各位版友： 孩子在做买的小五的名校试卷。在南华小学的试卷中，有这样一道题：A total of 360 teachers and pupils participated in tree planting. Each teacher planted 3 trees and each group of 3 pupils planted 2 trees. If 520 trees were planted, how many pupils were there?
答案是240没有问题。可是参考答案给出的解题过程用的是猜测的方法，我觉得非常不严谨；可我自己只能用方程来解这道题。
现想请教各位，能否用画model（不知道是不是这么拼，就是画图）的方法解出这道题？提前感谢各位。Assume all are teachers.
the total number of trees of planted should be: 360×3=1080 tress
actual number of trees: 520 trees
number of trees should be cut down by: 1080-520=560
every 3 teachers will plant 3×3=9 trees
every 3 pupils will plant 2 trees
change 3 teachers to 3 pupils, number of trees will decrease by : 9-2=7 trees
number of changes needed: 560 / 7 = 80 times
total number teachers changed to pupils is : 80×3=240 pupils
希望解释的清楚 ＝）Assume all are teachers.
the total number of trees of planted should be: 360×3=1080 tress
actual number of trees: 520 trees
number of trees should be cut down by: 1080-520=560
every 3 teachers will plant 3×3=9 trees
every 3 pupils will plant 2 trees
change 3 teachers to 3 pupils, number of trees will decrease by : 9-2=7 trees
number of changes needed: 560 / 7 = 80 times
total number teachers changed to pupils is : 80×3=240 pupilseach teacher plant 3 trees, each pupil plants 2/3 trees.
Teachers: 000000000 000000000 000000000 000000000 000000000 000000000 000000000…
Pupils: 00 00 00 00 00 00 00 …
Each unit 0 = 1/3 tree
By adding a 0000000(7’0’s to each pupil, each of them can plant as many trees as teachers. in total they will plant 9 x 360 = 3240 units. The fact is, there is a total of 520 x 3 = 1560 units.
3240-1560=1680 units, this diffence is due to adding 7 units to each pupil.
1680 / 7 = 240, there are 240 pupilsA total of 120 groups of teachers and pupils participated in tree planting. Every group has 3 persons. Each group of teachers planted 9 trees and each group of pupils planted 2 trees. If 520 trees were planted, how many pupils were there? 这就变成了小三或小四题了(鸡兔同笼）
120 x9 -520 = 560
540 / (9-2) = 80 group of students
80X3 = 240@jjrchome ： 谢谢您～ ^_^非常感谢上面各位热心老师的解答。可是女儿天资一般，尤其不擅长数学。她刚才看了几种解法，每种解法都说有不懂的地方。我还要硬着头皮消化了之后再讲给女儿听。其实这种题目如果用方程来解答一目了然，不用方程绕的弯太多了。但是自己多年不用数学，又不知如何教起。真是着急啊我也有同感！
我的也是小五，考卷还没开始做呢！眼看考试要到了！小五不学方程么?小六开始学 而且也不鼓励用 :)可能全发的英文的缘故 不好意思 ^^!~why?需要的话 翻成中文吧 我把每步的解释也写出来了 :)按大纲 是从小六开始教一些基础的代数 就是xyz
但是几年来带不同学校学生总结出来的是 如果用代数 答案错了很有可能就完全没分了 （不是每个学校 但我接触的大都是这样）
再一个 希望孩子在小学阶段搞清楚这些复杂的关系 有助于思维培训
上了中学列代数关系式的时候也比较理解得清楚
＝）
两位老师的优秀解答在下佩服！
不过可能对有些孩子还不容易理解，在下不才，在两位的解答基础上再稍作改动，不知能否让孩子更容易理解？还请两位老师和J版及各位网友的指正，谢谢！
第一步：把1颗树转换成3颗糖
这样，每个老师种3棵树 ==〉每个老师有9颗糖。
每3个学生种2颗树 ==〉每3个学生有6颗糖 ==〉每个学生有2颗糖。
520颗树 ==〉1560颗糖。
最终，本题变成如下： 老师和学生总人数是360，每个老师有9颗糖，每个学生有2颗糖，总共有1560颗糖，
请问学生人数。
第二步：每个老师拿出7颗糖，然后放入一个箱子
这样，每个老师手上有2颗糖，每个学生有2颗糖，总共有360*2=720颗糖。
放入箱子里的糖一共有1560-720=840颗糖，因为每个老师放入7颗，所以总共
有840/7=120个老师。
学生人数：360-120=240个。顶～
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