起来--但是你怎样能计算出它们的大小呢?)