Ho Soo Thong
The problem solving approach to the following problem illustrates a bar modelling approach to mathematical deductions.
Buying Apples and Oranges
Four pupils bought a total of 7 apples and oranges each.
Kim paid $ 6.60 for 5 apples and 2 oranges. Ann paid $ 6.0 for 2 apples and 5 oranges.
(a) Lee bought 4 apples and 3 oranges, how much did Lee paid for?
(b) Mei bought 7 oranges, how much did Mei paid for each orange ?
Comparing the bar models for the situations of Kim and Ann, Kim have 3 more apples than Ann and Kim paid $0.603 more than Ann.
We deduce that an apple costs $ 0.20 ( = $0.60÷3 ) more than an orange.
(a) Comparing the situations of Ann and Lee, Lee has 2 apples more than Lee and we deduce that Lee paid 2× $ 0.20 = $ 0.40 more than Ann.
(b) Finally, Mei bought two apple less than Ann and we deduce that she paid 2 × $ 0.20 = $ 0.04 less than Ann.
Mei paid $ 5.60 ÷7 = $0.80 for each orange
接下来,我们將注重于如何应用分配法 (Distributive Law)来处理同等分配情况 (Distributive Property Situations)，并进行数学推理来解答问题。
首先， 比较 王原与陳安的 情境， 推断 ( =>) 出一个结果: 一个苹果比一个橘子貴0.20元。
接下来，以同样推断 ， 得到李进和杨兰的花費，如杆模型所示。