![]() Of which the last three have been given in Zhang Qiujian suanjing. So the complete set of solutions is given by Since y should be a non-negative integer, the only possible values of t are 0, 1, 2 and 3. Hence the general solution of the system of equations can be expressed using an integer parameter t as follows: x = 4 t y = 25 − 7 t z = 75 + 3 t Since x, y and z all must be integers, the expression for y suggests that x must be a multiple of 4. Obviously, only non-negative integer values are acceptable. Let x be the number of cocks, y be the number of hens, and z be the number of chicks, then the problem is to find x, y and z satisfying the following equations: In each case, find the number of cocks, hens and chicks bought." Mathematical formulation It is required to buy 100 fowls with 100 qian. The Hundred Fowls Problem as presented in Zhang Qiujian suanjing can be translated as follows: "Now one cock is worth 5 qian, one hen 3 qian and 3 chicks 1 qian. The name "Hundred Fowls Problem" is due to the Belgian historian Louis van Hee. However, the problem and its variants have appeared in the medieval mathematical literature of India, Europe and the Arab world. The problem appears as the final problem in Zhang Qiujian suanjing (Problem 38 in Chapter 3). It is one of the best known examples of indeterminate problems in the early history of mathematics. How teachers could present or develop this resource? Do you have any comments? It is always useful to receiveįeedback and helps make this free resource even more useful for Maths teachers anywhere in the world.The Hundred Fowls Problem is a problem first discussed in the fifth century CE Chinese mathematics text Zhang Qiujian suanjing (The Mathematical Classic of Zhang Qiujian), a book of mathematical problems written by Zhang Qiujian. How did you use this starter? Can you suggest In fact, it is intriguing enough to direct students attention and interest to the lesson. William-west, Premier Intl Sch., Abuja, Nigeria Having said all of that, there is no denying this this is a classic simultaneous equations problem that can be solved in a number of different ways. Other pupils may need practice using their graphic display calculator to solve this problem. Some pupils may have learned the basics of JavaScript and could write a looping program to find the solution. How many chickens must there be if we know the total number of heads? What is the total number of legs if this is the case? Is that more or less than the actual number of legs? How might we change our rabbit number guess to increase or decrease the number of legs? (Increasing the number of rabbits will decrease the number of chickens and as rabbits have more legs than chickens the total number of legs will go up).Īlternatively pupils might be at the stage where they could use a spreadsheet to quickly create columns of possible rabbit and chicken numbers with another column showing the number of legs. Start of by proposing that there are ten rabbits. There are so many ways pupils could engage with this problem and possibly the most basic strategy could be one of trial and improvement.Excellent starter improves students thinking skills !!- Thank you. ![]() ![]() Joan Morgan, All Saints Academy Plymouth.This maths stater was just the thing I wanted before I wrote my algebra test.Simbarashe Mukumbira, Mazowe High School.Then 4x + 2(total heads-x)= total number of legs. I let the number of rabbits be represented by x. My class was just introduced to constructing and solving linear equations at the time, and I constructed a linear equation to find a solution for this starter.But our teacher showed us how to use simultaneous equations to get the answer quickly. We all tried our best to find the answer by guessing.The Best Maths Class Ever 7cd/M2, King Alfred's College, Oxfordshire.Good timing! Just the starter I needed for my simultaneous equation topic.
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